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“The win-win-win

papakonstantinidisModel”

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Social Welfare: Collection of bibliographic

references.

and

The “win-win-win papakonstantinidis Proposal”

Bargaining - Agency -Set- Efficiency

Justice-Egalitarian-Socialchoice- Utilitarianism-

Sharing

Incompleteness-Recursion - Impossibility

2016

Papakonstantinidis l.

….when the impossible comes true888

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ABSTRACT

lp: “The rainbow concept”

This work intends to prove that "social welfare" can coexist with the capitalist economic model

but if based on a "tri-polar" (instead of bipolar) perception of any interaction between people,

local communities, organizations, states, blocs Member ...including the Community (The

Intermediate Community- the "C" factor), in 3D space, with the community as “rainbow”

synthesis/analysis It is the “rainbow concept”1 If it is true, then it will be feasible a social

welfare policy in a new world that will not resemble the current (centralized structure) It also is

about the classification of the simplest singular theoretical points on an hypothetic surface C

(all bargaining behaviors) that do not depend on the orientation of C in space. This scientific

proposal, once recorded as such, classified and analyzed a number of other theories and

models, tried to put down a "new" concept of an alternative approach of "socio-economic

welfare" for the sole purpose to demonstrate that it is possible a new tri- polar concerning2

instead of bipolar crumbling over time, producing increasingly more injustice, inequality,

misery, depression This is able:

a. By defining and analyzing the set theory(Cantor3,4 and Zemelo5), Principal –Agent

theory6 the Ultimatum theory7 and the bargaining Nash theory8,9,10,11

1 Papakonstantinidis L.A (2016) the “Rainbow Concept”: “Social Welfare” Part of the Book, Dardanos Ed.

2 Papakonstantinidis L.A (2002) the “win-win-win model” Euracademy Thematic Guide “Rural Development’ vol 1 iss 1 University of Visby, Gotland,SW Aug 14, 2002 3 Cantor, Georg (1874), "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen" Journal für die Reine und Angewandte Mathematik 77: 258–262, 4 Johnson, Phillip E. (1972), "The Genesis and Development of Set Theory", The Two-Year College Mathematics Journal 3 (1): 55 5 Zermelo, Ernst (1908), "Untersuchungen über die Grundlagen der Mengenlehre I", Mathematische Annalen 65 (2): 261–281English translation: Heijenoort, Jean van (1967), "Investigations in the foundations of set theory", From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Source Books in the History of the Sciences, Harvard Univ. Press, pp. 199–215 6 Eisenhardt, K.M.. (1989). Agency Theory: An Assessment and Review. The Academy of Management Reivew, 14(1), 57-74.

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b. by demonstrating and analyzing the incompatibilities of 5 famous theorems ant 3

theories:

It is a set theory (or an application of the set theory) because it is included in SET THEORY: Set

theory is the mathematical theory of well-determined collections, called sets, of objects that

are called members, or elements, of the set. Pure set theory deals exclusively with sets, so the

only sets under consideration are those whose members are also sets. it also obeys in the

axioms of extensionality, regularity (also called the Axiom of foundation), schema of

specification (also called the axiom schema of separation or of restricted comprehension),

pairing, union schema of replacement infinity power set Well-ordering theorem The theory of

"win-win-win” is included in the in ZFC set theory because it obeys the basic axioms of ZFC

Set Theory (Axiom of extensionality, Axiom of regularity (also called the Axiom of foundation),

Axiom schema of specification (also called the axiom schema of separation or of restricted

comprehension), Axiom of pairing Axiom of union Axiom schema of replacement Axiom of

infinity Axiom of power set Well-ordering theorem

The win-win-win papakonstantinidis model, consists from discrete and independed “parts”

with independed will and way of thinkings.These are fundamental prequisitions of a SET

From this point of view, win-win-win theory may be seen as “agency theory”, in the frame of

“SET theory” (Cantor)12 (ZFC)13: The concept here is that the "set theory" deals with sets which

informally are collections of objects. Any type of object can be collected into a set From this

point of view, the win-win-win perception includes “sets of behaviors” that obey in common

rules (axioms)

It is an “Agency Theory” (or an application of the agency theory) because the individual must

go beyond narrow personal interest and thought about the man who is to him and negotiates

with him. This is the core of the suggestion Due to agency theory win-win-win

papakonstantinidis “theory” help the researchers and University students to think twice (a) as

the principle and (b) as agent of the whole community so to win So, “agency theory”

introduces us to the double thinking leading thus, in limit, to a triple pole win (win-win-win)

Furthermore, the "agency theory" produces “behaviors” of a double direction: one for

him/her/self and the other for the "principle" The third part of negotiations (even under-

informed) can induce the other party to reveal their information. They can provide a menu of

choices in such a way that the choice depends on the private information of the other party14.

7 Sanfey, Alan; Rilling, Aronson, Nystrom, Cohen (13 June 2003). "The Neural Basis of Economic Decision-Making in the Ultimatum Game" Science 300 (5626): 1755–1758. 8 Nash, John (1950). "The Bargaining Problem" Econometrica 18 (2): 155–162. 9 Nash J.F. (1950) "Equilibrium Points in N-person Games", Proceedings of the National Academy of Sciences (36): 48–9, 1950, http://www.pnas.org/cgi/reprint/36/1/48, 10 Nash J.F (1950) "Equilibrium Points in N-person Games", Proceedings of the National Academy of Sciences (36): 48–9, 1950, 11 Nash J.F (1951) "Non-cooperative Games", Annals of Mathematics (54): 286–95, 1951 12

Cantor (1879) "Ueber unendliche, lineare Punktmannichfaltigkeiten (1)"Mathematische Annalen 15 (1): 1–7. 13

Zermelo, Ernst (1908). "Untersuchungen über die Grundlagen der Mengenlehre I", Mathematische Annalen 65 (2): 261–

281, doi:10.1007/bf01449999. English translation: Heijenoort, Jean van (1967), "Investigations in the foundations of set theory", From Frege to Gödel: A Source Book in Mathematical Logic 14

Stiglitz Joseph E. (1975) The Theory of "Screening," Education, and the Distribution of Income- The American Economic

Review Vol. 65, No. 3 (Jun., 1975), pp. 283-300

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It is finally a bargaining theory (or an application of bargaining theory) as it relates to each

infinitesimal agreement or disagreement that people have when dealing with each other and

produce results fairly, or (most times) unjustly and even inequalities

The aim of this theoretical contribution (if it exists) is to highlight the "SENSITIZATION ability"

that everyone of us either relates to refugees, or in countries, whether in claiming or even in

our daily transactions It is time to stop looking only personal interest or “individual defense”

In particular, the proposal deals with the collecting, classifying and comparing the theoretical

material from various sources on the functioning of Social Welfare Function (SWF), towards

building a strong case with logical and coherent arguments, towards the one Triple Pole (A-B-

COMMUNITY) Equilibrium (TPE), different from N.E, that leads to the Social Bargaining

Solution” (SBS) and coincide with the "optimal" Community Collective Choice (CCC) in order to

create a highly versatile tool, “the win-win-win papakonstantinidis model” of well-formed

formulas (wffs),

Based on this model, in practical level, the ambitious is to create a series of new policies to

strengthen social welfare, despite the "impossibility theorem" (K. Arrow 1955)

I supported with arguments, that through "a simultaneous, reflective, strong effective (Pareto),

Flexible, fair (Rawls), collective (Amartya Sen) Social Welfare Function (SWF) in the frame of a

General Equilibrium (Walras), incompatibilities that incorporate the values of equality,

justice, harmony, symmetry, and the hypothesis, of self-organization (Papakonstantinidis) as

well as the hypothesis of self-supporting bargaining solution in a community level, should

exist and be the only one: the win-win-win equilibrium Win-win-win papakonstantinidis

situation is proposed as an extension of both “non-cooperative game”15 and the principal–

agent problem (also known as agency dilemma or theory of agency)16 under the constrains put

by the five theorems Especially, Pareto efficiency , as an economic state where resources are

allocated in the most efficient manner Pareto efficiency is obtained when a distribution

strategy exists where one party's situation cannot be improved without making another party's

situation worse. Pareto efficiency does not imply equality or fairness. Also known as "Pareto

optimality” (INVESTOPEDIA) Also, the theory of justice focus on the "veil of ignorance", along

with the original position, is a method of determining the morality of a certain issue (e.g.,

slavery) based upon the following thought experiment: parties to the original position know

nothing about their particular abilities, tastes, and position within the social order of society.

When such parties are selecting the principles for distribution of rights, positions, and

resources in the society they will live in, the veil of ignorance prevents them from knowing

about who they will be in that society. The question in which the paper gives answers is if it

possible and how to focus on social welfare (as the Arrow’s (1951) “Impossibility Theorem”

today disputed. We believe that the proposed (from the present work) and routed (by the

original applications in the Greek countryside) "win-win-win papakonstantinidis model" (since

2002), succeeds in "passing" of economic forms, and giving a welfare’s perspective

16 INVESTOPEDIA –DEFINITION conflict of interest inherent in any relationship where one party is expected to act in another's

best interests The problem is that the agent who is supposed to make the decisions that would best serve the principal is

naturally motivated by self-interest, and the agent's own best interests may differ from the principal's best interests. The agency

problem is also known as the "principal–agent problem."-also, see at Joseph E. Stiglitz and Andrew Weiss (1981) Credit

Rationing in Markets with Imperfect Information The American Economic Review Vol. 71, No. 3 (Jun., 1981), pp. 393-410

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In practical level, the “win-win-win papakonstantinidis theory” produces results that may be

measured by application of the Central Limit Theory (CLT)17. Applying the CLT on a series of

answers from 512 people given to specific "closed" questions (questionnaire), -concerning

their appreciation for themselves negotiating behavior, enhances the theoretical structure of

the “win-win-win papakonstantinidis model”, adding a direct practical utility to it Since

thousands of negotiations that we do every day with other people who realize that "winners" -

"losers" converge as the number of negotiations (N) tends to infinity and from this point they

would accept a "third pole (Community)" above their own forces as long as necessary for this

pole should ensure fairness, equality, respect, self-organization over people

Finally, “win-win-win” may be suggested for CONTRASTING the dual systems’ (i.e Boolean

Algebra as well as Pirahã" linguistic recursion) transformation into a unique 3-pole system of

MIND

To strengthen the arguments in favor of a triangular perception of things, we will try to bring

it in Set Theory and see how the qualities of the "win-win-win” 'correspond 1-1 to basic

Axioms

Keywords:

“win - win- win”, social welfare, the Impossibility Theorem (Arrow) the Incompleteness

Theorem (Gödel) Pareto Efficiency, Nash Equilibrium, the Rawls Theorem on Justice,

Caratheodory (one case) “umbilical points” sensitization, team psychology, The “Principle-

Agent Theory”, Egalitarianism, Utilitarianism

17Rice, John (1995), Mathematical Statistics and Data Analysis (Second ed.), Duxbury Press: In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables each with a well-defined expected value and well-defined variance will be approximately normally distributed regardless of the underlying distribution To illustrate what this means, suppose that a sample is obtained containing a large number of observations each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution (commonly known as a "bell curve"). A simple example of this is that if one flips coin many times the probability of getting a given number of heads should follow a normal curve, with mean equal to half the total number of flips.

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papakonstantinidis 43

win

win

win

Structure

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a/a TITLE OF PARAGRAPH

1 OBJECTIVE-Aims

2 Papakonstantinidis conjectures

3 questionaire

4 The problem-the necessity

5 CONCEPT and the Study Design

6 SET Cantor theory/preliminary

7 METHODOLOGY

8 Basic Definitions of the 5 theorems

9 Analysis of theorems

10 Results from a number of qualifying studies concerned the “social welfare”

11 Analysis of the results-focus of the research on the incompatibility of these

12 Specific reference to psychology-personality-language expression and

structure within the Incompleteness Theorem (Gödel) and the principal–agent

problem (theory of agency) in the frame of an “adverse selection”

13 Utilitarianism- Egalitarianism- Prionitarianism

14 Historical Review of “win-win-win papakonstantinidis model”

15 SUGGESTION: win-win-win papakonstantinidis situation, as an extension, both

of “non-cooperative game” and the “theory of agency” (the principal-agent

problem)

16 Win-win-win as a “risk aversion theory”

17 Win-win-win as “Prinvipal-Agent Theory”

18 Win-win-win as an “arbitrator theory “

19 Win-win-win in the centre of recent “philosophical currents”

20

21 Results of the research

22 Conclusions

22 Application:

“win-win-win” application in Epirus GR-one of the less developed area of EU

The LEADER EU Commission’s Initiative

23 Appendix (pp562)

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OBJECTIVE: To prove that “social welfare” exists and can coexist with the capitalist economic

model, if and only if it will be based on the contradiction of the relevant literature, thus leading

in a 3-polar "contract" between any parties, including the Community (The Intermediate

Community- the "C" factor), in a 3-dimensional space.

If it is true, then it will be feasible a social welfare policy in a new world that will not resemble

the current (centralized structure)

AIMS

1. To prove that a "social welfare” is within our grasp

2. To create a highly versatile tool, “win-win-win papakonstantinidis model” able to adapt or

be adapted to many different functions or activities, by well-formed formulas (wffs), thus

contributing in changing the 2-pole (black –white) perception, in a three pole [0,01,1]

welfare cognition,

3. to document the necessity and usefulness of the "win-win-win" based on incompatibilities

of five classical theorems and 4 theories, as each of them exclude others

4. To find a base-role for the third win (=the Community) in any bargain between 2

5. to deal with the incompatibilities of 5 basic theorems that concern the concept of "welfare

economics" These theorems are: The impossibility theorem (1951 Kenneth Arrow:

OBJECTIVE-AIMS

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book: Social Choice and Individual Values18, as well as the Amartya Sen “liberal paradox”19

(either Pareto optimality20,21,22,or liberty) the theorem of incompleteness (Kurt Gödel

(1931)23,24, the Rawls Theorem on Justice, 1958(“Justice as fairness, in his Philosophical

Review,1958)25 the Nash Equilibrium in Nash “Non cooperative Game Theory 1951(annals

of Mathematics,1951 Vol. 54, No. 2 (Sep., 1951), pp. 286-295)26 and the “Pareto optimal27

in a 3D space according to Caratheodory conjecture (umbilical points in a sphere)28, then

the main issue in this research concerns the possibility that a win-win-win

communication should exist in real terms, due to logical mind contractures (logical

forms)29 expressed by psychology and personality’s factors, as well as from linguistic

forms30 or creating cognition by linguistic recursion31,32 Furthermore33, there is an

18 Kenneth Arrow 1951, 2nd ed., 1963 Social Choice and Individual Values, Yale University Press 19 Amartya K. Sen, 1970, Collective Choice and Social Welfare, ch. 3.4 20 Pareto optimality: whenever all individuals of a society strictly prefer an outcome x over an outcome y, the choice function

doesn't pick y. Formally, a social choice function F is Pareto optimal if whenever p∊Rel(X)N is a configuration of preference

relations and there are two outcomes x and y such that x⪲iy for every individual i∊N, then y∉ F(p). Minimal liberalism: More

than one individual in the society is decisive on a pair of social outcomes. (An individual is decisive on a pair of social

outcomes x and y if, whenever he prefers x over y, the social choice function prefers xover y regardless of what other members

of the society prefer. (And similarly whenever he prefers y over x, the social choice function prefers y over x.) 21

Vilfredo Pareto.(1906) Manual of Political Economy. 1906. 22

Vilfredo Pareto(1896) Cours d' Économie Politique Professé a l' Université de Lausanne. Vol. I, 1896,Vol. II, 1897. 23

Kurt Godel,(1931) ‘ ¨ Uber formal unentscheidbare S ¨ atze ¨ der Principia mathematica und verwandter Systeme I’ (1931)

Richard ZachFirst publication: Monatshefte fur Mathematik und Physik ¨ , 37, 173–198 Reprints: S. Feferman et al., eds., Kurt Godel. Collected Works Volume I: Publications 1929–1936 New York: Oxford University Press, 1986, pp. 116–195. 24 Gödel, K (1930). "Die Vollständigkeit der Axiome des logischen Funktionenkalküls". Monatshefte für Mathematik (in German) 37 25 John Rawls.(1958) “Justice as Fairness. The Philosophical Review”, Vol. 67, No. 2 (Apr., 1958), pp. 164-194. Stable URL:. 26 Nash John (1951) “Non cooperative Game Theory (annals of Mathematics,1951 Vol. 54, No. 2 (Sep., 1951), pp. 286-295

27 Pareto optimal (comparative more Pareto optimal, superlative most Pareto optimal)

(game theory, economics) Describing a situation in which the profit of one party cannot be increased without reducing the

profit of another. AND (game theory) Describing a strategy that cannot be made to perform better against

one opposing strategy without performing less well against another

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28 Caratheodory (1935) Einfache Bemerkungen über Nabelpunktskurven, in: Festschrift 25 Jahre Technische Hochschule Breslau zur Feier ihres 25jährigen Bestehens, 1910—1935, Verlag W. G. Korn, Breslau, 1935, pp 105 - 107, and in: Constantin Carathéodory,1957 Gesammelte Mathematische Schriften, Verlag C. H. Beck, München, 1957, vol 5, 26–30 Carathéodory did publish this paper on a related subject but never committed the Conjecture into writing. The “Caratheodory Conjecture” claims that any convex, closed and sufficiently smooth surface in three dimensional Euclidean space needs to admit at least two umbilic points. In the sense of the Conjecture, the spheroid with only two umbilic points and the sphere, all points of which are umbilic, are examples of surfaces with minimal and maximal numbers of umbilics. For the conjecture to be well posed, or the umbilic points to be well-defined, the surface needs to be at least twice differentiable. 29As we have no better proof of thought-emotion expression from the language, we have approach this linguistic expression

and construction, in order to raise arguments accepting or rejecting the model. The emphasis is given to (a) psychological and

(b) personality factors, as well as to (c) linguistic recursion, as they help us to use surrogate proposals i. e "Mother told him,

that had been told that Penelope left her home" (Piraha linguistic determinism Language may shape human thought – suggests

a counting study in a Brazilian tribe whose language does not define numbers above two. Hunter-gatherers from the Pirahã

tribe, whose language only contains words for the numbers one and two, were unable to reliably tell the difference between

four objects placed in a row and five in the same configuration, revealed the study.

30 Chomsky N. (2010). Some simple evo devo theses: how true might they be for language? in The Evolution of Human Language, eds Larson R. K., Deprez V., Yamakido H., editors. (Cambridge: Cambridge University Press; ), 45–62

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incompatibility between “Justice Theory” (Rawls) and “Prioritarianism”34 : According to

Moreno-Ternero, Juan D. Roemer35, John E. The Veil of Ignorance (the fundamental

Principle of Justice Theory) violates Priority36: According to Professors (Moreno and

Roemer+) the veil of ignorance (of the Rawlsian “Justice” Philosophy), has been used often

as a tool for recommending what justice requires with respect to the distribution of

wealth. They completed Harsanyi’s model of the veil of ignorance by appending

information permitting objective comparisons among persons. For this, they introduced

the concept of objective empathy. They showed that the veil of ignorance conception of

John Harsanyi, so completed, and Ronald Dworkin’s37, when modeled formally,

recommend wealth allocations in conflict with the prominently espoused view that priority

should be given to the less able in wealth allocation38. They suggested that the veil of

ignorance should be rejected as a tool for discovering what justice requires. One of the

most obvious incapability concerns the “pair” “Social Justice-Utilitarianism”

6. to build a well-formed formulas (wffs) theorem, as to formulate an application of the

theory of sets free of paradoxes such as Russell’s paradox39:

7. To find “links” between different forms of “social welfare” The conjecture of “Justice versus

Utilitarianism”, especially in the light of Political Liberalism40 should focus on the essence

of the two concepts: Utilitarianism and social justice are two terms perfectly linked

together as critique of utilitarianism forms a crucial subplot in the complex analysis of

social justice Besides, social justice cannot be prioritarian The weaknesses of utilitarianism

indicate the need for an alternative theory, and at many stages of the argument the test

for the adequacy of the new theory that Rawls elaborates is whether it can be

demonstrated to be superior to the utilitarian rival. The account of social justice shifts in

the transition to Rawls’s second great book, Political Liberalism. Utilitarianism may be

understood as the doctrine that an institutional arrangement, a social policy, or an

individual action is morally right just in case it is the one that, compared to the available

alternatives, maximizes utility. Rawls assumes that justice is the overriding, preeminent

part of the morality of institutions, so he formulates the doctrine in this way: “society is

rightly ordered, and therefore just, when its major institutions are arranged so as to

achieve the greatest net balance of satisfactions summed over all the individuals

31 Everett D. L. (2005) Cultural constraints on grammar and cognition in Pirahã: another look at the design features of human

language. Current Anthropology. 46, 621–646

32 Everett D. L. (2012) Language: The Cultural Tool. New York, NY: Pantheon Books 33 RAWLS VERSUS UTILITARIANISM IN THE LIGHT OF POLITICAL LIBERALISM (published in The Idea of a Political Liberalism: Essays on Rawls (Lanham: Md: Rowman and Littlefield, 2000) Richard J. Arneson 34 Moreno-Ternero-, Juan, D. Roemer John E. (2005) Impartiality and priority. Part 1: the veil of ignorance” –Yale University (February 9, 2005) 35 Moreno-Ternero, Juan D. Roemer, John E (2011) "A common ground for resource and welfare egalitarianism," Working Papers 11.12, Universidad Pablo de Olavide, Department of Economics 36 Moreno-Ternero, Juan D. Roemer, John E (2008) The Veil Of Ignorance Violates Priority -Economics and Philosophy, 24 (2008) 233–257

37 Dworkin Ronald (2004) “From Liberal Values to Democratic Transition: Essays in Honor of Janos Kis”-. Ed. Budapest: Central

European University Press, 2004.

38 Dworkin Ronald (2006) “Justice in Robes” Cambridge, MA: Harvard University Press, 2006. 39 Russell’s paradox: According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves. This contradiction is Russell's paradox. See at chapter 6 40 Arneson Richard J.(2000) RAWLS VERSUS UTILITARIANISM IN THE LIGHT OF POLITICAL LIBERALISM published in The Idea of a Political Liberalism: Essays on Rawls (Lanham: Md: Rowman and Littlefield, 2000)

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belonging to it He understands utility (human welfare) as the satisfaction of rational

desire. Rawls’s proposal that we should maximin rather than maximize leads to an

interesting standoff. The argument for maximin is not compelling, but straight additive

maximization of the utilitarian sort is revealed to be merely one possible function among

many, any of which (for all we know) correct morality might instruct us to maximize. Rawls

further urges that utilitarianism goes astray in taking the maximandum, the thing to be

maximized, to be utility rather than primary social goods. The argument for primary social

goods is not compelling, but it does not follow that utility alone is to be maximized. The

espousal of the ideal of legitimacy in Political Liberalism does not affect these conclusions,

8. To deal with the Utilitarianism We see below that Utilitarianism may be understood as the

doctrine that an institutional arrangement, a social policy, or an individual action is

morally right just in case it is the one that, compared to the available alternatives,

maximizes utility. Rawls assumes that justice is the overriding, preeminent part of the

morality of institutions, so he formulates the doctrine in this way: “society is rightly

ordered, and therefore just, when its major institutions are arranged so as to achieve the

greatest net balance of satisfactions summed over all the individuals belonging to it” He

understands utility (human welfare) as the satisfaction of rational desire. TAKING RIGHTS

SERIOUSLY Perhaps the animating philosophical idea in A Theory of Justice is that

utilitarianism does not take rights seriously, that not taking rights seriously is a grave

defect, and so we need a theory of justice that better fits our core convictions about ways

that people must not be treated. Slavery is morally wrong because it violates fundamental

moral rights of the persons who are enslaved. Suppression of speech intended to

persuade that concerns public affairs and how people might best conduct their lives is

morally wrong at least when the ground for suppression is the prospect of harm that

might be caused via the audience’s understanding of the speech. If the fundamental moral

requirement were to maximize human welfare, then it would seem that whether or not

slavery and suppression that violates the core of freedom of expression are morally wrong

would depend on the outcome of complex and uncertain empirical calculation about which

policies work best over the long run to achieve the utilitarian aim. Rawls observes that our

convictions regarding slavery and freedom of expression are not tentatively and

uncertainly held, and not held on the basis that utilitarianism posits. Even if a utilitarian

theory conjoined to a complex set of plausible empirical claims could support the

positions that slavery and violation of freedom of expression are morally wrong,

utilitarianism is in tension with the strength of our moral conviction in these matters and

seems not to capture our intuitive grounds for these convictions.

9. To “deal” with the “individuals rights. Hence we need a theory of rights, a genuine theory

of justice that makes sense of our core convictions about individual rights and extends

these core judgments to controversial cases in a plausible way. In a utilitarian moral

system, individual rights, if present at all, will be derived from the single fundamental aim

of utility or welfare maximization. Roughly, the idea is that the recognition and protection

of individual rights better promote the utilitarian goal than alternative practices, policies,

and acts. Rights function to simplify and coordinate decision making among imperfectly

informed individuals of limited reasoning powers and limited altruism. If we were to

eschew rights and directly apply the test of utility on each occasion of acting or

implementing social policies, the results would predictably be less successful, from the

standpoint of utility maximization, than the results of instituting and promoting the

recognition of rights. Recognition of rights involves proclaiming their moral importance

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and socializing and training individuals to give extra weight to rights that impinge on their

practical deliberations than to their own fallible utility calculations when these conflict

with rights. In this sense a utilitarian theory can take rights seriously without assigning

rights any non derivative moral significance. The utilitarian will also note that common-

sense agreement that rights are un-controversially decisive determinants of what we

ought to do is in a sense illusory. Many rights appear uncontroversial when they are stated

vaguely and at a high level of abstraction, so that the practical implications for policy of

acceptance of these abstract rights are highly uncertain. Take freedom of expression, for

example. Almost everyone is for free speech, but this appearance of unanimity quickly

dissolves if we ask what a right to free speech is supposed to entail in a host of complex

circumstances. It does not follow that there is no way to proceed except by appeal to

utility as John Stuart Mill argues, but the appearance that the embrace of utilitarianism

would force us to regard what are really simple and obvious moral truths as contingent

and uncertain matters is misleading. THE SEPARATENESS OF PERSONS Rawls urges that

utilitarianism “does not take seriously the distinction between persons” The objection is

that utilitarianism extends to interpersonal conflicts of interest a rule of maximizing

aggregate benefit that is morally unproblematic when what is at issue is conflict between

a person’s interests at earlier and later times of his life. Prudence dictates accepting a

smaller pain now to avoid a larger pain at a later time, and utilitarian maximization

dictates imposing on one person a smaller pain in order to avoid a larger pain for another

person. But in the intrapersonal case Jones now is compensated by the gain to the same

Jones later, whereas in the interpersonal case, a loss imposed on Smith is not

compensated by greater benefits that accrue to other persons. This last formulation might

suggest that Rawls intends to assert the principle that there should be no sacrifice

imposed on one individual for the benefit of others unless the individual who suffers

imposition is compensated.

10. To examine the compatibility or rejection of the veil of ignorance: the veil of ignorance, in

either its amended Harsanyi form or its amended Dworkin form, when viewed as a

mechanism for allocating wealth, is non-prioritarian. For those committed to

prioritarianism, as we have defined it in this article, this demonstration therefore provides

reason to reject the use of veil-of-ignorance arguments. But, perhaps more objectively,

one can ask, why should one not take their demonstration as implying that we should

reject prioritarianism as a principle of justice (and keep the veil of ignorance) They are

concerned with the following syllogism:

o Justice requires impartiality.

o Impartiality, as far as justice is concerned, is properly captured by the veil of

ignorance.

o The veil of ignorance is in general non-prioritarian.

o Therefore justice cannot (in general) be prioritarian41.

11. To deal with the TWO (2) basic Gödel's incompleteness theorems (1931)42 : Gödel's

incompleteness theorems43 are among the most important results in modern logic44.

41 See appendix (6) 42 Kurt Gödel,(1931) '¨Uber formal unentscheidbare Sätze der Principia mathematica und verwandter. Systeme I' (1931). Richard Zach ... Undecidable Propositions of Principia Mathematica and Related Systems, Edinburgh: Oliver and Boyd, 1962 Richard ZachFirst publication: “Monatshefte fur Mathematik und Physik”, 37, 173–198 Reprints: S. Feferman et al., eds., Kurt Godel. Collected Works Volume I: Public- citation 1929–1936. New York: Oxford University Press, 1986, pp. 116–195. 43 Stanford Encyclopedia of Philosophy DEFINITION 44 , Kurt Godel 1941, “In What Sense is Intuitionistic Logic Constructive?” in Gödel 1995: 189–200.

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These discoveries revolutionized the understanding of mathematics and logic, and had

dramatic implications for the philosophy of mathematics. There have also been attempts

to apply them in other fields of philosophy, but the legitimacy of many such applications

is much more controversial.

o The first incompleteness theorem: Any effectively generated theory capable of

expressing elementary arithmetic cannot be both consistent and complete In

particular, for any consistent, effectively generated formal theory that proves

certain basic arithmetic truths, there is an arithmetical statement that is true,

but not provable in the theory.

EXAMPLE: For each consistent formal theory T having the required small

amount of number theory, the corresponding Gödel sentence G asserts:

"G cannot be proved within the theory T". This interpretation of G leads to

the following informal analysis

If G were provable under the axioms and rules of inference of T,

then T would have a theorem, G, which effectively contradicts itself, and thus

the theory T would be inconsistent. This means that if the theory T is

consistent then G cannot be proved within it, and so the theory T is

incomplete. Moreover, the claim G makes about its own un-provability is

correct. In this sense G is not only unprovable but true, and provability-

within-the-theory-T is not the same as truth. The formal proof reveals

exactly the hypotheses required for the theory T in order for the self-

contradictory nature of G to lead to a genuine contradiction

o The second incompleteness theorem, an extension of the first, shows that

such a system cannot demonstrate its own consistency. Given that the

consistency of a system can be proven outside of the given formal system,

Gödel says, The Second Incompleteness Theorem One big reason for the

expressed disconnect is that Gödel’s theorems are about formal axiom

systems of a kind that play no role in daily mathematical work. Informal

axiom systems for various kinds of structures are of course ubiquitous in

practice, viz. axioms for groups, rings, fields, vector spaces, topological

spaces, Hilbert spaces, etc., etc.; these axioms and their basic consequences

are so familiar it is rarely necessary to appeal to them explicitly, but they

serve to define one’s subject matter. They are to be contrasted with

foundational axiom systems for the “mother” structures--the natural numbers

(Peano) and the real numbers (Dedekind)--on the one hand, and for the

general concepts of set and function (Zermelo-Fraenkel)45,46 used throughout

mathematics, on the other47. Mathematicians may make explicit appeal to the

principle of induction for the natural numbers or the least upper bound

principle for the real numbers or the axiom of choice for sets, but reference

to foundational axiom systems in practice hardly goes beyond that. One

45 Tony Lian (2013) Fundamentals of Zermelo-Fraenkel Set Theory 46 Zermelo, E..(1908) "Untersuchungen über die Grundlagen der Mengenlehre. I."Mathematische Annalen 65 (1908): 261"Investigations in the foundations of set theory". From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Source Books in the History of the Sciences Harvard University Press pp. 199–215. 47 Gödel Kurt 1951, “Some Basic Theorems on the Foundations of Mathematics and their Implications” (Gibbs Lecture), in Gödel 1995: 304–323

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informal statement of the basic Peano axioms for the natural numbers is that

they concern a structure (N, 0, s) where 0 is in N, the successor function s

is a unary one-one map from N into N which does not have 0 in its range, and

the Induction Principle is satisfied in the following form: (IP) for any property

P(x), if P(0) holds and if for all x in N, P(x) implies P(s(x)) then for all x in N,

P(x) holds. But this is too indefinite to become the subject of precise logical

studies, and for that purpose one needs to say exactly which properties P are

admissible in (IP), and to do that one needs to specify a formal language L

within which we can single out a class of well-formed formulas (wffs) A which

express the admitted properties. And to do that we have to prescribe a list of

basic symbols and we have to say which finite sequences of basic symbols

constitute well-formed terms and which constitute wffs. Finally, we have to

specify which wffs are axioms (both logical and non-logical), and which

relations between wffs are instances of rules of inference. The wffs without

free variables are 3 those that constitute definite statements and are called

the closed formulas or sentences of L. All of this is what goes into specifying

a formal axiom system S. In the case of a formal version of the Peano axioms,

once its basic symbols are specified, and the logical symbols are taken to be

¬ (“not”), ∧ (“and”), ∨ (“or”), → (“implies”), ∀ (“for all”), and ∃ (“there exists”),

one puts in place of the Induction Principle an Induction Axiom Scheme: (IA)

)()((()0( xxAxAAxA

o where A is an arbitrary wff of the language L and A(t) indicates the result of

substituting the term t for all free occurrences of the variable x in A. N. B.

(IA) is not a single axiom but an infinite collection of axioms, each instance of

which is given by some wff A of our language. Besides zero and successor,

nothing of number-theoretical interest can be derived without expanding it to

include at least addition and multiplication. As shown by Dedekind, the

existence of those operations as given by their recursive defining conditions

can be established using (IP) applied to predicates P involving quantification

over functions. But for a formal axiom system PA (“Peano Arithmetic”) for

elementary number theory in which one quantifies only over numbers, one

needs to posit those operations at the outset. The basic vocabulary of PA is

thus taken to consist of the constant symbol 0 and the operation symbols s,

+ and × together with the relation symbol =. Then the axioms indicated

above for zero and successor are supplemented by axioms giving the

recursive characterizations of addition and multiplication, namely:

xyxysxandxyxsysxxx )*()(*..(..00*),..()(,..0

For example, "Theorem Impossible" (Kenneth Arrow, 1951) is a coherent

theorem proven by rigorous logic and mathematical thinking However,

according to the Theory of incompatibility (Gödel) precisely because it has the

consistency and provability with Axioms used through its own system,

theorem of Kenneth Arrow cannot have the required accessibility

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papakonstantinidis Page 16

o It follows that possibly the "Theorem fails” (“Impossibility theorem") have

"gaps" that covers them through its own reasoning Informally, the reasoning

leading to the second incompleteness theorem is relatively simple. Given the

arithmetized provability predicate, it is also easy to present an arithmetized

consistency statement: pick some manifestly inconsistent formula (in

arithmetical theories, a standard choice is (0 = 1)); let us denote it by ⊥;

(the arithmetized counterpart of) the consistency of the system can then be

defined as ¬Prov (⌈⊥⌉). Let us abbreviate this formula by Cons(F). The

proof of the first part of the first incompleteness theorem (i.e., the case (i)

above) can then presumably be formalized inside F (in practice this would

certainly be intricate). This gives: F ⊢ Cons (F) → GF, where GF is the

Gödel sentence for F provided by the first theorem. If Cons (F) were provable

in F, so would be GF, by simple logic. This would contradict Gödel's first

theorem. Consequently, Cons (F) cannot be provable in F either.

o Gödel's second incompleteness theorem Assume F is a consistent formalized

system which contains elementary arithmetic. Then F ⊬ Cons (F).

o There is a question of philosophical importance that should be mentioned

here: As it stands, Gödel's second incompleteness theorem only establishes

the un-provability of one sentence, Cons (F). But does this sentence really

express that F is consistent? (Compare this with the remark above

that GF does not, strictly speaking, express its own un-provability.)

Furthermore, might there not be other sentences which are provable and also

express the consistency of F? Giving a rigorous proof of the second theorem

in a more general form that covers all such sentences, however, has turned

out to be very complicated. The basic reason for this is that, unlike in the first

theorem, not just any,merely extensionally adequate provability predicate

works for the formalization of the consistency claim. The manner of

presentation makes all the difference. For example, Rosser's provability

predicate mentioned above would not do; one can prove the “consistency”

of F in F, if consistency is expressed in terms of Rosser's provability predicate

One must thus add some further conditions for the provability predicate in

order for the proof of the second incompleteness theorem to go through.

Following Feferman (1960), it is customary to say that whereas the first

theorem and its relatives re-extensional results the second theorem

is intentional: it must be possible to think that Cons (F) in some

sense expresses the consistency of F—that it really means that F is consistent.

o Why is Gödel's Second Incompleteness Theorem important? Given that the

consistency of a system can be proven outside of the given formal system,

Gödel says, It must be noted that proposition XI... represents no contradiction

to the formalities viewpoint of Hilbert.... Why do others disagree? Who cares

whether a system cannot prove its own consistency? Why would we expect

such a thing? Is it possible that a theory without multiplication, but with some

other axiom or axioms (i.e., weaker in one sense but stronger in another)

could prove P consistent and itself consistent?

o

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12. To deal with the SET THEORY: Set theory is a branch of mathematics that studies

collections of objects. Each collection is called a set and the objects in the collection are

called elements of the set. “win-win-win papakonstantinidis model” is –first of all a “set

theory” based on its Axioms Modern set theory began in the 1870s with the works of

Georg Cantor48 and Richard Dedekind49. Later work over the course of the 19th and 20th

centuries revealed many paradoxes in set theory (some of which will be discussed later).

This created a need for an axiomatic system that corrects these paradoxes. Ernst Zermelo

proposed the 1st axiomatic set theory in 1908. Later, Abraham Fraenkel and Thora lf

Skolem proposed some revisions including the addition of the Axiom Schema of

Replacement. The resulting axiomatic set theory became known as Zermelo-Fraenkel (ZF)

set theory50. To strengthen the arguments in favor of a triangular perception of things, we

will try to bring it in Set Theory and see how the qualities of the "win-win-win”51,52

'correspond 1-1 to basic Axioms

13. To deal with the extension of the Zermelo-Fraenkel (ZF) set theory, i.e the von Neumann–

Bernays–Gödel set theory (NBG) In the foundation of maths von Neumann–Bernays–Gödel

set theory (NBG) is an axiomatic set theory that is a conservative extension of the

canonical Zermelo–Fraenkel set theory (ZFC). A statement in the language of ZFC is

48 Cantor, Georg (1874), "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen" Journal für die Reine und

Angewandte Mathematik 77: 258–262, AND Cantor Georg (1874) , "Über eine Eigenschaft des Inbegriffes aller reellen

algebraischen Zahlen" ( in Greek:"Σε μία ιδιοκτησία της συλλογής όλων των αλγεβρικών πραγματικών αριθμών")

49 Dedekind Richard 1890. "Letter to Keferstein" in Jean van Heijenoort 1967 A Source Book in Mathematical Logic 1879 –1931

Harvard Univ. Press: 98–103 AND 1996. Theory of Algebraic Integers Stillwell, John, ed. and trans. Cambridge Uni. Press A

translation of Über die Theorie der ganzen algebraischen Zahlen.( The invention of ideals by Dedekind in the 1870s was well

ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir "Sur la

Theorie des Nombres Entiers Algebriques" first appeared in installments in the Bulletin des sciences mathematiques in 1877.

This book is a translation of that work by John Stillwell, who adds a detailed introduction giving historical background and who

outlines the mathematical obstructions that Dedekind was striving to overcome

Dedekind's theorem states that if there existed a one-to-one correspondence between two sets, then Dedekind said that the

two sets were "similar". He invoked similarity to give the first precise definition of an infinite set: a set is infinite when it is

"similar to a proper part of itself," in modern terminology, is equi-numerous to one of its proper subsets. Thus the

set N ofnatural numbers can be shown to be similar to the subset of N whose members are the squares of every member of N,

(N→ N2):

100.................16.9.4.1.

...................

10.9.8.7.6.5.4..3.2.1...

2N

N

50 See at “Set Theory Chapter 7 (p. 300) 51 Papakonstantinidis LA(2012/ Jan) “The intermediate Community: A behavioral/ Bargaining Approach, for Conflict Resolution at the Local Level/ Bayesian Analysis International Journal of Research in Commerce It and Management” I.J.R.C.M (Indexed & Listed at: Ulrich's Periodicals Directory ©, Pro Quest, U.S.A., EBSCO Publishing, U.S.A., Index Copernicus Publishers Panel, Poland, Open J-Gage, India [link of the same is duly available at Inflibnet of University Grants Commission (U.G.C.)] as well as in Cabell’s Directories of Publishing Opportunities, U.S.A. Circulated all over the world & Google has verified that scholars of more than Hundred & Twenty One countries/territories are visiting our journal on regular basis) .[IJRCM VOLUME NO. 2 (2012), ISSUE NO. 1 (JANUARY 2012) /the EUROMED Conf) – 2blind reviewers evaluation system 52 Papakonstantinidis LA(2012The win-win-win Papakonstantinidis model (2012:book of Proceedings) A behavioral analysis in dynamical systems The Non Instrumental Rationality Paradox Case-study: Hellenic Benefactors(2 blind reviewers evaluation - 1st International Symposium on Business, Economics and Financial Applications,(ISBEFA) 1-2 June 2012, Kefalonia, Greece

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provable in NBG if and only if it is provable in ZFC. The ontology of NBG includes proper

classes, objects having members but that cannot be members of other entities. NBG's

principle of class comprehension is predicative; quantified variables in the defining

formula can range only over sets. Allowing impredicative comprehension turns NBG into

Morse-Kelley set theory (MK). NBG, unlike ZFC and MK, can be finitely axiomatized

Motivation via the cumulative hierarchy: One motivation for the ZFC axioms is

the cumulative hierarchy53 cumulative hierarchy of sets introduced byJohn von

Neumann (Shoenfield 1977, sec. 2). In this viewpoint, the universe of set theory is built up

in stages, with one stage for each ordinal numer At stage 0 there are no sets yet. At each

following stage, a set is added to the universe if all of its elements have been added at

previous stages. Thus the empty set is added at stage 1, and the set containing the empty

set is added at stage 2; see Hinman (2005, p. 467). The collection of all sets that are

obtained in this way, over all the stages, is known as V. The sets in V can be arranged into

a hierarchy by assigning to each set the first stage at which that set was added to V To

deal with and analyze the “Set Theory: The concept here is that the "set theory" deals with

sets which informally are collections of objects. Any type of object can be collected into a

set, . From this point of view, the win-win-win perception includes “sets of behaviors”

that obey in common rules (axioms)

14. The "win-win-win theory” is included in the in ZFC (Zemelo-Fraenkel- Ciesielski) set

theory because it obeys the basic axioms of ZFC Set Theory (Axiom of extensionality,

Axiom of regularity (also called the Axiom of foundation), Axiom schema of specification

(also called the axiom schema of separation or of restricted comprehension), Axiom of

pairing Axiom of union Axiom schema of replacement Axiom of infinity Axiom of power

set Well-ordering theorem

15. To deal with “systems”: For transferring of dual systems' perception (YES-NO) on which

the Western capitalist patterns have been based, (i.e "Boolean Algebra, Digital logic gates

or/and Linguistic Recursion, correspond by the "0-1" and "one-many") towards a unique

Triple-Pole (win-win-win )54 system

16. To deal with the “Calkin-Wilf tree: In number theory, the Calkin-Wilf tree is a tree in

which the vertices correspond 1-for-1 to the positive rational numbers. Tree is rooted The

at the number 1, and any rational number expressed in simplest terms as the fraction a /

53 John von Neumann The cumulative hierarchy is a collection of sets Vα indexed by the class of ordinal numbers; in particular, Vα is the set of all sets having ranks less than α. Thus there is one set Vα for each ordinal number α. Vα may be defined by transfinite recursion as follows:

Let V0 be the empty set: For any ordinal number β, let Vβ+1 be the power set of Vβ:

For any limit ordinal λ, let Vλ be the union of all the V-stages so far: 54

Papakonstaninidis, 2015, this study- oct pp 288-295

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papakonstantinidis Page 19

b has as its two children the numbers a / (a + b) and (a + b) / b. Every positive rational

number appears exactly once in the tree.

.)(

.....)(

................2...........b

baand

ba

aeiresultedarenumberschildren

b

afractionFrom

&& CALKIN-WILF TREE

17. To examine, analyze and deal with alternative scenarios-seemingly unrelated to each

other; from the fields of

o Bargaining Theory55,56

o Agency Theory57,58,59,60

o “Ultimatum Game" 61

o linguistic recursion62

as “incompatibilities” on which of “social welfare” used by the “papakonstantinidis

conjectures”:

o The Nash’ “Bargaining Theory”

As mentioned above, the “agency theory” introduces us to the double thinking leading thus, in

limit, to a triple pole win (win-win-win) This is a very important one: According to

“papakonstantinidis conjectures63,64,65,66”:

55 Bargaining or haggling is a type of negotiation in which the buyer and seller of a good or service debate the price and exact nature of a transaction. If the bargaining produces agreement on terms, the transaction takes place. 56 Nash, John (1950). "The Bargaining Problem" Econometrica 18 (2): 155–162.

57 DEFINITION OF 'AGENCY THEORY' A supposition that explains the relationship between principles and agents in business.

Agency theory is concerned with resolving problems that can exist in agency relationships; that is, between principals (such as

shareholders) and agents of the principals (for example, company executives). The two problems that agency theory addresses

are: 1.) the problems that arise when the desires or goals of the principal and agent are in conflict, and the principal is unable

to verify (because it difficult and/or expensive to do so) what the agent is actually doing; and 2.) the problems that arise when

the principal and agent have different attitudes towards risk. Because of different risk tolerances the principal and agent may

each be inclined to take different actions. 58 Ross, Stephen A. 1973. The economic theory of agency: The principal's problem. American Economic Review 62(2): 134-139. 59 Mitnick, Barry M. 1974a. The theory of agency: The concept of fiduciary rationality and some consequences. Unpublished Ph.D. dissertation Department of Political Science, University of Pennsylvania Univ. Microfilms No. 74-22,881. 60 Stiglitz, Joseph and Andrew Weiss (1989) “Sorting out the Differences Between Screening and Signalling Models,” in Papers in Commemoration of the Economic Theory Seminar at Oxford University, edited by Michael Dempster, Oxford: Oxford University Press. 61

Sanfey, Alan; Rilling, Aronson, Nystrom, Cohen (13 June 2003). "The Neural Basis of Economic Decision-Making in the

Ultimatum Game" Science 300 (5626): 1755–1758. 62 Daniel Everett (2005), "Cultural Constraints on Grammar and Cognition in Pirahã", Current Anthropology Volume 46, Number 4, August–October 2005, pp. 621-46.

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Papakonstantinidis conjectures:

1. “at any bargain, each one from the 2 bargainers represents the rest of the community and

(at the same time) him/her self

So, "what is good for the Community (the third “win”) incorporated in each one from the

bargainers’ expectations (in the frame of the “agency theory” or “the principal-agent -

problem”

AND

2. “a win-win-win situation may be possible if and only if the human mind, as expressed in

terms of interaction, is built to accept this situation (the universal cooperation) The answer to

this question gives us the linguistic recursion”

Papakonstantinidis 2002

1. Furthermore, an application of the Central Limit Theory (CLT) on a series of answers

from 512 given to specific "closed" questions (questionnaire), concerning their

appreciation for their negotiating behavior enhances the theoretical structure of the

“win-win-win papakonstantinidis model”, adding to it a direct practical utility,

especially in less developed regions, and the local development domain in general To

prove that “win-win-win papakonstantinidis model works , giving excellent results

Finally, an application of the Central Limit Theory (CLT) on a series of answers from

512 people given to specific "closed" questions (questionnaire), -concerning their

appreciation for their negotiating behavior - enhances the theoretical structure of the

“win-win-win papakonstantinidis model”, adding to it a direct practical utility,

especially in less developed regions, and the local development domain in general

Indeed, applying the Central Limit Theory (CLT) on a sample of 512 responses to the

following written questionnaire on the personal assessment of the outcome of any

negotiation involving a time, see how it works and gives excellent results which in

turn adapted to the curve-function a "normal distribution" Since thousands of

63 Papakonstantinidis Leonidas A (2012). The “win-win-win papakonstantinidis model” as a bargaining solution analysis for

local government decision From territory- community to “behavioral” Community Case study: the Greek Case – Chinese

Business Review Vol 11 Number 6 Jun 2012- CHINA 64Papakonstantinidis L.A (2013) Involving Communities In Rural Tourism: A “Win-Win-Win Papakonstantinidis Model” Methodological Approach Case Studies: Women Rural Tourism Cooperatives: A) Gargaliani, Peloponnesus Area (South-West Gr) B) Wert (Women Entrepreneurs In Rural Tourism) Eu Program : Win – Win –Win Papakonstantinidis Model” As A Recognized (In European- Wert Net- Level) Rural Tourism Methodological Tool WORLD CONGRESS titled “Communities as A part of Sustainable Rural Tourism – Success Factor Or Inevitable Burden? Proceedings Of The Community Tourism Conference, 10th – 11th September 2013 In Kotka, Finland Merja Lδhdesmδki Ja Anne Matilainen (Eds.) 65Papakonstantinidis Leonidas A The Intermediate Community: A Behavioral/Bargaining Approach For Conflict Resolution At The Local Level/Bayesian Analysis International Journal Of Research In Commerce, It & Management (IJRCM) VOLUME NO. 2 (2012), ISSUE NO. 1 (JANUARY) 66 Papakonstantinidis L.A Papakonstantinidis S Spais G (2009)An innovative bargaining solution analysis for vertical cooperative promotion management decisions Innovative Marketing, Volume 5, Issue 3, 2009

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negotiations that we do every day with other people who realize that "winners" -

"losers" converge as the number of negotiations (N) tends to infinity and from this

point they would accept a "third pole (Community)" above their own forces as long as

necessary for this pole should ensure fairness, equality, respect, self-organization

over people It can help us make decisions about our data. Prof Calkin Neil (2015)67

should add a cautionary note as to *why* something like the Lyapunov condition is

necessary when considering sums of independent variables with different expected

values: my favourite example is X_i is 1/2^i or 0, each with probability 1/2. Then the

sum of the X_i for I>=1 is uniform in [0,1]. He prefer - very much *not* the central

limit theorem68 ……………………………………………………………………………………………………

See at the practical “win-win-win” application: APPLICATION: THE P.A.C case: Kotca

(FIN) world conference, 2013/SEPT

THE PROBLEM- THE NECESSITY

"Social welfare" was strongly contested, from the Neoclassical School of Thought

67

Calkin, Neil; Wilf, Herbert (2000), “Recounting the rationals” American Mathematical Monthly (Mathematical Association of

America) 68Calkin, Neil; Wilf, Herbert (2000), "a list of all positive rational numbers, each appearing once and only once, can be made by writing down 1/1, then the fractions on the level just below the top of the tree, reading from left to right, then the fractions on

the next level down, reading from left to right, etc."

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In the opposite, the Classical School of Thought, as “moral philosophy” believed that the free

market should achieve the social welfare automatically

Let’s take an idea,: The problem-which was an incentive for me to deal with - is much more

complicated: At the heart of the debate, is the term “social welfare”

In the real world, where people cannot negotiate costlessly, there may be collective action

problems of those who caused a nuisance, for instance by smoke emissions from a factory to

many neighboring farms, and so getting together to negotiate effectively can be difficult

against a single polluter because of coordination problems. If it is efficient for the farmers to

pay the factory to reduce its emissions, some of those farmers may hold off paying their fair

share, hoping to get a free ride. The factory may be in a better position to know what

measures to take to reduce harm, and can be the cheapest avoider, illustrating Coase's

argument.

WHAT the SOCIAL PROBLEMS are ?

A social problem is an issue within the society that makes i t di ff icult for

people to achieve their ful l potential . Poverty, unemployment, unequal

opportunity, racism, and malnutr it ion are examples of social problems. So

are substandard housing, employment disc r imination, and chi ld abuse and

neglect. Crime and substance abuse are also examples of social problems.

Not only do social problems affect many people directly, but they also affect

al l of us indirectly. The drug-abusing driver becomes the potential traff ic

accident that doesn 't choose its vict ims by race, color, or creed but does so

randomly. The chi ld of abusive parents al l too often becomes the vict im or

perpetrator of family v iolence as an adult.

Social problems tend to develop when we become neglectfu l and fai l to

see that serious problems are developing. Between 1988 and 1993, for

example, the United States saw a phe nomenal increase in youth violence. In

my book about chi ldren who commit violent acts (Gl icken, 2004b), I

documented that chi ldren younger than age 12 cause one third of al l f i res

result ing in death and that the average age of chi ldren who sexual ly abuse

other chi ldren is younger than age 10. According to Osofsky and Osofsky

(2001), "The homicide rate among males 15 -24 years old in the Uni ted States

is 10 t imes higher than in Canada, 15 t imes higher than in Austral ia, and 28

times higher than in France or Germany" (p. 287). These are troubl ing

examples of social problems that affect al l of us.

Could these problems have been prevented if our social insti tutions had

been working wel l? I think so, but this is where pol i t ical phi losophies are

important to understand. Some people bel ieve that government should be

very involved in providing services to people most at r isk. I don't know if the

labels liberal and conservative have much meaning anymore, but in t imes past,

we might have cal led these folks l iberals. Liberals bel ieve that where our

usual VgtJ'X institutions fai l , the government and the private sector should

help out. Conservatives bel ieve that intruding in people's l ives often leads to

a weakening of social institutions and the values that have served us wel l in

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the past. Conservatives might say that what we should be doing to reduce

juveni le cr ime is to promote good family values and loo k to our tradit ional

institutions (e.g. , rel ig ious organizations and schools) to help prevent social

problems from developing. They also bel ieve that the more government has

become involved in people 's l ives in the past, the more serious our social

problems have become. And f inal ly, although this is true of l iberals as wel l ,

conservatives bel ieve in the concept of social capital : that " the good wil l ,

fel lowship, sympathy, and social intercourse among the individuals and

famil ies who make up a social lKSL unit" (Hanifan, 1916, p. 130) 69 wi l l reduce

social problems if used wisely. The tension between pol it ical phi losophies is

often the underlying reason why we respond to or neglect social prob lems.

This tension can be seen in the grass-roots organizations that often develop

in the United States, such as the Tea Party movement and the radical groups

of the 1960s, that seek to correct pol i t ical problems through direct and

sometimes aggressive social action.

In addit ion to l iberal ism and conservatism, there are fo ur major pol i t ical

phi losophies that affect the way we approach social problems in America.

Libertarianism bel ieves in maximum personal l iberty and a small and wel l -

defined role for government, and opposes most social legislation aimed at

providing social just ice and equity. The fol lowing posi t ion on a minimum

wage might help you understand the posi t ion l ibertarians take on many

social programs:

Skilled, experienced workers make high wages because employers compete to hire them.

Poorly educated, inexperienced young people can't get work because minimum wage laws

make them too expensive to hire as trainees. Repeal of the minimum wage would allow many

young, minority and poor people to work. It must be asked, if the minimum wage is such a

good idea, why not raise it to $200 an hour? Even the most die-hard minimum wage advocate

can see there's something wrong with that proposal. The only "fair" or "correct" wage is what

an employer and employee voluntarily agree upon. We should repeal minimum wage now

o As we know from the f inancial meltdown of 2008, this posit ion on

noninterference by government can sound very distant from the real i ty

of l i fe when unemployment and l i tt le income force people who

otherwise might take a "hands-off" posit ion on the role of government

to ask for substantial help.

o Socialism is the exact opposite of l ibertarianism

because it values the posit ive r ights of cit izens

including the r ights to heal th care, food, shelter,

work, and so forth. Under social ism the economy is

run for the good of society as a whole where

resources are divided equal ly among the society and

69 Hanifan, L. J. (1916). The Rural School Community Centre Annals of the American Academy of Political and Social Sciences 67,

130-38 This is the seminal paper where Lyda Hanifan first provided a definition of the concept of social capital in 1916.

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there is neither great weal th nor great poverty.

Communitarianism values tradit ion; ethnic, regional, or

national identity; and the common culture that

comes from rel igion or shared moral values. I t

emphasizes the importance of belonging to a certain

community and sharing in i ts tradi t ions, values, and

culture. Communitarians bel ieve that l ibertarians

and l iberals overemphasize the importance of the

individual. Radicalism bel ieves that government and

the private for-profi t sectors often exclude many

less aff luent cit izens from justice and equity and

that the primary tool avai lable to have social and

economic r ights maintained is to form strong

al l iances based on se lf-interest and to use social

action including marches, str ikes, and civi l

disobedience to maintain social equity. Radical ism is

a much more assertive phi losophy and bel ieves that

unless people aggressively protect their self -

interest, they wi l l lose social , pol i t ical , and

economic strength. Mahoney (2003) bel ieves that the

fol lowing four condit ions must exist before an issue

or a situation is considered a social problem:

o The condition or situation must be publicly seen as a social

problem because of a public outcry. The condi t ions in New

Orleans a f t er the d i kes broke and th e c i ty was f looded

fo l lowing Hurr ican e Kat r ina began a publ ic outcry tha t

focused on the s low resp onse to the cr i s i s by government ,

concerns about people in pover ty who were l e f t in t he c i ty to

fend for th emselves , concerns about the la ck o f law and order

during the cr is i s , and , cer ta in ly , concern s about racism and

a bel ie f tha t the fed era l g overnment had acted s lowly becau se

most o f th e people remain ing in New Orleans a f t er the f lood

were poor and Bla ck.

o The condition must be at odds with the values of the larger

society. Although people have varying degrees o f concern

about the poor , there was un iversa l anger and gr ie f a t wha t

happened to poor people in New Orleans and a growing

recogni t ion tha t government w a s po ten t ia l l y inca pable o f

help ing most American s i f they found themselves in a s imi lar

cr i s i s .

o Most people must be in agreement that a problem exists. During

a 10-year p er iod f ro m 1983 to 1993 , Amer ica saw

astronomical in creases in juven i le cr ime. People were awa re

and concerned a t th e sa me t ime because thei r person al sa fe t y

was a t i ssu e.

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o There must be a solution to a social problem. In the ca se o f New Orleans and fu ture

d isast ers , mo st people mu st bel ieve tha t government i s capable o f handl ing la rge -

sca l e d i sast ers , wh eth er man -made or t er rori s t . I f people don ' t bel i eve th is , they

fa l l in to apathy; and whi l e the p roblem ma y s t i l l ex i s t , they don ' t bel i eve anyth ing

can be done about i t .

o Mahoney also notes that the more inf luent ial people

are who might be affected by a social problem, the

more l ikely there is to be recognit ion of the problem

and a proper response. The mass media also play a

role in the recognit ion of social problems because

they highl ight problems in such a graphic way that

many people are touched by i t . How many people

bel ieved John Edwards (before his unfortunate

behavior and fal l from grace) when he spoke of two

Americas during the 2004 presidential campaign?

But people whose houses lost much, i f not al l , of

their value in the current real estate col lapse and

who have had their houses foreclosed on because

they can no longer make their mortgage payments

are far moreaware of the prob lems of poverty now

than they were when their houses were dramatical ly

increasing in value. The media have made a point of

tel l ing us how at r isk we are and how much we

potential ly have in common with those in poverty. In

the aftermath of Katr ina, pictures of people strug -

gl ing to survive during the New Orleans f lood had a

devastating impact on the perceptions pe ople had

about poverty. The media were responsible for

informing us that, as much as we might l ike to think

that poverty is nonexistent in America, i t does exist,

and its negative impact is substantial . But the media

are not always unbiased or objective in the way they

report the news. During the New Orleans f loods, for

example, some networks focused on cr ime and

violence whereas others focused on the pl ight of

poor people and the slow and befuddled response by

the government. There are many people who bel i eve

that the media ref lect a l iberal bias, and there are

also many who think that the media are control led

by their corporate owners who, some think, skew the

news to ref lect a more conservative orientation

o Conservatives believe the mass media, predominantly television

news programs, slant reports in favor of the liberal position on

issues. Members of the media argue [that] while personally

liberal, they are professionally neutral. They argue their opinions

do not matter because as professional journalists, they report

what they observe without letting their opinions affect their

judgment. But being a journalist is not like being a surveillance

camera at an ATM, faithfully recording every scene for future

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playback. Journalists make subjective decisions every minute of

their professional lives.

o They choose what to cover and what not to cover, which sources

are credible and which are not, which quotes to use in a story

and which to toss out.

o Liberal bias in the news media is a reality. It is not the result of a

vast left-wing conspiracy; journalists do not meet secretly to

plot how to slant their news reports. But everyday pack

journalism often creates an unconscious "groupthink" mentality

that taints news coverage and allows only one side of a debate

to receive a fair hearing. When that happens, the truth suffers

o No one we know starts out life wanting to be a substance abuser or to be poor. Most

of us want to be lucky, cool, rich, and successful. Some of us are, fortunately, but

many of us aren't. Part of the reason for individual success and failure has to do with

what we were given biologically in terms of good health, intelligence, and the ability

to stick with projects and finish them. The other part of it has to do with the families

we grow up in, the social and economic conditions of our lives, and the parents,

teachers, and friends who influence us. Some parents do wonderful things for their

children and provide safe and happy homes. Other parents fight, use substances, and

sometimes abuse and neglect their children. It doesn't take a genius to know that the

child who grows up in a happy family has a better chance of being successful in life

than the child growing up in a troubled family. Child abuse is everything it's cracked

up to be and so are poverty, abandonment, unsafe neighborhoods, and poorly

functioning schools. Some of us start life out on the right track, but a lot of us don't.

Often those people whose families function poorly overcome early life problems by

the inner strength some people call resilience. But many children who grow up in

difficult, unloving, and abusive homes suffer harm to their bodies and to their spirit.

It's difficult for them to be as successful as many of us who grew up in healthier

homes. People sometimes pull themselves up by their bootstraps, but for those who

don't professional help can make an enormous difference generous nature of people

when they're asked to volunteer.

o

o I think that people become volunteers as they begin to realize that someone

else's tragedy can easily be their own, and while many of us feel a

responsibility to give back to our communities, so often we feel powerless to

make the changes that seem beyond our personal scope.

o Volunteers have the power to make those changes by using the skills we

already have. Attorneys donate their time with legal services for the poor.

Doctors provide services to the neighborhoods and communities with

marginal health care. Helping professionals offer their time and expertise to

the many social welfare organizations without professionals to supervise

services and as board members and grant writers.

o With all of the options for helping, some of us are gifted at what is sometimes

called "impact work." Impact work is the attorney who chooses to represent

600 new immigrants from Mexico rather than simply representing the one

immigrant who walked into her office. Impact work is going beyond providing

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shelter and counseling services to victims of domestic violence by looking at

the causes of violence and finding new ways of preventing it. Impact work is

building more low and no income housing rather than just providing

temporary shelters for those without homes.70

o

To understand the problem of "Social Welfare" should refer in principle in the concept

of "Cost of Social Welfare” In his famous work “The Problem of Social Cost”71, Prof

Coase RH (1960) διατυπώνει belief that legal rules are only justified by reference to a

cost–benefit analysis, and that nuisance that are often regarded as being the fault of

one party are more symmetric conflicts between the interests of the two parties. If

there are sufficiently low costs of doing a transaction, legal rules would be irrelevant

to the maximization of production. Because in the real world there are costs of

bargaining and information gathering, legal rules are justified to the extent of their

ability to allocate rights to the most efficient right-bearer. Coase argued that if we

lived in a world without transaction costs, people would bargain with one another to

produce the most efficient distribution of resources, regardless of the initial

allocation. This is superior to allocation through litigation Coase used the example of

a nuisance case named “Stugers vs Bridgman72 where a noisy sweet-maker and a quiet

doctor were neighbours and went to court to see who should have to move.[2] Coase

said that regardless of whether the judge ruled that the sweet-maker had to stop

using his machinery, or that the doctor had to put up with it, they could strike a

mutually beneficial bargain about who moves that reaches the same outcome of

productive activity.

However, many welfare-maximizing reallocations are often forgone because of the transaction

costs involved in bargaining For instance, the sweet-maker may have many neighbors who

claim "nuisance" — some legitimate and some not, that the firm would have to sort through,

and some of those neighbors who do claim nuisance may try to hold out for excessive

compensation. In these cases, the transaction costs eat away, and ultimately eclipse, the price

signals that would have led to the most efficient distribution of resources.

In cases like these with potentially high transaction costs, the law ought to produce an

outcome similar to what would result if the transaction costs were eliminated. Hence courts

should be guided by the most efficient solution.

70 Glicken Morley (2010) ”Social Work in the 21st Century: An Introduction to Social Welfare, Social Issues, and the Profession

. SAGE Publications Inc

71 Coase RH (1960), 'The Problem of Social Cost' (1960)-3 Journal of Law and Economics 1-44 72 Facts and Judgment: Sturges v Bridgman (1879) LR 11 Ch D 852 is a landmark case in nuisance It decides that what constitutes reasonable use of one's property depends on the character of the locality and that it is no defense that the plaintiff "came to the nuisance". A doctor moved next door to a confectioner, who had produced sweets for sale in his kitchen for many years. The doctor constructed a small shed for the purpose of private practice. He built the shed on the boundary. However, the loud noises from the confectioner's industrial mortars and pestles could be clearly heard, disrupting his use and enjoyment of his land. He sought an injunction. The facts were described by Thesiger LJ in the Court of Appeal as follows, The Court of Appeal held that the fact the doctor had "come to the nuisance", by which the Judge meant moved to an area where the nuisance had been operating for years without harming anyone, was no defence. The doctor's legal right to have the nuisance stopped was not lessened by the confectioner's longstanding practice.

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The ultimate thesis is that law and regulation are not as important or effective at helping

people as lawyers and government planners believe. Coase and others like him wanted a

change of approach, to put the burden of proof for positive effects on a government that was

intervening in the market, by analyzing the costs of action

Three-dimensional freeform object matching to interpret events and relations corresponding to

whole-social pattern,(the win-win-win situation)

It seems that It concerns a number of selected theories and theorems used by different directions

The Classical School of Thought (mainly expressed by Adam Smith, David Ricardo, Karl Marx,

John Stuart Mill) put the focus on the free market and full competition: Their attempt

concerned on "how competition could be fairer” They believed that the free market could

correct any deviation from perfect competition that would lead to economic and social

disparities Even Marx based his theory on the critique of the capitalist system Their thoughts

influenced all the subsequent economists

Especially the Patriarch of the Economic Thought ADAM SMITH in his monumental work,

Wealth of Nations73,74 -two and half centuries ago- had more influence on the development of

the economic discipline than any other work in the history of the subject. And perhaps none

has held such a way, not only over professional economics, but also over all those who

concerned about how best to organize society to promote the General Welfare than his

concept of the invisible hand: this, in spite of the fact that he explicitly used the term only

once In the Wealth of Nations,. Smith argued not only that individuals were led in the pursuit

of their self interest by an invisible hand to pursue the Nation's interest, but also that this

pursuit of self interest was a far more reliable way to ensure that the Public Interest would be

served than any alternative -surely better than relying on some government leader, as well-

intentioned as that leader might be.

The New-classical School of Thought rejected any idea of social welfare and more importantly

proved with the mathematical logic that social welfare is impossible (Arrow Kenneth: The

Impossibility Theorem, 1950)75 :

ARROW IMPOSSIBILITY THEOREM’S CONCEPT

"If we exclude the possibility of interpersonal comparisons of utility, then the only methods

of passing from individual tastes to social preferences which will be satisfactory and which

73 Adam Smith (1776). An Inquiry into the Nature and the Causes of the Wealth of Nations “1 (1 ed.). London: W. Strahan.

Retrieved2012-12-07., volume 2 via Google Books

74Adam Smith (1778). An Inquiry into the Nature and the Causes of the Wealth of Nations 2 (2 ed.) London: W. Strahan;

T.Cadell. Retrieved 10 March 2015 via Google Books 75 Kenneth Arrow 1951, 2nd ed., 1963 Social Choice and Individual Values, Yale University Press

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will be defined for a wide range of sets of individual orderings are either imposed or

dictatorial" (see at the voting system)

PRELIMINARIES

The field of welfare economics is associated with two fundamental theorems. The first states

that given certain assumptions, competitive markets (price equilibria with transfers,

e.g. Walrasian equilibria) produce Pareto efficient outcomes. The assumptions required are

generally characterized as "very weak" More specifically, the existence of competitive

equilibrium implies both price-taking behaviour and complete markets, but the only

additional assumption is the local non-satiation of agents' preferences – that consumers

would like, at the margin, to have slightly more of any given good. The first fundamental

theorem is said to capture the logic of Adam Smith's invisible hand, though in general there is

no reason to suppose that the "best" Pareto efficient point (of which there are a set) will be

selected by the market without intervention, only that some such point will be

The second fundamental theorem states that given further restrictions, any Pareto efficient

outcome can be supported as a competitive market equilibrium These restrictions are stronger

than for the first fundamental theorem, with convexity of preferences and production

functions a sufficient but not necessary condition. A direct consequence of the second

theorem is that a benevolent social planner could use a system of lump sum transfers to

ensure that the "best" Pareto efficient allocation was supported as a competitive equilibrium

for some set of prices. More generally, it suggests that redistribution should, if possible, be

achieved without affecting prices (which should continue to reflect relative scarcity), thus

ensuring that the final (post-trade) result is efficient. Put into practice, such a policy might

resemble pre-distribution Because of welfare economics' close ties to social choice theory

Arrows impossibility Theorem is sometimes listed as a third fundamental theorem76

a. Homo Economicus

Following a summary of the empirical findings:

1. On the biological level people have their preferences, but on the cultural level

people rather make than have their preferences.

2. Behavior systematically deviates from happiness maximization, both intentionally

and erroneously. People sometimes account for moral considerations at the cost

76 Kenneth Arrow, J. (1951, 2nd ed., 1963) Social Choice and Individual Values -Yale University Press, New Haven AND

Kenneth Arrow, J., and Gérard Debreu ed., 2002 Landmark Papers in General Equilibrium Theory, Social Choice and Welfare.

Edward Elgar Publishing,

Atkinson Anthony B. (1975). The Economics of Inequality, Oxford University Press, London

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of subjective well-being; and sometimes they take decisions mindlessly.

Consequently the assumption that everyone is the best judge of what will make

him/her happy is by no means unchallenged. This conclusion should not come as

a surprise.

3. After all, economic decision theory is built upon psychological ad hoc assumptions

which qualified primarily on formal, rather than substantive grounds. They were

convenient because they warrant internal consistency and analytical versatility,

making them amenable to quantitative analyses. Similarly in the context of

consumption, welfare economics relies on an uncritical generalization of the

casual observation of individual consumption decisions and their motivations.

4. The Homo Economicus is an inadequate description of human behavior. Welfare

Economics will have to be reassessed in the light of empirical findings. All the

important theories in this field (in particular the general equilibrium theory)

depend on the relation between behavior and welfare through the intermediary of

preferences

b. Pareto (1848-1923)77introduced –among many others- the concept of Pareto

Efficiency and helped develop the field of microeconomics- ordinal utility function

77

Vilfredo Pareto.(1906) Manual of Political Economy. 1906.

Definitions: Pareto Efficiency (or unanimity) or Pareto optimality is a state of allocation of

resources in which it is impossible to make any one individual better off without making

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at least one individual worse off. The concept has applications in academic fields such as

economics, engineering and the life sciences

Pareto Efficiency: A particular distribution of goods or outcome of any social process is

regarded as Pareto efficient if there is no way to improve one or more people's situations

without harming another. Put another way, an outcome is not Pareto efficient if there is a

way to improve at least one person's situation without harming anyone else.Pareto

optimality: whenever all individuals of a society strictly prefer an outcome x over an

outcome y, the choice function doesn't pick y.

The very clear definition of “Pareto Efficiency” states that: Given a set of alternative

allocations of goods or outcomes for a set of individuals, a change from one allocation to

another that can make at least one individual better off without making any other individual

worse off is called a "Pareto improvement". An allocation is defined as "Pareto efficient" or

"Pareto optimal" when no further Pareto improvements can be model (Pareto Efficiency- see

graph) It includes the random simple (not only the initial)

An alternative definition of Pareto Efficiency states: “Given an initial allocation of goods

among a set of individuals, a change to a different allocation that makes at least one

individual better off without making any other individual worse off is called a Pareto

improvement. An allocation is defined as "Pareto efficient" or "Pareto optimal" when no

further Pareto improvements can be made”

Formally, a social choice function F is Pareto optimal if whenever p∊Rel(X)N is a configuration of

preference relations and there are two outcomes x and y such that x⪲iy for every individual i∊N,

then y∉ F(p).

1. Minimal liberalism: More than one individual in the society is decisive on a pair of social

outcomes. (An individual is decisive on a pair of social outcomes x and y if, whenever he

prefers x over y, the social choice function prefers xover y regardless of what other

members of the society prefer. (And similarly whenever he prefers y over x, the social

choice function prefers y over x.)

Formally, a social choice function F respects minimal liberalism if there is more than one

individual i∊N for which there exists a pair of outcomes xi, yi on which he is decisive—that is, for

every configuration of preference relations p∊Rel(X)N, yi∊ F(p) only when xi≼iyi (and

similarly, xi∊ F(p) only when yi≼ixi).

As an example of decisiveness: in the Lewd/Prude case, Lewd was decisive on the pair of outcomes

⟨"Lewd reads", "No one reads"⟩ and Prude was decisive on the pair of outcomes ⟨"Prude reads", "No

one reads"⟩.

In other words, the liberal paradox states that for every social choice function F, there is a

configuration of preference relations p∊Rel(X)N for which F violates either Pareto optimality or

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Now construct the Pareto frontier as a subset of Y, the feasible criterion points. It can be

assumed that the preferable values of each criterion parameter are the lesser ones, thus

minimizing each dimension of the criterion vector. Then compare criterion vectors as follows:

One criterion vector x strictly dominates (or "is preferred to") a vector y if each parameter of x

is no greater than the corresponding parameter of y and at least one parameter is strictly less:

that is, for each i and for some i. This is written as to mean

78 Hammond (1998) :Subjective expected Utility Theory”,, in S.Barbera,Hammond….Handbook of Utility Theory”(Dordrecht-Kluwer) 79

Vilfredo Pareto(1896) Cours d' Économie Politique Professé a l'Université de Lausanne. Vol. I, 1896,Vol. II, 1897

Minimal liberalism (or both). In the examples of Sen and Gibbard noted above, the social choice

function satisfies Minimal liberalism at the expense of Pareto optimality

In the social choice rule approach …, local dictatorship becomes a desideratum, provided that the

‘localities’ are appropriate. Our feelings of revulsion should be reserved for non-local dictatorships,

or local dictatorships affecting issues that should not be treated as personal78

.

If every individual prefers a certain option to another, then so must the resulting societal

preference order This again, may be a demand that the social welfare function will be

minimally79sensitive to the preference profile

The later version of this theorem is stronger—has weaker conditions—since monotonicity, non-

imposition, and independence of irrelevant alternatives together imply Pareto efficiency, whereas

Pareto efficiency and independence of irrelevant alternatives together do not imply monotonicity.

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that x strictly dominates y. Then the Pareto frontier is the set of points from Y that are not

strictly dominated by another point in Y.

Formally, this defines a partial order on Y, namely the (opposite of the) product order on

(more precisely, the induced order on Y as a subset of ), and the Pareto frontier is the set

of maximal elements with respect to this order.

Algorithms for computing the Pareto frontier of a finite set of alternatives have been studied

in computer science. There, this task is known as the maximum vector problem or as skyline

query.

Relationship to marginal rate of substitution

An important fact about the Pareto frontier in economics is that at a Pareto efficient allocation,

the marginal rate of substitution is the same for all consumers. A formal statement can be

derived by considering a system with m consumers and n goods, and a utility function of each

consumer as zi = fi(xi) where is the vector of goods, both for all i.

The supply constraint is written for . To optimize this

problem, the Lagrangian is used:

where λ

and Γ are multipliers.

Taking the partial derivative of the Lagrangian with respect to one good, i, and then taking the

partial derivative of the Lagrangian with respect to another good, j, gives the following system

of equations:

for j=1,...,n. for i = 2,...,m and

j=1,...,m, where f(x) is the marginal utility on f' of x (the partial derivative of f with respect to

x).

for i,k=1,...,m and j,s=1,...,n...,.

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Pareto Optimal Condition80

Pareto efficiency, or Pareto optimality, is an important concept in economics with broad

applications in game theory, engineering and the social sciences. The term is named after

Vilfredo Pareto, an Italian economist who used the concept in his studies of economic

efficiency and income distribution. Informally, Pareto efficient situations are those in which

any change to make any person better off would make someone else worse off.

Given a set of alternative allocations of, say, goods or income for a set of individuals, a change

from one allocation to another that can make at least one individual better off without making

any other individual worse off is called a Pareto improvement. An allocation is defined as

Pareto efficient or Pareto optimal when no further Pareto improvements can be made. This is

often called a strong Pareto optimum (SPO).

A weak Pareto optimum (WPO) satisfies a less stringent requirement, in which a new allocation

is only considered to be a Pareto improvement if it is strictly preferred by all individuals (i.e.,

all must gain with the new allocation). In other words, when an allocation is WPO there are no

possible alternative allocations where every individual would gain. An SPO is a WPO: a WPO is

an allocation where every change causes some individual to NOT IMPROVE, whereas with an

SPO every change causes some individual to DO WORSE (and hence not improve).

Formally, a (strong/weak) Pareto optimum is a maximal element for the partial order relation

of Pareto improvement/strict Pareto improvement: it is an allocation such that no other

allocation is "better" in the sense of the order relation.

A common criticism of a state of Pareto efficiency is that it does not necessarily result in a

socially desirable distribution of resources, as it makes no statement about equality or the

overall well-being of a society; notably, allocating all resources to one person and none to

anyone else is Pareto efficient if preference relations are monotone increasing

80

Vilfredo Pareto(1896) Cours d' Économie Politique Professé a l'Université de Lausanne. Vol. I, 1896,Vol. II, 1897

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An economic system that is Pareto inefficient implies that a certain change in allocation of

goods (for example) may result in some individuals being made "better off" with no individual

being made worse off, and therefore can be made more Pareto efficient through a Pareto

improvement. Here 'better off' is often interpreted as "put in a preferred position." It is

commonly accepted that outcomes that are not Pareto efficient are to be avoided, and

therefore Pareto efficiency is an important criterion for evaluating economic systems and

public policies.

If economic allocation in any system (in the real world or in a model) is not Pareto efficient,

there is theoretical potential for a Pareto improvement — an increase in Pareto efficiency:

through reallocation, improvements to at least one participant's well-being can be made

without reducing any other participant's well-being.

In the real world ensuring that nobody is disadvantaged by a change aimed at improving

economic efficiency may require compensation of one or more parties. For instance, if a

change in economic policy dictates that a legally protected monopoly ceases to exist and that

market subsequently becomes competitive and more efficient, the monopolist will be made

worse off. However, the loss to the monopolist will be more than offset by the gain in

efficiency. This means the monopolist can be compensated for its loss while still leaving an

efficiency gain to be realized by others in the economy. Thus, the requirement of nobody

being made worse off for a gain to others is met.

In real-world practice, the compensation principle often appealed to is hypothetical. That is,

for the alleged Pareto improvement (say from public regulation of the monopolist or removal

of tariffs) some losers are not (fully) compensated. The change thus results in distribution

effects in addition to any Pareto improvement that might have taken place. The theory of

hypothetical compensation is part of Kaldor-Hicks efficiency, also called Potential Pareto

Criterion. (Ng, 1983)

Under certain idealized conditions, it can be shown that a system of free markets will lead to a

Pareto efficient outcome. This is called the first welfare theorem. It was first demonstrated

mathematically by economists Kenneth Arrow and Gerard Debreu. However, the result does

not rigorously establish welfare results for real economies because of the restrictive

assumptions necessary for the proof (markets exist for all possible goods, all markets are in

full equilibrium, markets are perfectly competitive, transaction costs are negligible, there must

be no externalities, and market participants must have perfect information). Moreover, it has

since been demonstrated mathematically that, in the absence of perfect competition or

complete markets, outcomes will generically be Pareto inefficient.

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c. Utility Function: The concept of the utility function is sufficiently flexible in order to

address all relevant problems of individual rationality. It allows taking account of

(a) social inter- dependencies (b) external effects and (c) public goods

The problem with utility functions is not a theoretical but a practical one. There are no

comparable (cardinal) estimations for the welfare of society; there is not even a

complete utility function for a single individual. Approximations used so far are (a)

income (b) CDP, calculated by the income approach for the welfare of society.

But welfare cannot be reduced to income.

Marginal utility81: Instead of the price of a good or service reflecting the labor

that has produced it, it (the price) reflects the marginal usefulness (utility) of

the last purchase. This meant that in equilibrium, people's preferences

determined prices, including, indirectly the price of labor (…).

Consumers act rationally by seeking to maximize satisfaction of all their

preferences. People allocate their spending so that the last unit of a commodity

bought creates no more satisfaction than a last unit bought of something else

d. General Impossibility Theorem: Social choice failure82

The impossibility of converting individuals’ ranked preferences in ranking order

voting

According to bibliography, social welfare seems to be an utopia, since Kenneth Arrow (1951)83

has formulated his “impossibility theorem” or the “Arrow’s paradox”, concerned the “social

choice theory” According to Arrow’s impossibility theorem, when voters have three or more

distinct alternatives (options), no rank order voting system can convert the ranked

preferences of individuals into a community-wide (complete and transitive) ranking while also

81

William Vickrey (1945)Measuring Marginal Utility by Reactions to Risk Econometrica Vol. 13, No. 4 (Oct., 1945), pp. 319-333

Published by: the econometric society

82Arrow, Kenneth J. (1951).Social Choice and Individual values (1st ed.). New Haven, New York / London: J. Wiley / Chapman & Hall

83The same

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meeting a pre-specified set of criteria. These pre-specified criteria are called unrestricted

domain, non- dictatorship, Pareto efficiency and independent of irrelevant alternatives84

(axiomatic theorem)

An interesting experiment is taking place in Bhutan, the only country that replaced the GDP by

the Gross National Happiness. Recently, economics turned back to the classical utilitarian goal

to make people happier. Happiness Economics builds on empirical data about individual

happiness instead of inappropriate mathematical models and bureaucratic indicators like

the GDP and GNI.For a philosophical criticism of happiness economics see Moral Relativism

and the Search for Happiness

Especially, Kenneth Arrow formulated (1951) a theorem based on follow axioms:

The theorem states that no rank-order voting system can be designed that always satisfies

these three "fairness" criteria85

If every voter prefers alternative X over alternative Y, then the group prefers X over Y.

If every voter's preference between X and Y remains unchanged, then the group's

preference between X and Y will also remain unchanged (even if voters' preferences

between other pairs like X and Z, Y and Z, or Z and W change).

84Arrow, Kenneth J. (1951b).Social Choice and Individual values (1st ed.). New Haven, New York / London: J. Wiley / Chapman & Hall.

85Arrow Kenneth (1951a) “Alternative Approaches to the theory of choice in risk- tanking situations” Econometrica (The Econometric Society via JSTOR) 19 (4): 404–437

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There is no "dictator": no single voter possesses the power to always determine the

group's preference.

The theorem considers the following properties, assumed to be reasonable requirements of a

fair voting method:

Non-dictatorship

The social welfare function should account for the wishes of multiple voters. It cannot simply

mimic the preferences of a single voter:

Unrestricted domain (or universality)

For any set of individual voter preferences, the social welfare function should yield a unique

and complete ranking of societal choices. Thus:

It must do so in a manner that results in a complete ranking of

preferences for society.

It must deterministically provide the same ranking each time voters'

preferences are presented the same way.

Independence of irrelevant alternatives (IIA)

The social preference between x and y should depend only on the individual preferences

between x and y (Pairwise Independence). More generally, changes in individuals' rankings

of irrelevant alternatives (ones outside a certain subset) should have no impact on the societal

ranking of the subset. For example, the introduction of a third candidate to a two-candidate

election should not affect the outcome of the election unless the third candidate wins.

Positive association of social and individual values (or monotonicity)

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If any individual modifies his or her preference order by promoting a certain option, then the

societal preference order should respond only by promoting that same option or not

changing, never by placing it lower than before. An individual should not be able to hurt an

option by ranking it higher.

Non-imposition (or citizen sovereignty)

Every possible societal preference order should be achievable by some set of

individual preference orders. This means that the social welfare function

is surjective86: It has an unrestricted target space.

Arrow's theorem says that if the decision-making body has at least two members and

at least three options to decide among, then it is impossible to design a social welfare

function that satisfies all these conditions at once.

A later (1963) version of Arrow's theorem can be obtained by replacing the monotonicity and

non-imposition criteria:

e. Decision Making Problems

Decision-Theory and Social Choice87

Welfare economics is closely tied to Decision Theory and Social Choice Theory

1. Neoclassical microeconomics is nothing but the theory of individual economic decisions.

2. Kenneth Arrow realized that the aggregation of individual utilities has to be treated as a

collective decision process (social choice)

Individual decisions88

86 In mathematics, a function f from a set X to a set Y is surjective or a surjection, if every element y in Y has a corresponding

element x in X such that yxf )( The function f may map more than one element of X to the same element of Y.

An infinite sequence of real numbers (in blue) This sequence is neither increasing, nor decreasing It is, however, bounded

87 Arrow, Kenneth J. (1951b).Social Choice and Individual values (1st ed.). New Haven, New York / London: J. Wiley /

Chapman & Hall.

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Economic theory assumes that an individual acts rational and attempts to maximize utility

under given side constraints.

In economics, game theory and decision theory the expected utility theorem or expected

utility hypothesis predicts that the "betting preferences" of people with regard to uncertain

outcomes (gambles) can be described by a mathematical relation which takes into account the

size of a payout (whether in money or other goods), the probability of occurrence, risk

aversion and the different utility of the same payout to people with different assets or

personal preferences. It is a more sophisticated theory than simply predicting that choices will

be made based on expected value (which takes into account only the size of the payout and

the probability of occurrence)

88

Hillel J. Einhorn and Robin M. Hogarth (1981) Behavioral Decision Theory: Processes of Judgment and Choice Journal of

Accounting Research Vol. 19, No. 1 (Spring, 1981), pp. 1-31 Published by Wiley company

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Statement of the theorem

The need to aggregate preferences occurs in many disciplines: in welfare economics, where

one attempts to find an economic outcome which would be acceptable and stable; in decision

theory, where a person has to make a rational choice based on several criteria; and most

naturally in voting systems, which are mechanisms for extracting a decision from a multitude

of voters' preferences.

The framework for Arrow's theorem assumes that we need to extract a preference order on a

given set of options (outcomes). Each individual in the society (or equivalently, each decision

criterion) gives a particular order of preferences on the set of outcomes. We are searching for

a ranked voting system, called a social welfare function (preference aggregation rule), which

transforms the set of preferences (profile of preferences) into a single global societal

preference order. The theorem considers the following properties, assumed to be reasonable

requirements of a fair voting method:

Non-dictatorship

The social welfare function should account for the wishes of multiple voters. It cannot simply

mimic the preferences of a single voter.

Unrestricted domain

(or universality) For any set of individual voter preferences, the social welfare function should

yield a unique and complete ranking of societal choices. Thus:

It must do so in a manner that results in a complete ranking of preferences for society.

It must deterministically provide the same ranking each time voters' preferences are presented

the same way.

Independence of irrelevant alternatives (IIA)

The social preference between x and y should depend only on the individual preferences

between x and y (Pair-wise Independence). More generally, changes in individuals' rankings

of irrelevant alternatives (ones outside a certain subset) should have no impact on the societal

ranking of the subset. For example, the introduction of a third candidate to a two-candidate

election should not affect the outcome of the election unless the third candidate wins. (See

Remarks below.)

Positive association of social and individual values

(or monotonicity) If any individual modifies his or her preference order by promoting a certain

option, then the societal preference order should respond only by promoting that same option

or not changing, never by placing it lower than before. An individual should not be able to

hurt an option by ranking it higher.

Non-imposition

(or citizen sovereignty) Every possible societal preference order should be achievable by some

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Arrow's death-of-a-candidate example (1963, page 26) suggests that the agenda (the set of

feasible alternatives) shrinks from, say, X = {a, b, c} to S = {a, b} because of the death of

candidate c. This example is misleading since it can give the reader an impression that IIA is a

condition involving two agenda and one profile. The fact is that IIA involves just one agendum

({x, y} in case of Pairwise Independence) but two profiles. If the condition is applied to this

confusing example, it requires this: Suppose an aggregation rule satisfying IIA chooses b from

the agenda {a, b} when the profile is given by (cab, cba), that is, individual 1 prefers c to a to

b, 2 prefers c to b to a. Then, it must still choose b from {a, b} if the profile were, say, (abc,

bac) or (acb, bca) or (acb, cba) or (abc, cba).

Although Arrow's theorem is a mathematical result, it is often expressed in a non-

mathematical way with a statement such as "No voting method is fair," "Every ranked voting

set of individual preference orders. This means that the social welfare function is surjective: It

has an unrestricted target space.

Arrow's theorem says that if the decision-making body has at least two members and at least

three options to decide among, then it is impossible to design a social welfare function that

satisfies all these conditions at once.

A later (1963) version of Arrow's theorem can be obtained by replacing the monotonicity and

non-imposition criteria with:

Pareto efficiency

(or unanimity) If every individual prefers a certain option to another, then so must the

resulting societal preference order. This, again, is a demand that the social welfare function

will be minimally sensitive to the preference profile.

The later version of this theorem is stronger—has weaker conditions—since monotonicity,

non-imposition, and independence of irrelevant alternatives together imply Pareto efficiency,

whereas Pareto efficiency and independence of irrelevant alternatives together do not imply

monotonicity. (Incidentally, Pareto efficiency on its own implies non-imposition.)

Remarks on IIA

The IIA condition can be justified for three reasons (Mas-Colell, Whinston, and Green, 1995,

page 794): (i) normative (irrelevant alternatives should not matter), (ii) practical (use of

minimal information), and (iii) strategic (providing the right incentives for the truthful

revelation of individual preferences). Though the strategic property is conceptually different

from IIA, it is closely related.

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method is flawed," or "The only voting method that isn't flawed is a dictatorship". These

statements are simplifications of Arrow's result which are not universally considered to be

true. What Arrow's theorem does state is that a deterministic preferential voting mechanism -

that is, one where a preference order is the only information in a vote, and any possible set of

votes gives a unique result - cannot comply with all of the conditions given above

simultaneously.

Various theorists have suggested weakening the IIA criterion as a way out of the paradox.

Proponents of ranked voting methods contend that the IIA is an unreasonably strong criterion.

It is the one breached in most useful voting systems. Advocates of this position point out that

failure of the standard IIA criterion is trivially implied by the possibility of cyclic preferences. If

voters cast ballots as follows:

1 vote for A > B > C

1 vote for B > C > A

1 vote for C > A > B

then the pairwise majority preference of the group is that A wins over B, B wins over C, and C

wins over A: these yield rock-paper-scissors preferences for any pairwise comparison

With these assumptions, it is possible to construct a social welfare function simply by

summing all the individual utility functions. Note that such a measure would still be concerned

with the distribution of income (distributive efficiency) but not the distribution of final utilities.

In normative terms, such authors were writing in the Benthamite tradition.

▲

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Sen's original example

Sen's original example used a simple society with only two people and only one social issue to

consider. The two members of society are named "Lewd" and "Prude". In this society there is a

copy of a Lady Chatterley's Lover and it must be given either to Lewd to read, to Prude to read,

or disposed of unread. Suppose that Lewd enjoys this sort of reading and would prefer to read

it himself rather than have it disposed of. However, he would get even more enjoyment out of

Prude being forced to read it.

Prude thinks that the book is indecent and that it should be disposed of unread. However, if

someone must read it Prude would prefer that he, himself read it rather than Lewd since Prude

thinks it would be even worse for someone to read and enjoy the book rather than read it in

disgust.

Given these preferences of the two individuals in the society, a social planner must decide

what to do. Should the planner force Lewd to read the book, force Prude to read the book, or

let it go unread? More particularly, the social planner must rank all three possible outcomes in

terms of their social desirability. The social planner decides that she should be committed to

individual rights, each individual should get to choose whether he, himself will read the book.

Lewd should get to decide whether the outcome "Lewd reads" will be ranked higher than "No

one reads," and similarly Prude should get to decide whether the outcome "Prude reads" will

be ranked higher than "No one reads."

Following this strategy, the social planner declares that the outcome "Lewd reads" will be

ranked higher than "No one reads" (because of Lewd's preferences) and that "No one reads"

will be ranked higher than "Prude reads" (because of Prude's preferences). Consistency then

requires that "Lewd reads" be ranked higher than "Prude reads," and so the social planner

gives the book to Lewd to read.

Notice that this outcome is regarded as worse than "Prude reads" by both Prude and Lewd, and

the chosen outcome is therefore Pareto inferior to another available outcome—the one where

Prude is forced to read the book.

The liberal paradox, also Sen paradox or Sen's paradox, is a logical paradox discovered by

Amartya Sen which purports to show that no social system can simultaneously

1. be committed to a minimal sense of freedom,

2. always result in a type of economic efficiency known as Pareto Efficiency and

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3. be capable of functioning in any society whatsoever89

This paradox90

is contentious because it appears to contradict the classical liberal claim that

markets are both efficient and respect individual freedoms. If, as Sen claims, classical

liberalism means Pareto efficiency by the word efficiency, there is a paradox, then this liberal

claim cannot be true.

The paradox is similar in many respects to Arrow’s Impossibility Theorem and uses similar

mathematical techniques.

The theorem

Suppose there is a society N consisting of two or more individuals and a set X of two or more

social outcomes. (For example, in the Lewd and Prude case, N consisted of Lewd and Prude,

and X consisted of the four color options ⟨Blue, Yellow⟩, ⟨Blue, Green⟩, ⟨Red, Yellow⟩, and ⟨Red,

Green⟩.)

Suppose each individual in the society has a total and transitive preference relation on the set

of social outcomes X. For notation, the preference relation of an individual i∊N is denoted by

≼i. Each preference relation belongs to the set Rel(X) of all total and transitive relations on X.

A social choice function is a map which can take any configuration of preference relations

of N as input and produce a subset of ("chosen") social outcomes as output. Formally, a social

choice function is a map

from the set of functions between N→Rel(X), to the power set of X. (Intuitively, the social

choice function represents a societal principle for choosing one or more social outcomes

based on individuals' preferences. By representing the social choice process as

a function on Rel(X)N, we are tacitly assuming that the social choice function is defined for any

possible configuration of preference relations; this is sometimes called the Universal Domain

assumption.)

89 Sen, Amartya (1984) [1970] Collective Choice and Social Welfare New Holland

90 Sen, Amartya (2004). Rationality and Freedom Belknap Press of Harvard University Press

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Gibbard's example91

Another example was provided by philosopher Allan Gibbard. Suppose there are two

individuals Alice and Bob who live next door to one another. Alice loves the color blue and

hates red. Bob loves the color green and hates yellow. If each were free to choose the color of

their house independently of the other, they would choose their favorite colors. But Alice hates

Bob with a passion, and she would gladly endure a red house if it meant that Bob would have

to endure his house being yellow. Bob similarly hates Alice, and would gladly endure a yellow

house if that meant that Alice would live in a red house.

If each individual is free to choose their own house color, independently of the other, Alice

would choose a blue house and Bob would choose a green one. But, this outcome is not Pareto

efficient, because both Alice and Bob would prefer the outcome where Alice's house is red and

Bob's is yellow. As a result, giving each individual the freedom to choose their own house

color has led to an inefficient outcome—one that is inferior to another outcome where neither

is free to choose their own color92

.

Mathematically, we can represent Alice's preferences with this symbol: and Bob's

preferences with this one: . We can represent each outcome as a pair: (Color of Alice's

house, Color of Bob's house). As stated Alice's preferences are:

(Blue, Yellow) (Red, Yellow) (Blue, Green) (Red, Green)

And Bob's are:

(Red, Green) (Red, Yellow) (Blue, Green) (Blue, Yellow)

If we allow free and independent choices of both parties we end up with the outcome

(Blue, Green) which is dispreferred by both parties to the outcome (Red, Yellow) and is

therefore not Pareto efficient.

Measurability and interpersonal comparability of welfare93

By assigning real numbers to alternatives, welfare profiles contain a lot of information over

and above the profiles of orderings on X they induce. In particular, many different

assignments of numbers to alternatives can give rise to the same orderings. But we may not

consider all this information meaningful. Some of it could be an artifact of the numerical

representation. For example, the difference between the profile <W1, W2, …, Wn> and its

91Gibbard, “Contingent Identity” (2004) “Gibbard’s example: a clay statue that is contingently identical to a piece of clay” 92 Blau, Julian (1975). Liberal Values and Independence The Review of Economic Studies 42 (3) pp. 395–401 93 Christian List (2000)A Note on Introducing a 'Zero-Line' of Welfare as an Escape-Route from Arrow's Theorem”- Nuffield College Oxford OX1 1NF, U.K

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scaled-up version <10*W1, 10*W2, …, 10*Wn>, where everything is the same in proportional

terms, could be like the difference between length measurements in centimeters and in

inches. The two profiles might be seen as alternative representations of the exact same

information, just on different scales.

To express different assumptions about which information is truly encoded by a profile of

welfare functions and which information is not (and should thus be seen, at best, as an artifact

of the numerical representation), it is helpful to introduce the notion of meaningful

statements. Some examples of statements about individual welfare that are candidates for

meaningful statements are the following:

A level comparison: Individual i's welfare under alternative x is at least as great as

individual j's welfare under alternative y, formally Wi(x) ≥ Wj(y). (The comparison is

intrapersonal if i = j, and interpersonal if i ≠ j.)

A unit comparison: The ratio of [individual i's welfare gain or loss if we switch from

alternative y1 to alternative x1] to [individual j's welfare gain or loss if we switch from

alternative y2 to alternative x2] is λ, where λ is some real number, formally (x1 − y1) / (x2− y2)

= λ. (Again, the comparison is intrapersonal if i = j, and interpersonal if i ≠ j.)

A zero comparison: Individual i's welfare under alternative x is greater than / equal to / less

than zero, formally sign(Wi(x)) = λ, where λ ∈ {−1, 0, 1} and sign is a real-valued function that

maps strictly negative numbers to −1, zero to 0, and strictly positive numbers to +1.

Arrow's view, as noted, is that only intrapersonal level comparisons are meaningful, while all

other kinds of comparisons are not. Sen (1970b)94

formalized various assumptions about

measurability and interpersonal comparability of welfare by (i) defining an equivalence relation

on welfare profiles that specifies when two profiles count as ‘containing the same

information’, and (ii) requiring any profiles in the same equivalence class to generate the same

social preference ordering. Of the three kinds of comparison statements introduced above, the

meaningful ones are those that are invariant in each equivalence class. Arrow's ordinalist

assumption can be expressed as follows:

Ordinal measurability with no interpersonal comparability (ONC):

Two profiles <W1,W2, …, Wn> and <W*1, W*2, …, W*n> contain the same information

whenever, for eachi ∈ N, W*i = φi(Wi), where φi is some positive monotonic transformation,

possibly different for different individuals.

Thus the individual welfare functions in any profile can be arbitrarily monotonically

transformed (‘stretched or squeezed’) without informational loss, thereby ruling out any

interpersonal comparisons or even intrapersonal unit comparisons.

If welfare is cardinally measurable but still interpersonally non-comparable, we have:

94 Amartya Sen (1970b)”Limited Rights as Partial Veto and Sen's Impossibility Theorem ... “paper The first edition of Hausman and McPherson appeared in 1996. .

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Cardinal measurability with no interpersonal comparability (CNC): Two profiles <W1,W2,

…, Wn> and <W*1, W*2, …, W*n> contain the same information whenever, for each

i ∈ N, W*i = aiWi + bi, where the ais and bis are real numbers (with ai > 0), possibly different

for different individuals.

Here, each individual's welfare function is unique up to positive affine transformations

(‘scaling and shifting’), but there is still no common scale across individuals. This renders

intrapersonal level and unit comparisons meaningful, but rules out interpersonal comparisons

and zero comparisons.

Interpersonal level comparability is achieved under the following enriched variant of ordinal

measurability:

Ordinal measurability with interpersonal level comparability (OLC): Two profiles <W1,W2,

…, Wn> and <W*1, W*2, …, W*n> contain the same information whenever, for each

i ∈ N, W*i = φ(Wi), where φ is the same positive monotonic transformation for all individuals.

Here, a profile of individual welfare functions can be arbitrarily monotonically transformed

(‘stretched or squeezed’) without informational loss, but the same transformation must be

used for all individuals, thereby rendering interpersonal level comparisons meaningful.

Interpersonal unit comparability is achieved under the following enriched variant of cardinal

measurability:

Cardinal measurability with interpersonal unit comparability (CUC): Two profiles <W1,W2,

…, Wn> and <W*1, W*2, …, W*n> contain the same information whenever, for each

i ∈ N, W*i = aWi + bi, where a is the same real number for all individuals (a > 0) and thebis are

real numbers.

Here, the welfare functions in each profile can be re-scaled and shifted without informational

loss, but the same scalar multiple (though not necessarily the same shifting constant) must be

used for all individuals, thereby rendering interpersonal unit comparisons meaningful.

Zero comparisons, finally, become meaningful under the following enriched variant of ordinal

measurability

Ordinal measurability with zero comparability (ONC+0): Two profiles <W1, W2, …,Wn> and

<W*1, W*2, …, W*n> contain the same information whenever, for each i ∈ N,W*i = φi(Wi),

where φi is some positive monotonic and zero-preserving transformation, possibly different

for different individuals. (Here zero-preserving means that φi(0) = 0.)

This allows arbitrary stretching and squeezing of individual welfare functions without

informational loss, provided the welfare level of zero remains fixed, thereby ensuring zero

comparability.

Several other measurability and interpersonal comparability assumptions have been discussed

in the literature. The following ensures the meaningfulness of interpersonal comparisons of

both levels and units:

CARDINAL UTILITY

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Cardinal measurability with full interpersonal comparability (CFC): Two profiles <W1,W2,

…, Wn> and <W*1, W*2, …, W*n> contain the same information whenever, for

eachi ∈ N, W*i = aWi + b, where a, b are the same real numbers for all individuals (a > 0).

Lastly, intra- and interpersonal comparisons of all three kinds (level, unit, and zero) are

meaningful if we accept the following:

Ratio-scale measurability with full interpersonal comparability (RFC): Two profiles <W1, W2,

…, Wn> and <W*1, W*2, …, W*n> contain the same information whenever, for

each i ∈ N, W*i = aWi, where a is the same real number for all individuals (a > 0).

Which assumption is warranted depends on how welfare is interpreted. If welfare is hedonic

utility, which can be experienced only from a first-person perspective, interpersonal

comparisons are harder to justify than if welfare is the objective satisfaction of subjective

preferences or desires (the desire-satisfaction view) or an objective good or

state (anobjective-list view) (e.g., Hausman 199595

;). The desire-satisfaction view may render

interpersonal comparisons empirically meaningful (by relating the interpersonally significant

maximal and minimal levels of welfare for each individual to the attainment of his or her most

and least preferred alternatives), but at the expense of running into problems of expensive

tastes or adaptive preferences (Hausman 1995)96

. Resource-based, functioning-based, or

primary-goods-based currencies of welfare, by contrast, may allow empirically meaningful

and less morally problematic interpersonal comparisons.

The possibility of welfare aggregation

Once we introduce interpersonal comparisons of welfare levels or units, or zero comparisons,

there exist possible SWFLs satisfying the analogues of Arrow's conditions as well as stronger

desiderata. In a welfare-aggregation context, Arrow's impossibility can therefore be traced to

a lack of interpersonal comparability.

As noted, a SWFL respects a given assumption about measurability and interpersonal

comparability if, for any two profiles <W1, W2, …, Wn> and <W*1, W*2, …, W*n> that are

deemed to contain the same information, we have F(W1, W2, …, Wn) = F(W*1, W*2, …,W*n).

Arrow's conditions and theorem can be restated as follows:

Universal domain: The domain of F is the set of all logically possible profiles of individual

welfare functions.

Ordering: For any profile <W1, W2, …, Wn> in the domain of F, the social preference

relation R is complete and transitive.

Weak Pareto principle: For any profile <W1, W2, …, Wn> in the domain of F, if for alli∈N Wi(x)

> Wi(y), then xPy.

Independence of irrelevant alternatives: For any two profiles <W1, W2, …, Wn> and <W*1, W*2,

…, W*n> in the domain of F and any x, y ∈ X, if for all i ∈ N Wi(x) =W*i(x) and Wi(y) = W*i(y),

then xRy if and only if xR*y.

95 Bernice L. Hausman (1995) Changing Sex: Transsexualism, Technology, and the Idea of Gender Duke University Press, 1995 96 As above

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Non-dictatorship: There does not exist an individual i ∈ N such that, for all <W1, W2, …, Wn>

in the domain of F and all x, y ∈ X, Wi(x) > Wi(y) implies xPy.

Theorem: Under ONC (or CNC, as Sen 1970b has shown), if |X| > 2, there exists no SWFL

satisfying universal domain, ordering, the weak Pareto principle, independence of irrelevant

alternatives, and non-dictatorship.

Crucially, however, each of OLC, CUC, and ONC+0 is sufficient for the existence of SWFLs

satisfying all other conditions:

Theorem (combining several results from the literature, as illustrated below): Under each of

OLC, CUC, and ONC+0, there exist SWFLs satisfying universal domain, ordering, the weak

Pareto principle, independence of irrelevant alternatives, and non-dictatorship (as well as

stronger conditions).

Some examples of such SWFLs come from political philosophy and welfare economics. A

possible SWFL under OLC is a version of Rawls's difference principle (1971).

Maximin: For any profile <W1, W2, …, Wn> and any x, y ∈ X, xRy if and only

ifmini∈N(Wi(x)) ≥ mini∈N(Wi(y)).

While maximin rank-orders social alternatives in terms of the welfare level of the worst-off

individual alone, its lexicographic extension (leximin), which was endorsed by Rawls himself,

uses the welfare level of the second-worst-off individual as a tie-breaker when there is tie at

the level of the worst off, the welfare level of the third-worst-off individual as a tie-breaker

when there is a tie at the second stage, and so on. (Note, however, that Rawls focused on

primary goods, rather than welfare, as the relevant ‘currency’.) This satisfies the strong(not

just weak) Pareto principle, requiring that if for all i∈N Wi(x) ≥ Wi(y), then xRy, and if in

addition for some i ∈ N Wi(x) > Wi(y), then xPy.

An example of a possible SWFL under CUC is classical utilitarianism.

Utilitarianism: For any profile <W1, W2, …, Wn> and any x, y ∈ X, xRy if and only ifW1(x)

+ W2(x) + … + Wn(x) ≥ W1(y) + W2(y) + … + Wn(y).

Finally, an example of a possible SWFL under ONC+0 is a variant of a frequently used, though

rather simplistic poverty measure.

A head-count rule: For any profile <W1, W2, …, Wn> and any x, y ∈ X, xRy if and only

if |{i ∈ N : Wi(x) < 0}| < |{i ∈ N : Wi(y) < 0}| or [|{i ∈ N : Wi(x) < 0}| =|{i ∈ N : Wi(y) <

0}| and xRjy], where j ∈ N is some antecedently fixed tie-breaking individual.

More general impossibility and possibility theorems

As we have seen, in preference aggregation, the ‘boundary’ between possibility and

impossibility results is easy to draw: when there are only two decision alternatives, all of the

desiderata on a preference aggregation rule reviewed above can be satisfied (and majority rule

does the job); when there are three or more alternatives, there are impossibility results. In

judgment aggregation, by contrast, the picture is more complicated. What matters is not the

number of propositions in X but the nature of the logical interconnections between them.

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Impossibility results in judgment aggregation have the following generic form: for a given

class of agendas, the aggregation rules satisfying a particular set of conditions (usually, a

domain condition, a rationality condition, and some responsiveness conditions) are non-

existent or degenerate (e.g., dictatorial). Different kinds of agendas trigger different instances

of this scheme, with stronger or weaker conditions imposed on the aggregation rule

depending on the properties of those agendas (for a more detailed review, see List 2012)97

.

The significance of combinatorial properties of the agenda was first discovered by Nehring

and Puppe (2002)98

in a mathematically related but interpretationally distinct framework

(strategy-proof social choice over so-called property spaces). Three kinds of agenda stand

out:

A non-simple agenda: X has a minimally inconsistent subset of three or more propositions.

A pair-negatable agenda: X has a minimally inconsistent subset Y that can be rendered

consistent by negating a pair of propositions in it. (Equivalently, X is not isomorphic to a set of

propositions whose only connectives are ¬ and ↔;

A path-connected agenda (or totally blocked, in Nehring and Puppe 2002): For any p, q∈ X,

there is a sequence p1, p2, …, pk ∈ X with p1 = p and pk = q such that p1conditionally

entails p2, p2 conditionally entails p3, …, and pk−1 conditionally entails pk.

(Here, pi conditionally entails pj if pi ∪ Y entails pj for some Y ⊆ X consistent with each

of pi and ¬pj.)

Some agendas have two or more of these properties. The agendas in our ‘doctrinal paradox’

and ‘discursive dilemma’ examples are both non-simple and pair-negatable. The preference

agenda, X = {‘x is preferable to y’, ‘y is preferable to x’, ‘x is preferable to z’, ‘z is preferable

to x’, …}, is non-simple, pair-negatable, and path-connected (assuming preferability is

transitive and complete). The following result holds:

Theorem (Dietrich and List 2007b)99

building on Nehring and Puppe 2002): If X is non-simple,

pair-negatable, and path-connected, there exists no judgment aggregation rule satisfying

universal domain, collective rationality, independence, unanimity preservation (requiring that,

for any unanimous profile <J, J, …, J>, F(J, J, …, J) = J), and non-dictatorship.

Applied to the preference agenda, this result yields Arrow's theorem (for strict preference

orderings) as a corollary (predecessors of this result can be found in List and Pettit 2004 and

Nehring (2003)100

Thus Arrovian preference aggregation can be reinterpreted as a special case

of judgment aggregation.

The literature contains several variants of this theorem. One variant drops the agenda property

of path-connectedness and strengthens independence to systematicity. A second variant

drops the agenda property of pair-negatability and imposes a monotonicity condition on the

aggregation rule (requiring that additional support never hurt an accepted proposition)

97 As above 98 Klaus Nehring; Clemens Puppe “A Theory of Diversity” Econometrica, Vol 70, No. 3 (May, 2002), pp. 1155-1198 99 Dietrich and List (2007b)Judgment Aggregation by Quota Rules-Majority Voting geheralized-Journal of Theoretical Politics 19(4) pp 391-427 (2007) 100 Klaus Nehring (2002)”Arrow’s Theorem as a Corollary”University of California, Davis October 2002

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(Nehring and Puppe 2010)101

; the latter result was first proved in the above-mentioned

mathematically related framework by Nehring and Puppe 2002). A final variant drops both

path-connectedness and pair-negatability while imposing both systematicity and

monotonicity (ibid.).

In each case, the agenda properties are not only sufficient but also (if n ≥ 3) necessary for the

result (Nehring and Puppe 2002,)102

Note also that path-connectedness implies non-

simplicity. Therefore, non-simplicity need not be listed among the theorem's conditions,

though it is needed in the variants dropping path-connectedness.

Non-dictatorial judgment aggregation rules

Relaxing universal domain

As in preference aggregation, one way to avoid the present impossibility results is to relax

universal domain. If the domain of admissible profiles of individual judgment sets is restricted

to those satisfying specific ‘cohesion’ conditions, propositionwise majority voting produces

consistent collective judgments.

The simplest cohesion condition is unidimensional alignment (List 2003c). A profile <J1, J2,

…, Jn> is unidimensionally aligned if the individuals in N can be ordered from left to right

(e.g., on some cognitive or ideological dimension) such that, for every proposition p ∈ X, the

individuals accepting p (i.e., those with p ∈ Ji) are either all to the left, or all to the right, of

those rejecting p (i.e., those with p ∉ Ji), as illustrated in Table . For any such profile, the

majority judgments are consistent: the judgment set of the median individual relative to the

left-right ordering will prevail (where n is odd). This judgment set will inherit its consistency

from the median individual, assuming individual judgments are consistent. By implication, on

unidimensionally aligned domains, propositionwise majority voting will satisfy the rest of the

conditions on judgment aggregation rules reviewed above.

Table: Unidimensional alignment

Individual 1 Individual 2 Individual 3 Individual 4 Individual 5

p True True False False False

q True True True True False

r False False False True True

p ∧ q ∧ r False False False False False

In analogy with the case of single-peakedness in preference aggregation, several less

restrictive conditions already suffice for consistent majority judgments. One such condition

(introduced in Dietrich and List 2010a, where a survey is provided) generalizes Sen's triple-

wise value-restriction. A profile <J1, J2, …, Jn> is value-restricted if every minimally

101 Nehring, K. and C. Puppe, 2002, “Strategyproof Social Choice on Single-Peaked Domains: Possibility, Impossibility and the

Space Between.” Unpublished manuscript, University of California at Davis

102 above

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inconsistent subset Y ⊆ X has a pair of elements p, q such that no individual i ∈ N has {p, q}

⊆ Ji. Value-restriction prevents any minimally inconsistent subset of X from becoming

majority-accepted, and hence ensures consistent majority judgments. Applied to the

preference agenda, value-restriction reduces to Sen's equally named condition.

3. LIBERAL PARADOX (Amartya Sen)103,104

In general (K Arrow) "If we exclude the possibility of interpersonal comparisons of utility, then

the only methods of passing from individual tastes to social preferences which will be

satisfactory and which will be defined for a wide range of sets of individual orderings are

either imposed or dictatorial" (see at the voting system)

The theorem has implications for welfare economics and theories of justice. It was extended

by Amartya Sen to the liberal paradox which argued that given a status of "Minimal Liberty"

there was no way to obtain Pareto optimality nor to avoid the problem of social choice of

neutral but unequal results. liberal paradox105 The liberal paradox states that Arrow's theorem

says that if the decision-making body has at least two members and at least three options to

decide among, then it is impossible to design a social welfare function that satisfies all these

conditions at once

The theorem has implications for welfare economics and theories of justice It was extended by

Amartya Sen to the “liberal paradox” which argued that given a status of "Minimal Liberty"

there was no way to obtain Pareto optimality nor to avoid the problem of social choice of

neutral but unequal results.

An example of this would be to have the following choices to divide a cake between three

people. Let us call them A, B and C.

choice Payoffs payoffs payoffs

Choice1 A gets nothing B gets half C gets half

Choice 2 B gets nothing A gets half C gets half

103 Greg Fried 2011 What is the philosophical significance of Sen's ‘Liberal Paradox’? Philosophical Papers, vol 40 No 1 (March

2011) pp 129-147 104 Sen, Amartya (1970). "The Impossibility of a Paretian Liberal". Journal of Political Economy 78: 152–157. 105 Sen, Amartya (1970) "The Impossibility of a Paretian Liberal"- Journal of Political Economy 78: 152–157.

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Choice 3 C gets nothing A gets half B gets half

Choice 4 A gets 1/3 B gets 1/3 C gets 1/3*

* Choice 4: divide the cake equally.

▲

Thus, if each person votes to get as much cake as possible, choice 4 would be third from the

top in everyone's list, and would in any direct choice lose 2 to 1 against an unequal

distribution. Since all of these choices are Pareto-optimal – no one's welfare can be improved

without reducing the welfare of others – choice 4 would not be chosen, since there would

always be other preferred choices.

every social choice function satisfies at most one of the following properties, never both106

:

But, in my mind these theorems have some difficulties to be accepted, i.e

I have focused (in PART V of the book) on “mutually incompatible theories” i.e the impossibility

theorem (1951 Kenneth Arrow: Social Choice and Individual Values) the theorem of

incompleteness (Kurt Gödel (1931): If the Impossibility Theorem is correct, then the theorem

of incompleteness (Kurt Gödel (1931): must have some difficulties to be accepted:

Impossibility Theorem is an absolute complete theorem based on its Axioms But, in this case,

the theorem itself will be inconsistent For any formal effectively generated theory T including

basic arithmetical truths and also certain truths about formal provability, if T includes a

statement of its own consistency then T is inconsistent

SPECIAL CASE: According to INVESTOPEDIA , a multinational corporation (MNC) is a

corporation that has its facilities and other assets in at least one country other than its home

country. Such companies have offices and/or factories in different countries and usually have

a centralized head office where they co-ordinate global management. Very large

multinationals have budgets that exceed those of many small countries Advocates of

multinationals say they create jobs and wealth and improve technology in countries that are in

need of such development. On the other hand, critics say multinationals can have undue

political influence over governments, can exploit developing nations as well as create job

losses in their own home countries, In their excellent work, titled "Strategy process

management in multinational companies: status quo, deficits and future perspectives" the

106

Stanford Encyclopedia of Philosophy,2015

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authors Dirk Ulrich Gilbert (Germany), Michael Behnam (USA) (Problems and Perspectives in

Management, Volume 7, Issue 1, 2009)analyzed the under-investigated field of strategy

process management in German multinational companies (MNCs).

Whereas the emphasis of research in the field of strategic management had a traditionally

been laid on the investigation of the strategy content, the knowledge of the strategy process

and how promising strategies can be shaped and implemented within firms still remains

limited.

As from my side, i would provide you with the "win-win-win papakonstantinidis concet (or

"Rainbow Concept") thus introducing the study of a "high risk management competition,

which could include also the "social welfare pattern, or standard, in a new troubled economic

environment

Concluding the Social choice

In his dissertation Social Choice and Individual Values107 Arrow proved that there is no

democratic decision process which aggregates individual preferences into an unambiguous

result

The difficulties are caused by the assumption that individual preferences aren’t comparable.

There are basically two approaches to find a way out of this trap:

1. Individual preferences are made comparable by a normative act. They are subjected to

the judgment of an impartial observer, who makes a distinction between comparable

preferences (those which correspond to the Conditio Humana and individual

extravagances. The former are morally relevant and therefore considered in the

aggregation, whereas the latter are neglected. The most important representative of this

approach is John Harsanyi (1920-2000). Comparable preferences are called:

(a) fundamental preferences or human nature and (b) basic psychological laws or

extended preferences (Harsanyi)108.

2. Individual preferences are given up as a criterion for the valuation of social welfare and

replaced by capabilities. Capabilities are defined in constitutions and laws. (Extended

preferences are a tool to model the impartial observer)

3. The Capability Approach emphasizes functional capabilities ("substantive freedoms", such

as the ability to live to old age, engage in economic transactions, or participate in political

activities); these are construed in terms of the substantive freedoms people have reason

107 Kenneth Arrow (1963)Social Choice and Individual Values o John Wiley & Sons, Inc., New York, London, Sydney- 2nd edition

108Harsanyi J.C (1977[1988]) “Rational behavior and bargaining equilibrium in games and social situation Cambridge

University Press 1977

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to value, instead of utility /happiness desire-fulfillment) (…) Someone could be deprived

of such capabilities in many ways, e.g. by ignorance, government oppression, lack of

financial resources, or false consciousness109

4. Social situations are valuated according to potentials (resources) which are offered to

individuals. The usage of these potentials is then a concern of the individuals and not of

society. Similar to above attempt to find morally relevant preferences, an attempt was

made to find morally relevant potentials by subjecting them to the judgment of an

impartial and empathic observer. The most important representative of this approach

is John Rawls (1921-2002)110

CONCEPT AND THE STUDY DESIGN

INTRODUCTION: Is this work a “theoretical contribution?

Two main objectives, five arguments, incobabilities:

Objectives (a) Social Welfare is possible to exist (b) For this, the “win-win-win

papakonstantinidis model” concept must be built ( c ) to prove with arguments that this work

constitutes a "theoretical construction" that can autonomously interpret other theorems

(without the Gödel threat i.e the Theorem of incompleteness

Five arguments: Ancient Greek Philosophy (Socrates, Plato, Aristotle) “incompleteness

(Goedel), Justice (Rawls), Utilitarian Philoophy (Jeremy Bentham) the bargaining Problem (J,

F.Nash)

Incobabilities: By defining and analyzing “rational” Incobabilities in: the set

theory(Cantor111,112 and Zemelo113), Principal –Agent theory114 the Utilitarian School of

109 Kenneth Arrow, J. (1951). Alternative Approach to the theory of choice in risk-taking situations- Econometrica (The Econometric Society via JSTOR) 19 (4): 404–437.

110John Rawls (1963) "The Sense of Justice" Philosophical Review (July 1963), 72 (3): 281-305. 111 Cantor, Georg (1874), "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen" Journal für die Reine und Angewandte Mathematik 77: 258–262,

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Thought (cardinal utility) The Incompleteness (Kurt Gödel, the Ultimatum theory115 and the

bargaining Nash theory

Expected payoffs: a new perception on “social welfare”, coexisting with the capitalist system –

a new methodological tool (win-win-win papakonstantinidis model) for building a “new” world

, the “word of social welfare” and for crisis resolution

a. This work started with a simplistic syllogism: Capitalism with its fundamental axioms

of the "free market" and "competition" has solved many problems but created more

One of these is the "social inequality" and the consequent absence of "social welfare"

The "bargain" and the subsequent “bargaining power” manifested in and by this are on the

basis of the capitalist system

In the bargain there are two (2) quite rational negotiators with totally opposite interests that

try to achieve an agreement (or even disagreement), pursuing each one to gain the greatest

individual (and not collective) profit

It seems to me, that the "social welfare"(the objective of a probable “social choice”) is

impossible within the capitalist system that has at its center the man who acts rationally and

always for his personal interests

It was very easy for Kenneth Arrow (1950)116 to prove the "impossibility” of Social Choice

(inside the capitalist system) in his homonymous theorem (which earned him the Nobel Prize

in Economics in 1972)

“Game Theory” [especially, the “Non-cooperative Game Theory”] has an important contribution

to restart the “New-classical economic school” due to its character, as a conflict game between

2: The theory of games117 is a mathematical discipline designed to treat rigorously the

question of optimal behavior of participants in games of strategy and to determine the

resulting equilibria. Thus, in games of strategy118 there is conflict of interest as well as

possible cooperation among the participants. There may be uncertainty for each participant

because the actions of others may not be known with certainty. Such situations, often of

extreme complexity, are found not only in games but also in business, politics, war, and other

social activities. Therefore, the theory serves to interpret both games themselves and social

phenomena with which certain games are strictly identical. The theory is normative in that it

aims at giving advice to each player about his optimal behavior; it is descriptive when viewed

112 Johnson, Phillip E. (1972), "The Genesis and Development of Set Theory", The Two-Year College Mathematics Journal 3 (1): 55 113 Zermelo, Ernst (1908), "Untersuchungen über die Grundlagen der Mengenlehre I", Mathematische Annalen 65 (2): 261–281English translation: Heijenoort, Jean van (1967), "Investigations in the foundations of set theory", From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Source Books in the History of the Sciences, Harvard Univ. Press, pp. 199–215 114 Eisenhardt, K.M.. (1989). Agency Theory: An Assessment and Review. The Academy of Management Reivew, 14(1), 57-74. 115 Sanfey, Alan; Rilling, Aronson, Nystrom, Cohen (13 June 2003). "The Neural Basis of Economic Decision-Making in the Ultimatum Game" Science 300 (5626): 1755–1758. 116 Kenneth Arrow 1951, 2nd ed., 1963 Social Choice and Individual Values, Yale University Press 117Martin Shubik 1953 (with J. P. Mayberry and J. F. Nash), "A Comparison of Treatments of a Duopoly Situation," Econometrica 21(1), pp. 141-154. 118 Martin Shubik, 1999. Political Economy, Oligopoly And Experimental Games: The Selected Essays of Martin Shubik, 2 v., Edward Elgar. Description and several chapter-preview links: Part I Political Economy; Part II Oligopoly; Part III Gaming; Part IVGame Theory and Operations Research.

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as a model for analyzing empirically given occurrences. In analyzing games the theory does

not assume rational behavior; rather, it attempts to determine what “rational” can mean when

an individual is confronted with the problem of optimal behavior in games and equivalent

situations119.

In contrast, if it were possible to import third party (natural or legal person, company, state,

associations of states) to negotiation between two (2) then this "new" person should have a

dual character, to produce results:

(a) as the third member of the bargaining

(b) as the "entity -omprella", or as an agent over the other two negotiators, claiming his share

of any agreement (or disagreement)

But why, the two original parts (A-B) must accept an entity, "C" (whatever it is), in a bargain

between them which do not come from the set of possible positions defined by the

competition of their individual interests?

This is the point, which the “win-win-win papakonstantinidis theory” has been based on

Generally, this point has the most important contribution in building the new perception

(step by step) that is suggested here

This central question is broken down into three sub-questions, each of which follows another

way in the order of priority that have been completed (and one question for its practical utility)

1. What is the real meaning of the term “social welfare”?

2. Can a theory or a model based on the incompatibilities other theorems and theories

be supported and interpreted?

3. Does exist the only one “win-win-win papakonstantinidis 3D equilibrium” or not?

4. If YES, then which is its practical utility? Are there examples on it?

119 Martin Shubik (2015) Economic applications Encyclopedia. com

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Answer to those questions build up the suggested “win-win-win papakonstantinidis theory”

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o The first sub-question is referred in the pure theoretical “moral” approach of the

"social welfare" thus building up the “philosophical side of the proposal: From

Socrates 470/469 – 399 BC, Plato 428/427 or 424/423 – 348/347 BC), Aristotle 384 –

322 BC) and Epicourus 341-270 BC till Hobbs, Hume, Kant and from them till Jeremy

Bentham120, John Stuart Mill121 John Rawls122 J.J Rousseau123, Kurt Friedrich

Gödel124 (The Incompleteness Theorem) or even Russell (1872 – 1970) (Russell’s

Paradox125, or Bernoulli Petesbourg Paradox126 (barbers paradox), the agency theory

Stefen Ross127:”… The relationship of agency is one of the oldest and commonest codified modes of social

interaction. We will say that an agency relationship has arisen between two (or more) parties when one, designated

as the agent, acts for, on behalf of, or as representative for the other, designated the principal, in a particular

domain of decision problems. Examples of agency are universal. Essentially all contractural arrangements, as

between employer and employee or the state and the governed, for example, contain important elements of

agency. In addition, without explicitly studying the agency relationship, much of the economic literature on

problems of moral hazard (see K. J. Arrow) is concerned with problems raised by agency. In a general equilibrium

context the study of information flows (see J. Marschak and R. Radner) or of financial intermediaries in monetary

models is also an example of agency theory. The canonical agency posed as follows. Assume that both the agent

and the principal possess state independent von Neumann-Morgenstern utility functions, G(.) and U(.)

respectively, and that they act so as to maximize their expected utility. The problems of agency are really most

interesting when seen as involving choice under uncertainty and this is the view we will adopt. The agent may

choose an act, aCA, a feasible action space, and the random payoff from this act, w(a, 0), will depend on the random

state of nature O(EQ the state space set), unknown to the agent when a is chosen. By assumption the agent and the

principal have agreed upon a fee schedule f to be paid to the agent for his services. T he fee, f, is generally a function

of both the state of the world, 0, and the action, a, but we will assume that the action can influence the parties and,

hence, the fee only through its impact on the payoff. T his permits us to write, (1) f = f(w(a,6);6). Two points deserve

mention. Obviously the choice of a fee schedule is the outcome of a bargaining problem or, in large games, of a

market process. Much of what we have to say is relevant for this view but we will not treat the bargaining problem

explicitly. Second, while it is possible to conceive of the fee as being directly functionally dependent on the act, the

theory loses much of its interest, since without further conditions, such a fee can always be chosen as a Dirac 8-

function forcing a particular act (see S. Ross). In some sense, then, we are assuming that only the payoff is

operational and we will take this point up below. Now, the agent will choose an act, a, so as to (2) max E{G[f(w(a, 0);

0)]}, a 0 where the agent takes the expectation over his subjectively held probability distribution. The solution to the

agent's problem involves the choice of an optimal act, ao, conditional on the particular fee schedule, i.e., ao=a((f)),

where a(.) is a mapping from the space of fee schedules into A. If the principal has complete information about the

fee to act mapping, a((f)), he will now choose a fee so as to max El U[wv(a((f)), 0) (3 (f) e (3) - f(w(a((f)), 0); 0)] where

the expectation is taken over the principal's subjective probability distribution over states of nature. If the principal

is not fully informed about a(.), then a(X) will be a random function from his point of view….” The problems of

agency are really most interesting when seen as involving choice under uncertainty and this is the view we will

adopt. The agent may choose an act, aCA, a feasible action space, and the random payoff from (and Stiglitz

120 Bentham Jeremy [1907 (1789) ]An Introduction to the Principles of Morals and Legislation Oxford: Clarendon Press

Retrieved on 1 October 2012 from the Library of Economics and Liberty. 121 Mill, John Stuart (1863). Utilitarianism (1 ed.). London: Parker, Son & Bourn, West Strand. Retrieved 6 June 2015 via

Google Books 122

Rawls John (1971) “A Theory of Justice” Harvard University Press USA, 1971 first edition 123 Rousseau Jean-Jacque (1762) Du contrat social ou Principes du droit politique; (Of the Social Contract, or Principles of Political Right) Publication,. Amsterdam, février-mars 1762, Marc Michel Rey, etc

124 Gödel Kurt Friedrich (1931),"Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme

I" Monatshefte für Mathematik und Physik 38: 173–98 (in English "On Formally Undecidable Propositions of "Principia

Mathematica" and Related Systems")

125 Russell Bertrand 1903. The Principles of Mathematics Cambridge University Press

126 Bernoulli, Daniel, 1954 [1738], “Exposition of a New Theory on the Measurement of Risk Econometrica, 22: 23–36 127Ross, Stephen A. 1973. The economic theory of agency: The principal's problem. American Economic Review 62(2): 134-139.

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Joseph128) the SET Cantor theory, and the “until now” bibliography has been used

(sometimes with the same wors as to support my argumentation:

o Set theory is the branch of MATHEMATICAL LOGIC that studies SETS which informally

are collections of objects. Although any type of object can be collected into a set, set

theory is applied most often to objects that are relevant to mathematics. The language

of set theory can be used in the definitions of nearly all MATHEMATICAL OBJECTS

o In MATHEMATICS the Cantor set is a set of points lying on a single LINE SEGMANT that

has a number of remarkable and deep properties (1883)

A bijective function. A=SET

o Cantor Dust: Cantor dust is a multi-dimensional version of the Cantor set. It can be

formed by taking a finite Cartesian product129 of the Cantor set with itself, making it

a Cantor Space Like the

The second sub-question: Does exist the only one “win-win-win papakonstantinidis 3D

equilibrium” or not?

MAIN WIN-WIN-WIN QUESTIONS:

a. Win-win-win equilibrium: The limit of convergence’s processes of different functions

and

b. Is a set formed by the Axioms?

Approaches, on win-win Equilibrium and the win-win-win model are starting from the “Pareto

Efficiency”; it is the reason for which that bargainers’ strategies (choices) are represented

under the “binomial (trinomial in my case) distributions” logic, as a “pie” and are the “payoff

or the prize times its probability”)

Pareto Efficiency: Definition A particular distribution of goods or outcome

128 Stiglitz, Joseph E. and all (1969) Readings in the modern theory of economic growthCambridge, Massachusetts: The M.I.T. Press 129 Helmberg, Gilbert (2007). Getting Acqainted with Fractals Walter de Gruyter p. 46

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of any social process is regarded as Pareto efficient if there is no way to

improve one or more people's situations without harming another. Put

another way, an outcome is not Pareto efficient if there is a way to improve at

least one person's situation without harming anyone else. Pareto optimality:

whenever all individuals of a society strictly prefer an outcome x over an

outcome y, the choice function doesn't pick y.

Informal and formal axiom systems

One big reason for the expressed disconnect is that Gödel’s theorems are about formal axiom

systems of a kind that play no role in daily mathematical work. Informal axiom systems for

various kinds of structures are of course ubiquitous in practice, viz. axioms for groups, rings,

fields, vector spaces, topological spaces, Hilbert spaces, etc., etc.; these axioms and their

basic consequences are so familiar it is rarely necessary to appeal to them explicitly, but they

serve to define one’s subject matter. They are to be contrasted with foundational axiom

systems for the “mother” structures--the natural numbers (Peano) and the real numbers

(Dedekind)--on the one hand, and for the general concepts of set and function (Zermelo-

Fraenkel) used throughout mathematics, on the other. Mathematicians may make explicit

appeal to the principle of induction for the natural numbers or the least upper bound principle

for the real numbers or the axiom of choice for sets, but reference to foundational axiom

systems in practice hardly goes beyond that.

One informal statement of the basic Peano axioms for the natural numbers is that they

concern a structure (N, 0, s) where 0 is in N, the successor function s is a unary one-one map

from N into N which does not have 0 in its range, and the Induction Principle is satisfied in the

following form: (IP) for any property P(x), if P(0) holds and if for all x in N, P(x) implies P(s(x))

then for all x in N, P(x) holds.

c.

b. Non-cooperative equilibrium One of the important open problems has been the

reconciliation of the various non-cooperative theories of oligopolistic competition

with general equilibrium theory. The major difficulty is that the oligopoly models are

open in the sense that the customers-are usually not considered as players with

strategic freedom, while the general equilibrium model considers every individual in

the same manner, regardless of his position in the economy. Since the firms are

players in the oligopoly models, it is necessary to specify the domain of the strategies

they control and their payoffs under all circumstances. In a general equilibrium model

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no individual is considered a player; all are regarded as individual maximizers. Walras’

law is assumed to hold, and supply is assumed to equal demand.

When an attempt is made to consider a closed economic model as a non-cooperative game,

considerable difficulties are encountered in describing the strategies of the players. This can

be seen immediately by considering the bilateral monopoly problem; each individual does not

really know what he is in a position to buy until he finds out what he can sell. In order to

model this type of situation as a game, it may be necessary to consider strategies which do

not clear the market and which may cause a player to become bankrupt—i.e., unable to meet

his commitments. Shapley and Shubik (in Shubik 1967) have successfully modeled the closed

two-sided two-commodity market without side payments and have shown that the non-

cooperative equilibrium point converges from below the Pareto-optimal surface to the

competitive equilibrium point. They also have considered more goods and markets on the

assumption of the existence of a transferable (but not necessarily comparable) utility.

When there are more than two commodities and one market, the existence of a unique

competitive equilibrium point appears to be indispensable in defining the strategies and

payoffs of players in a non-cooperative game. No one has succeeded in constructing a

satisfactory general market model as a non-cooperative game without using a side-payment

mechanism. The important role played by the side-payment commodity is that of a strategy

decoupler. It means that a player with a supply of this type of “money” can decide what to buy

even though he does not know what he will sell.

In summary, it appears that, in the limit, at least three considerably different game-theoretic

solutions are coincidental with the competitive equilibrium solution. This means that by

considering different solutions we may interpret the com petitive market in terms of

decentralization, fair division, the power of groups, and the attenuation of power of the

individual.

The stable-set solution of von Neumann and Morgenstern, the bargaining set of Aumann and

Maschler (1964), the “self-policing” properties of certain imputation sets of Vickrey (1959),

and several other related cooperative solutions appear to be more applicable to sociology, and

possibly anthropology, than to economics. There has been no indication of a limiting behavior

for these solutions as numbers grow on the contrary, it is conjectured that in general the

solutions proliferate. When, however, numbers are few, as in cartel arrangements and in

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international trade, these other solutions provide insights, as Nyblen has shown in his work

dealing with stable sets (1951).

Nonexistence of competitive equilibrium

When conditions other than those needed for the existence of a competitive equilibrium hold,

such as external economies or diseconomies, joint ownership, increasing returns to scale, and

interlinked tastes, then the different solutions in general do not converge. There may be no

competitive equilibrium; the core may be empty; and the definition of a non-cooperative game

when joint property is at stake will call for a statement of the laws concerning damages and

threats. (Similarly, even though the conditions for the existence of a competitive equi librium

are satisfied, the various solutions will be different if there are few participants.) When the

competitive equilibrium does not exist, we must seek another criterion to solve the problem of

distribution or, if possible, change the laws to rein-troduce the competitive equilibrium. The

other solutions provide different criteria. However, if a society desires, for example, to have its

distribution system satisfy conditions of decentralization and fair division, or of fair division

and limits on power of groups, it may be logically impossible to do so. Davis and Whinston

(1962), Scarf (1964), and Shapley and Shubik (1964) have investigated applications of game

theory to external economies, to increasing returns to scale, and to joint ownership. In the

case of joint ownership the relation between economics and politics as mechanisms for the

distribution of the proceeds from jointly owned resources is evident. It must be noted that the

“many solutions” approach to distribution is in contrast to the type of welfare economics that

considers a community welfare function or social preferences, which are not necessarily

constructed from individual preferences.

As for the third sub-question the most important for this work, a naive answer should be:

Because of the existence of this third entity (the “C” factor) in the bargaining process that

ensures itself the negotiation and further promotes overall collective welfare and prevents to

creating monopoly’s situation In such games each participant is striving for his greatest

advantage in situations where the outcome depends not only on his actions alone, nor solely

on those of nature, but also on those of other participants whose interests are sometimes

opposed, sometimes parallel, to his own.Game theory methods have provided several new

insights in general equilibrium economics. Under the appropriate conditions on preferences

and production, it has been proved that a price system that clears the market will exist,

provided that each individual acts as an independent maximizer. On this point, the “win-win-

win equilibrium (if it exists) could introduce the real meaning of “social” In this frame I’ve tried

to interpret the win-win-win situation, by maximizing the total utility objective function (for

the 3 parts of Bargain)

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papakonstantinidis Page 65

b2

The win-win-win papakonstantinidis model, as a tool for conflict resolution:

People have the attitude to cooperate by the nature : they are interested only

on payoffs.. they have lottery on strategies and payoffs

Solving the bargaining problem (1st approach) :

The win-win game theory (and the resulted EN. ) is mainly based on “shares of

distribution” Nash had imagined the bargain as a “distribution problem, where “shares” are the

important factor than the game itself and the resulted “zero sum two players game”(John von

Neumann-Oscar Morgenstern130 1944) itself Let see a random trinomial distribution of a

mixed strategies’ game (including the corresponding probabilities, in real terms, the “payoff or the prize times its probability”)131 )100,...(,.. yxyx and their correspond utilities-

payoffs(in real terms, the ‘expected payoff’ of each consequence

AN EXAMPLE:

Now, according to N.E, the objective is to maximize (or to find the max) of the product “

CBA UUU that means the max for all, A, B bargainers and all the “others” or the

“Community” (really, “of all the people, that leading in “social welfare” maximization:

130 John von Neumann-Oscar Morgenstern 1944) Theory of Games and Economic Behavior, Princeton University Press published in 1944 131 In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. A success/failure experiment is also called a Bernoulli experiment or Bernoulli trial; when n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.

)100(

.

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CBA

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UUUUUU

CBA

CBAGBA

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papakonstantinidis Page 66

).......(....

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papakonstantinidis Page 67

CASES:

MARKET SIDE:

STR

(PROB) A

STR(PROB)

B

U(A)PAYOFF U(B)PASYOFF STR(PROB)C U(C)PAYOFF CBA UUU

1 45 30 14 8 25 11 1232

2 17 43 4 24 40 31 2976

3 75 25 37 14 0 0 518

4 22 58 25 44 20 30 33000

5 60 0 120 0 40 22 2640

6 0 40 0 70 60 17 1190

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papakonstantinidis Page 68

132

Papakonstantinidis L.A(2002-August 14) “The win-win-win model” Euracademy Guide The Visby University-Gotland-SW 133

John von Neumann- Oscar Morgenstern (1944) “theory of games and economic behavior” –PRINCETON-

University..Press..ed

Concluding,

I tried to identify the "win-win-win" as a key tool for the approach to social welfare by clicking

on the incompatibility of five basic theorems that define it - each one of its own side-either

positive (justice theorem ) or negative (the impossibility theorem)

The suggested "win-win-win papakonstantinidis model”132is built up on these

incompatibilities, in particular as regards the pairs" Pareto efficiency – Impossibility Theorem”

"paradox liberty (Amartya Sen) - Pareto Efficiency” , “Theorem of Justice –Pareto Efficiency”

and (the most important) “the Theorem of incompleteness-the Impossibility Theorem”

The win-win-win papakonstantinidis model is a methodological tool for conflict resolution,

especially in the case of decision making, or in forming "instant reflection winning strategies"

in the BARGAIN (which is the frame) The “win-win-win papakonstantinidis model” concerns

the strategic decision making in a number of fields and domains (biology, psychology,

management, marketing, history- especially in interpretation of historic events-laography,

ethnology, anthropogeography, philosophy, economy, sociology, pure math, communication,

public speech, diplomacy, and go on The reason so many regards thinking and research

fields lies in the very nature of the model, especially in its triple pole perception, which leads

us to see things from another, alternative approach, the triple view, whether in psychology or

interpretation of historical events or diplomacy, or communication, or MANAGEMENT

Special regard is given to regional and local development field both as a regional and social

sciences. It proves that building social capital at local level mainly depends on social trust

links among local people: Social cohesion based on social capital may be measured by the

diversification Rate (R *) from strict globalization rules: From this point of view, local people’s

intervention should be useful, so as to diversify these "rules" at local level adjusting them to

local identity, including communication code, customs, ethics, culture. The Win-win-win

methodology [Papakonstantinidis Model] should facilitate local people to "readjust" bargaining

globalization rules locally, through a sensitization process: Community is defined as a discrete

spatial / cultural entity at its sensitization process' limit

The “win-win-win papakonstantinidis model” (2002, August, SW) may, thus, transform

individual winning –instant reflection –strategies (the win-win Nash Theory) in a NEW –three

poles-equilibrium point, including the COMMUNITY (Environmental Protection, Value Systems,

Ethic etc), which is the “absolute cooperation” limit point in the bargain between TWO

Since the game theory (exactly: the “non cooperative game theory”) saved the New-classical

School of Thought in Economics letting it to make a restart, focusing on the “bargaining

equilibrium” (Nash Equilibrium) and the equimarginal principle (consumer choice) it seems

that the bargaining behavior is in the centre of our research

Starting from the “zero sum two players game” (John von Neumann- Oscar Morgenstern

1944)133in the form of “win- lose” at any bargain, then was the John Forbs Nash who made the

difference, letting in both bargainers to win (win-win) But, for another time this bargain was

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▲

APPLICATION: THE P.A.C case: Kotca (FIN) world conference, 2013/SEPT

rather to the side of the winners (due to their bargaining force) than eliminating social

inequalities (the winner takes it all)

With this aim an hypothetical dipole bargain between 2 bargainers (*A,B) converted into 3-

pole by introducing the "Community" (the village, the town, the inhabitants of a country, a

continent, planet, after all) as a third pole in any bargain (win-win-win)

So the concept is to construct a theoretical-original-model so that it should respond better to

the conditions of "social welfare"

With this aim an hypothetical triple-pole bargain between 2 (A and B and the "Community"

included as the third pole) is a basis for scientific dialogue By the tem “Community” we can

imagine any common structure, i.e the village, the town, the inhabitants of a country, a

continent, planet, after all-

The point is that the third pole (the Community) will claim its own profits, in a future

negotiation It is about a "win-win-win" concept which is now the global requirement For

example, the first concrete example has to do with environmental protection Climate change

leaves no room to 2 competitors without considering the entire rest of the world Each

negotiation between 2 concerns the entire planet The how achieved in practice I think it can be

done with Laws, as long as there is the political will of Another Dimension It has to do with the

war see the two superpowers to compete by focusing on the war in the Middle East (Syria and

Iraq) But the agreement or disagreement affects millions of people in the two countries who

come as refugees to Europe

The recognition of the third pole in our daily life is connected with its social necessity

Without any imposition by dictatorial regimes, the 3-pole approach to bargaining, is necessary

and unavoidable if and only if humankind seeks survival solutions

In a “win-win-win” negotiation there is more possibility of achieving social welfare: This can

be proved by the math example below On the other side we have 5 basic foundational and

global known Theorems which are incompatible So the concept here was to put them one

against the other and seek "material" to build the new

For example, the Incompleteness Theorem (Gödel) fades the Impossibility Theorem (K. Arrow)

and the Pareto Efficiency is basic for the Impossibility Theorem, but not for the “Justice

theorem (Rawls) But from these incompatibilities arises a necessity of completeness,

effectiveness, universal justice, a necessity of "umbilical points" freedom , economic

equilibrium The synthesis of all these lead to a situation utopia (romantic, idealistic) will

certainly not get, but shows us, from the other, a path of self-preservation and survival if the

goal is not suicidal

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CASE SUDY: RESEARCH ON COMPLETED QUESTIONAIRES

Local Development: Sensitization of local people SKOPELOS/GLOSSA

Questionnaire

papakonstantinidis, 2015

a/a Questions YES N0 NOT AT

ALL

1 How many deals you remember that you do in one day?

(one, more than one, not at all)

2 Are you a businesslike? prepare strategies of dealing you

do with another person?

3 You want always winning? you want to even if you are

wrong in your position with another individual?

4 Usually lost or won in your transactions (not just

economic, but also social, political etc.) with other

people?

5 Have you regretted for a daily choice of yours (whatever

is)?

6 Do you gain experience (or try to correct your mistakes)

or not, in a subsequent transaction with individuals or

with the State?

7 Affected, usually from external sources in your choices

or not? Esis affects other people around you, trying to

force your will?

8 Do you believe that other people they interact with

follow Personal winning strategies in order to get as

much as possible from any agreement?

9

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▲

THEORETICAL CONTRIBUTION

It has “been adopted” through centuries, the concept that the human relations, the whole

life, our planet, our universe is a continuous big conflict In this concept, the simplest form of

conflict concerns two ID SEPARATE parts of thinking and behavior

If it were possible for us to "introduce" a third autonomous part (whatever it is) in a bargain

between two, then it should also be possible to imagine that this "personality" could be both a

"third part of the bargain" as well as the “overall monitoring” without violating individual rights

and freedom of negotiations Basically, the "state", the "community" is highlighted, having first

of all ensure its own functions. This study tries to set the framework for a well-governed state

/ community on simple rules that relate exclusively to "interaction" in all its versions

Is this work a “theoretical contribution?

To answer this question, it could be nessecary to understand of what is a “theoretical

contribution”:

o Basically, the intent is not to create a new conceptualization of theory, but rather to

propose several simple concepts for discussing the theory-development process.

o From the other hand, in this work is attempted a “new creation” to be launched over a

new path of thought as it is expected to be applicable in a wide field of sciences

(psychology,marketing, management,biology,history,economy,sociology,laography

To analyze these, it is nessecary 3 key-questions to be answered:

a. What are the building blocks of theory development?

b. What is a legitimate value-added contribution to theory development? and

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c. What factors are considered in judging conceptual papers? The first section describes

the constituent elements of a theory. The second section uses this framework to

establish standards for the theory-development process.

ANALYSIS

What is a theory?

The summary and synthesis of what is known about a field It is the reduction of our

knowledge to the basic ideas, presented in a way that shows their underlying patterns

and relationships. (David Moore, 1991) 134 Development theory is a conglomeration or

a collective vision of theories about how desirable change in society is best achieved.

Such theories draw on a variety of social science disciplines and approaches.

Theory explains how some aspect of human behavior or performance is organized. It

thus enables us to make predictions about that behavior.

The components of theory are concepts (ideally well defined) and principles.

A concept is a symbolic representation of an actual thing - tree, chair, table,

computer, distance, etc.

Construct is the word for concepts with no physical referent - democracy, learning,

freedom, etc. Language enables conceptualization.

A principle expresses the relationship between two or more concepts or constructs.

In the process of theory development, one derives principles based on oneΥs

examining/questioning how things/concepts are related.

Concepts and principles serve two important functions:

1) They help us to understand or explain what is going on around us.

2) They help us predict future events (Can be causal or correlational)

A theory is a related set of concepts and principles

- about a phenomenon

- the purpose of which is to explain or predict the phenomenon

Why theory is important

1. Theory provides concepts to name what we observe and to explain relationships

between concepts. Theory allows us to explain what we see and to figure out how to

bring about change. Theory is a tool that enables us to identify a problem and to plan

134

Moore, D. and Saunders, B. (1991) Youth drug use and the prevention of problems: Why we've got it all

wrong.International Journal on Drug Policy, 2, (5), pp. 29-33

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papakonstantinidis Page 73

a means for altering the situation.

2. Theory is to justify reimbursement to get funding and support - need to explain

what is being done and demonstrate that it works - theory and research

3. Theory is to enhance the growth of the professional area to identify a body of

knowledge with theories from both within and with out the area of distance learning.

That body of knowledge grows with theory and research. Theory guides research135.

According to David A. Whetten (1989) 136 and Robert Dubin,

(1959)137,138, on theory-development a complete theory must give

answers to the questions:

(a) What are the building blocks of theory development?

(b) What is a legitimate value-added contribution to theory development? and

(c) What factors are considered in judging conceptual ideas?

A. What Are the Building Blocks of Theory Development?

According to theory-development authorities (e.g., Dubin, 1978), a complete theory

must contain four essential elements, which are described in the following

paragraphs.

1. WHAT. Which factors (variables, constructs, concepts) logically should be considered as

part of the explanation of the social or individual phenomena of interest? Two criteria

exist for judging the extent to which we have included the "right" factors:

COMPREHENSIVENESS (i.e., are all relevant factors included?) and PARSIMONY (i.e., should

135Theory guides research http://www.jou.ufl.edu/faculty/mleslie/spring96/theory.html 136

DAVID A. WHETTEN What Constitutes a Theoretical Contribution? A c a d e m y of Management Review, 1 9 8 9 ,

V o l . 1 4 , N o . 4 , 4 9 0 - 4 9 5 137 Dubin Robert (1978) Theory Building 2nd Edition Publisher: Free Pr; 2nd edition (February 1978)

138 Dubin, R. (1959) "Deviant Behavior and Social Structure: Continuities in Social Theory." American Sociological Review24:147-

163. - Robert Dubin (1959) viewed deviance as a function of society, disputing the assumption that the deviant adaptations to

situations of anomie are necessarily harmful to society. For example, an individual in the ritualistic adaptation is still playing by

the rules and taking part in society. The only deviance lies in abandoning one or more of its culturally prescribed goals. Dubin

argued that Merton's focus on the relationship between society’s emphasized goals, and institutionalized prescribed means

was inadequate.Structural this refers to the processes at the societal level which filter down and affect how the individual

perceives his or her needs, i.e. if particular social structures are inherently inadequate or there is inadequate regulation, this

may change the individual's perceptions as to means and opportunities; or

Individual: this refers to the frictions and pains experienced by an individual as he or she looks for ways to satisfy his or her

needs, i.e. if the goals of a society become significant to an individual, actually achieving them may become more important

than the means adopted.

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papakonstantinidis Page 74

some factors be deleted because they add little additional value to our under-

standing?).

2. When authors begin to map out the conceptual landscape of a topic they should err in

favor of including too many factors, recognizing that over time their ideas will be

refined. It is generally easier to delete unnecessary or invalid elements than it is to

justify additions. However, this should not be interpreted as license to throw in the

kitchen sink. Sensitivity to the competing virtues of parsimony and

comprehensiveness is the hallmark of a good theorist.

3. How. Having identified a set of factors, the researcher's next question is, How are they

related? Operationally this involves using "arrows" to connect the "boxes." Such a step

adds order to the conceptualization by explicitly delineating patterns. In addition, it

typically introduces causality. Although the researcher may be unable to adequately

test these links, restrictions in methods do not invalidate the inherent causal nature of

theory.

4. Together the What and How elements constitute the domain or subject of the theory.

The more complex the set of relationships under consideration, the more useful it is

to graphically depict them. Not all theoretical treatises must contain figures with

boxes and arrows, but a visual representation often clarifies the author's thinking and

increases the reader's comprehension. In particular, formal models aid theory de-

velopers and users to assess the balance between parsimony and completeness.

5. WHY. What are the underlying psychological, economic, or social dynamics that justify

the selection of factors and the proposed causal relationships? This rationale

constitutes the theory's assumptions—the theoretical glue that welds the model

together. (Like Dubin, I do not distinguish between a model and a theory.)

6. The central question addressed here is: Why should colleagues give credence to this

particular representation of the phenomena? The answer lies in the logic underlying

the model. The soundness of fundamental views of human nature, organizational

requisites, or societal processes provide the basis for judging the reasonableness of

the proposed conceptualization.

c. Who, Where, When. These conditions place limitations on the propositions generated

from a theoretical model. These temporal and contextual factors set the boundaries of

generalizabil-ity, and as such constitute the range of the theory. Scholars who study

the effects of time and context on people and events keep asking nagging the

“research questions” Although it is unfair to expect that theorists should be sensitive

to all possible boundary constraints, clearly there is value in conducting some simple

mental tests of the generalizability of core propositions. For example, theorists should

be encouraged to think about whether their theoretical effects vary over time, either

because other time-dependent variables are theoretically important or because the

theoretical effect is unstable for some reason.

d. Sensitivity to context is especially important for theories based on experience.

According to the contextualist perspective (Gergen, 1982)139, meaning is derived from

139

Kenneth J. Gergen SWARTHMORE COLLEGE (1985) “The Social Constructionist Movement in Modern Psychology”

Reprinted from American Psychologist, Vol. 40, No. 3, March 1985 Primed in U. S. A.

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papakonstantinidis Page 75

context. That is, we understand what is going on by appreciating where and when it is

happening. Observations are embedded and must be understood within a context.

Therefore, authors of inductively generated theories have a particular responsibility

for discussing limits of generalizability. Although it is important for theorists to be

sensitive to context, the Who, Where, and When of a theory are typically discovered

through subsequent tests of the initial, rudimentary theoretical statement (What, How,

Why). In the process of testing these ideas in various settings, we discover the

inherent limiting conditions. In the absence of this breadth of experimental evidence,

we must be realistic regarding the extent of a theorist's foreknowledge of all the

possible limitations on a theory's applicability.

WHAT ARE THE BUILDING BLOCKS OF A RHEORETICAL CONTRIBUTION?

WHAT WHEN HOW WHAT

AND

HOW

WHY WHO,

WHERE,

WHEN

LIMITATIONS

REPRESENTATION

OF THE

PHENOMENA

B. What Is a Legitimate, Value-Added Contribution to Theory Development?

1. WHAT AND HOW. Although, in principle, it is possible to make an important theoretical

contribution by simply adding or subtracting factors (Whats) from an existing model,

this process seldom satisfies reviewers. The additions or deletions typically proposed

are not of sufficient magnitude to substantially alter the core logic of the existing

model. One way to demonstrate the value of a proposed change in a list of factors is

to identify how this change affects the accepted relationships between the variables

(Hows). Just as a list of variables does not constitute a theory, so the addition of a new

variable to an existing list should not be mistaken as a theoretical contribution.

Relationships, not lists, are the domain of theory. As Poincare (1983) so aptly noted,

"Science is facts, just as houses are made of stone. . . . But a pile of stones is not a

house, and a collection of facts is not necessarily science." Therefore, theoretical

insights come from demonstrating how the addition of a new variable significantly

alters our understanding of the phenomena by reorganizing our causal maps. For

example, the addition of "growth-need strength" to job-design theories transformed

extant views and altered research practice Important changes in a theory's What and

How are frequently stimulated by surprising research results. In the process of

gathering either quantitative or qualitative data, scholars are often confronted with an

inconsistency between their observations and conventional wisdom. Although contrary

results are frequently discounted by theorists on the basis of measurement error,

ongoing challenges to outmoded thinking about motivation (Organ, 1988) demon-

strate that sufficient data can be persuasive.

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2. WHY. This is probably the most fruitful, but also the most difficult avenue of theory

development. It commonly involves borrowing a perspective from other fields, which

encourages altering our metaphors and gestalts in ways that challenge the underlying

rationales supporting accepted theories. This profound challenge to our views of

human nature, group development, organizational transactions, and so forth,

generally precipitates a broad reconceptualization of affected theories.This aspect of

conceptual development is particularly critical, and generally overlooked. Theories

often are challenged because their assumptions have been proven unrealistic (gener-

ally by work imported from other areas). Although it is just as difficult to build

consensus around paradigmatic truth as around empirical fact, nonetheless, recent

macro theoretical developments involving ecology and economics demonstrate the

salience of this approach

3. Who, WHEN, WHERE. Generally, it is insufficient to point out limitations in current

conceptions of a theory's range of application. For example, discovering that a

mainstream personnel selection model has low predictive validity in a military setting

does not by itself constitute a theoretical contribution. In addition, theorists need to

understand why this anomaly exists, so that they can revise the HOW and WHAT of the

model to accommodate this new information.Conversely, applying an old model to a

new setting and showing that it works as expected is not instructive by itself. This

conclusion has theoretical merit only if something about the new setting suggests the

theory shouldn't work under those

C. What factors are considered in judging conceptual ideas, or what constitutes a

publishable theory study?

This question (the last key-question) is analyzed in six following questions:

1. WHAT'S NEW? Does the idea make a significant, value-added contribution to current

thinking? Scope tends to reflect the level of theorizing (general versus middle level),

while degree reflects the radicalness of the proposal.

2. So WHAT? Will the theory likely change the practice of organizational science in this

area? Are linkages to research evident (either explicitly laid out, or easily, reliably

deduced)?

3. WHY SO? Are the underlying logic and supporting evidence compelling? Are the

author's assumptions explicit? Are the author's views believable?

4. WELL DONE? Does the idea reflect seasoned thinking, conveying completeness and

thoroughness? Are multiple theoretical elements (What, How, Why, When-Where-Who)

covered? Do the arguments reflect a broad, current understanding of the subject? If

propositions are included, are they used properly? Does the argument have any

glaring logical flaws?

5. Done WELL? Is the idea well written? Does it flow logically? Are the central ideas easily

accessed? Is it enjoyable to read? Is the idea long enough to cover the subject but

short enough to be interesting?

6. WHY NOW? Is this topic of contemporary interest to scholars in this area? Will it likely

advance current discussions, stimulate new discussions, or revitalize old discussions?

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WHAT FACTORS ARE CONSIDERED IN JUDGING CONCEPTUAL PAPERS

WHAT'S

NEW SO WHAT? WHY SO? WELL

DONE DONE WELL

WHY NOW

Development theory:

Development theory is a conglomeration or a collective vision of theories about how desirable

change in society is best achieved. Such theories draw on a variety of social science disciplines

and approaches.

During the theory-development process, logic replaces data as the basis for evaluation. Theo-

rists must convince others that their propositions make sense if they hope to have an impact

on the practice of research. If the theoretical model is a useful guide for research, by

definition, all the relationships in the model have not been tested. If all links have been

empirically verified, the model is ready for the classroom and is of little value in the

laboratory. The mission of a theory-development journal is to challenge and extend existing

knowledge, not simply to rewrite it. Therefore, authors should push back the boundaries of

our knowledge by providing compelling and logical justifications for altered views. This

requires explaining the Whys underlying the reconstituted Whats and Hows.

Why research is conducted has important implications for the link between theory develop-

ment and empirical research. Combining the Hows and the Whats produces the typical model,

from which testable propositions can be derived. (The primary difference between prop-

ositions and hypotheses is that propositions involve concepts, whereas hypotheses require

measures.) Technically, these statements (e.g., A is caused by B) can be tested without under-

standing the Whys underlying the model. However, this tends to lead to empirically, rather

than theoretically, dominated discussions of the implications of a study's results. As a field,

when we have insufficient understanding of why we collectively started an investigative

journey, or what theoretical direction we are following, then our discourse tends to degenerate

into heated methodological debates over how fast we are traveling. To avoid vacuous discus-

sions, propositions should be well grounded in the Whys, as well as the Hows and the Whats.

To summarize thus far: What and How describe; only Why explains. What and How provide a

framework for interpreting patterns, or discrepancies, in our empirical observations. This is an

important distinction because data, whether qualitative or quantitative, characterize; theory

supplies the explanation for the characteristics. Therefore, we must make sure that what is

passing as good theory includes a plausible, cogent explanation for why we should expect

certain relationships in our data. Together these three elements provide the essential ingre-

dients of a simple theory: description and explanation.

The Social Constructionist Orientation

Next step in defining a “theoretical contribution” in social sciences is to approach the Social

Constructionist Orientation (SCO)

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papakonstantinidis Page 78

The Social Constructionist Orientation

Social constructionist inquiry is principally con¬cerned with explicating the processes by

which people come to describe, explain, or otherwise account for the world (including

themselves) in which they live. It attempts to articulate common forms of under¬standing as

they now exist, as they have existed in prior historical periods, and as they might exist should

creative attention be so directed. At the metatheoretical level most such work manifests one

or more of the following assumptions

1. What we take to be experience of the world does not in itself dictate the terms by which the

world is understood. What we take to be knowledge of the world is not a product of induction,

or of the building and testing of general hypotheses. The mounting criticism of the positivist-

empiricist con¬ception of knowledge has severely damaged the traditional view that scientific

theory serves to reflect or map reality in any direct or decontextualized manner

Social constructionism has been nurtured by the soil of such discontent. It begins with radical

doubt in the taken-for-granted world—whether in the sciences or daily life—and in a

specialized way acts as a form of social criticism. Constructionism asks one to suspend belief

that commonly accepted categories or understandings receive their warrant through

observation. Thus, it invites one to challenge the objective basis of conventional knowledge..

By exam¬ining the variations in the way differing cultures and subcultural groups understand

gender, the referents for the terms man and woman are obscured. Possi¬bilities are opened

for alternative means of under¬standing gender differences or of abandoning such

distinctions altogether. Emotions are not objects "out there" to be studied, ventured Sarbin;

emotion terms acquire their meaning not from real-world referents but from their context of

usage.

Social Constructionism in Historical Perspective

The significance of the constructionist movement is more fully appreciated against the

backdrop of history. Although a full treatment of the relevant background is beyond the scope

of this article, it does prove useful to understand constructionism in relation to two major and

competing intellectual traditions. These traditions can largely be distin¬guished in terras of

basic epistemologjcal orientations or models of knowledge. On the one hand, thinkers such as

Locke, Hume, the Mills, and various logical empiricists in the present century have traced the

source of knowledge (as mental representation) to events in the real world. Knowledge copies

(or should ideally copy) the contours of the world. This exogenic perspective (Gergen Kenneth,

1982) thus tends to view knowledge as a pawn to nature. Proper knowl¬edge maps or

mirrors the actualities of the real world. In contrast, philosophers such as Spinoza, Kant,

Nietzsche, and various phenomenologists have tended to adopt an endogenic perspective

regarding the origins of knowledge. In this case, knowledge depends on processes (sometimes

viewed as innate) endemic to the organism. Humans harbor inherent tendencies, it is said, to

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think, categorize, or process information, and it is these tendencies (rather than features of

the world in itself) that are of paramount importance in fashioning knowledge.

The exogenic-endogenic antinomy has also played a major role in the history of psychological

theory. As I have outlined elsewhere (Gergen, 1982), early German theorists often wrestled in

vain with means of cementing the two perspectives. The at¬tempt of classical psychophysical

research to plot the precise relationship between external and internal worlds is but one case

in point. As psychology developed in the United States, guided as it was by both pragmatist

and positivist philosophy, it took on a strong exogenic character. Behaviorism (along with

neobehaviorism) placed (and continues to place) the major determinants of human activity in

the envi¬ronment. If the organism is to adapt successfully, it is claimed, its knowledge must

adequately represent or reflect that environment. Until recently the en¬dogenic perspective

failed to flourish on American soil. A handful of Gestalf psychologists, with their emphasis on

autochthonous tendencies of perceptual organization, and a stalwart band of

phenomenolo¬gists virtually prevented the"orientation from other¬wise perishing.

Yet, within the past two decades we have wit¬nessed what appears to be a major reversal in

emphasis. The endogenic perspective has returned in full force in the guise of cognitive

psychology. The seeds for this evolution in social psychology were planted by Kurt Lewin,

whose central concern with the psychological field was essentially a holdover from continental

rationalism. In the hands of his students this emphasis reinstituted itself in such concepts as

social (as opposed to physical) reality (Festinger, 1954), the social comparison process

motivated perception (Pepitone, 1949), emotions as perceived (Schachter, 1964), and

cognitive dissonance (Festinger, 1957) . The centrality of this work in social psychology also

served to hone the sensibilities of subsequent generations of re¬searchers. Concerns with

logical inference, cognitive schemata, information storage and retrieval, and cognitive

heuristics have all extended the Lewinian premise , : Human action is critically dependent on

the cognitive processing of information, that is, on the world as cognized rather than the

world as it is. Of course, much the same shift in explanatory emphasis has taken place within

psychology more generally. The contours of the "cognitive revolution" are widely recognized.

▲

Analysis

The argumentation of the “win-win-win papakonstantinidis theory is suggested based on “Set

principles" "Agency principles" and the "Bargaining Equilibrium" It is obviously, that the

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papakonstantinidis Page 80

suggested “win-win-papakonstantinidis theory” could be a re-start of processes and

theoretical approaches to the "construction" of a new social sciences theory , which would at

the core of trimerization of any human interaction letting field in the overall, collective

welfare In particular, the intent is to propose several simple concepts for discussing the

theory-development process The objectives regards expectations and standards, which result

from the absence of a broadly accepted framework for discussing the merits of conceptual

writing in the organizational sciences.(see at the 3 tables below)

WHAT ARE THE BUILDING BLOCKS OF A THEORETICAL CONTRIBUTION?

WHAT WHEN HOW WHAT

AND

HOW

WHY WHO,

WHERE,

WHEN

LIMITATIONS

REPRESENTATION OF THE

PHENOMENA

WHAT FACTORS ARE CONSIDERED IN JUDGING CONCEPTUAL IDEAS?

WHAT'S NEW SO WHAT? WHY SO? WELL

DONE DONE WELL

WHY NOW

▲

ANALYSIS

Building Blocks

question Brief description “win-win-win papakonstantinidis model”

what What is the concept

logically should be

considered as part of the

explanation of the social or

individual phenomena of

interest

The concept:

o The concept:

MAIN OBJECTIVE: SOCIAL WELFARE’s MAXIMAZATION

Suggestion: Trimerization of the 2-pole's bargain by introducing a third part (the

community) acting both, as a third part as well as the overall umbrella with the

responsibility of effectiveness justice,egalitarianism, ASSOCIATIONISM,

UTILITARIANISM, set, and Prioritarianism. (Prioriatarianism or the priority

view is a view within ethics and political philosophy that holds that the goodness

of an outcome is a function of overall well-being across all individuals with extra

weight given to worse-off individuals. Prioritarianism thus resembles

utilitarianism. Indeed, like utilitarianism, prioritarianism is a form of

aggregative consequentialism; however, it differs from utilitarianism in that it

does not rank outcomes solely on the basis of overall well-being).

o dealing with social welfare theorems’ incompatibilities

o dealing with the “ZFC Agency Theory” concidering the win-win-win

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papakonstantinidis Page 81

papakonstantinidis theory as a collection of objects (SET)

what Which other factors

(variables, constructs),

logically should be

considered as part of the

explanation of the social or

individual phenomena of

interest

BASE : Preferences,Priorities, and the 5 theorems, as variables of “welfare”

(characteristics,quantities,numbers,behaviors,preferences, …that increases or

decreases overtime or takes different values,in different situations)

VARIABLE: SERVICESGOODSofsetsomeoverspreferenceareyxyxu ..&................,)..,(

2.VARIABLES:

The five( 5 basic) theorems that concern the concept of "welfare economics" These theorems

are: The impossibility theorem (1951 Kenneth Arrow: book: Social Choice and Individual

Values140, as well as the Amartya Sen “liberal paradox”141 (either Pareto optimality142,143,144,or

liberty) the theorem of incompleteness (Kurt Gödel (1931)145,146, the Rawls Theorem on

Justice, 1958(“Justice as fairness, in his Philosophical Review,1958)147 the Nash Equilibrium in

Nash “Non cooperative Game Theory 1951(annals of Mathematics,1951 Vol. 54, No. 2 (Sep.,

1951), pp. 286-295)148 and the “Pareto optimal149 in a 3D space according to Caratheodory

conjecture (umbilical points in a sphere)150, then the main issue in this research concerns

the possibility that a win-win-win communication should exist in real terms, due to logical

mind contractures (logical forms)151 expressed by psychology and personality’s factors, as

140 Kenneth Arrow 1951, 2nd ed., 1963 Social Choice and Individual Values, Yale University Press 141 Amartya K. Sen, 1970, Collective Choice and Social Welfare, ch. 3.4 142 Pareto optimality: whenever all individuals of a society strictly prefer an outcome x over an outcome y, the choice function

doesn't pick y. Formally, a social choice function F is Pareto optimal if whenever p∊Rel(X)N is a configuration of preference

relations and there are two outcomes x and y such that x⪲iy for every individual i∊N, then y∉ F(p). Minimal liberalism: More

than one individual in the society is decisive on a pair of social outcomes. (An individual is decisive on a pair of social

outcomes x and y if, whenever he prefers x over y, the social choice function prefers xover y regardless of what other members

of the society prefer. (And similarly whenever he prefers y over x, the social choice function prefers y over x.) 143

Vilfredo Pareto.(1906) Manual of Political Economy. 1906. 144

Vilfredo Pareto(1896) Cours d' Économie Politique Professé a l' Université de Lausanne. Vol. I, 1896,Vol. II, 1897. 145

Kurt Godel,(1931) ‘ ¨ Uber formal unentscheidbare S ¨ atze ¨ der Principia mathematica und verwandter Systeme I’ (1931)

Richard ZachFirst publication: Monatshefte fur Mathematik und Physik ¨ , 37, 173–198 Reprints: S. Feferman et al., eds., Kurt Godel. Collected Works Volume I: Publications 1929–1936 New York: Oxford University Press, 1986, pp. 116–195. 146 Gödel, K (1930). "Die Vollständigkeit der Axiome des logischen Funktionenkalküls". Monatshefte für Mathematik (in German) 37 147 John Rawls.(1958) “Justice as Fairness. The Philosophical Review”, Vol. 67, No. 2 (Apr., 1958), pp. 164-194. Stable URL:. 148 Nash John (1951) “Non cooperative Game Theory (annals of Mathematics,1951 Vol. 54, No. 2 (Sep., 1951), pp. 286-295

149 Pareto optimal (comparative more Pareto optimal, superlative most Pareto optimal)

(game theory, economics) Describing a situation in which the profit of one party cannot be increased without reducing the

profit of another. AND (game theory) Describing a strategy that cannot be made to perform better against

one opposing strategy without performing less well against another

}..2,1{,..0,....

)...(max...:....max 1

nxxMxp

xxUFunctionUtility

iiii

n

150 Caratheodory (1935) Einfache Bemerkungen über Nabelpunktskurven, in: Festschrift 25 Jahre Technische Hochschule Breslau zur Feier ihres 25jährigen Bestehens, 1910—1935, Verlag W. G. Korn, Breslau, 1935, pp 105 - 107, and in: Constantin Carathéodory,1957 Gesammelte Mathematische Schriften, Verlag C. H. Beck, München, 1957, vol 5, 26–30 Carathéodory did publish this paper on a related subject but never committed the Conjecture into writing. The “Caratheodory Conjecture” claims that any convex, closed and sufficiently smooth surface in three dimensional Euclidean space needs to admit at least two umbilic points. In the sense of the Conjecture, the spheroid with only two umbilic points and the sphere, all points of which are umbilic, are examples of surfaces with minimal and maximal numbers of umbilics. For the conjecture to be well posed, or the umbilic points to be well-defined, the surface needs to be at least twice differentiable. 151As we have no better proof of thought-emotion expression from the language, we have approach this linguistic expression

and construction, in order to raise arguments accepting or rejecting the model. The emphasis is given to (a) psychological and

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papakonstantinidis Page 82

well as from linguistic forms152 or creating cognition by linguistic recursion153,154

Furthermore155, there is an incompatibility between “Justice Theory” (Rawls) and

“Prioritarianism”156

: According to Moreno-Ternero, Juan D. Roemer157, John E. The Veil

of Ignorance (the fundamental Principle of Justice Theory) violates Priority158: According to

Professors (Moreno and Roemer+) the veil of ignorance (of the Rawlsian “Justice”

Philosophy), has been used often as a tool for recommending what justice requires with

respect to the distribution of wealth. They completed Harsanyi’s model of the veil of

ignorance by appending information permitting objective comparisons among persons. For

this, they introduced the concept of objective empathy.

3. These variables are examined in the frame of the “ZFC Sets Theory” which informally are

collections of objects. Although any type of object can be collected into a set, set theory is

applied most often to objects that are relevant to mathematics From this point of view, the

“win-win-win papakonstantinidis” variables could be concerned as “collections of objects”

4, U T I L I T Y (DEFINITIONS that the study took into consideration): In economics utility is a

measure of preferences over some set of goods and services. The concept is an important

underpinning of rational choice theory, or…“Utility Function is an important concept that

measures preferences over a set of goods and services. Utility is measured in units called

utils, which represent the welfare or satisfaction of a consumer from consuming a certain

number of goods. Because satisfaction or welfare is a highly abstract concept, economists

measure utility in terms of revealed preferences by observing consumer choices and creating

an ordering of consumption baskets from least desired to the most preferred. Economists

create a parametric functional form for the utility function based on the assumption of

observed consumer behavior, with the amount of goods as variables and certain fixed

parameters. After that, utility is calculated by substituting certain numerical values for the

consumption of goods in the utility function”.

(game theory) A mathematical function that assigns a real number to every element of the outcome space in a way that captures the agent's preferences over both simple and compound lotteries.

Utility Function (in relation with the “consumre’s welfare” (in personal level)

In economics, the utility function measures welfare or satisfaction of a consumer as a function of consumption of real goods, such as food, clothing and composite goods rather than nominal goods measured in nominal terms. Utility function is widely used in the rational

(b) personality factors, as well as to (c) linguistic recursion, as they help us to use surrogate proposals i. e "Mother told him,

that had been told that Penelope left her home" (Piraha linguistic determinism Language may shape human thought – suggests

a counting study in a Brazilian tribe whose language does not define numbers above two. Hunter-gatherers from the Pirahã

tribe, whose language only contains words for the numbers one and two, were unable to reliably tell the difference between

four objects placed in a row and five in the same configuration, revealed the study.

152 Chomsky N. (2010). Some simple evo devo theses: how true might they be for language? in The Evolution of Human Language, eds Larson R. K., Deprez V., Yamakido H., editors. (Cambridge: Cambridge University Press; ), 45–62 153 Everett D. L. (2005) Cultural constraints on grammar and cognition in Pirahã: another look at the design features of human language. Current Anthropology 46, 621–646

154 Everett D. L. (2012) Language: The Cultural Tool. New York, NY: Pantheon Books 155 RAWLS VERSUS UTILITARIANISM IN THE LIGHT OF POLITICAL LIBERALISM (published in The Idea of a Political Liberalism: Essays on Rawls (Lanham: Md: Rowman and Littlefield, 2000) Richard J. Arneson 156 Moreno-Ternero-, Juan, D. Roemer John E. (2005) Impartiality and priority. Part 1: the veil of ignorance” –Yale University (February 9, 2005) 157 Moreno-Ternero, Juan D. Roemer, John E (2011) "A common ground for resource and welfare egalitarianism," Working Papers 11.12, Universidad Pablo de Olavide, Department of Economics 158 Moreno-Ternero, Juan D. Roemer, John E (2008) The Veil Of Ignorance Violates Priority -Economics and Philosophy, 24 (2008) 233–257

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papakonstantinidis Page 83

choice theory to analyze human behavior.

Utility Calculation Example

To postulate the utility function, economists typically make assumptions about the human preferences for different goods. For example, in certain situations, tea and coffee can be considered perfect substitutes of each other and the appropriate utility function must reflect such preferences with a utility form of u(c, t) = c + t, where "u" denotes the utility function and "c" and "t" denote coffee and tea. A consumer who consumes 1 pound of coffee and no tea derives a utility of 1 util.

Von Neumann and O. Morgenstern

Utility functions Mathematically we need a function to map between the physical measure of

money and the perceived value of money. Such functions are called utility functions, and in

the context of wealth being a random variable on a probability space, they need to be

measurable functions on that space, and hence, utility functions are random variables.

Bernoulli was the first to suggest a utility function in 1738 as a solution to the St Petersburg

Paradox159 The theory was developed in its modern form by von Neumann and Morgenstern

in 1944.

159 Bernoulli, Daniel (1738); “Commentaries of the Imperial Academy of Science of Saint Petersurg” Originally published in

1738; translated by Dr. Louise Sommer. (January 1954). "Exposition of a New Theory on the Measurement of Risk"

Econometrica (The Econometric Society) 22 (1): 22–36. AND Weiss Michael D Conceptual foundations of risk theory By ,

United States. Dept of Agriculture Economic Research Service p.36

See at APPENDIX (19) The St. Petersburg game: (This problem was discovered by the Swiss eighteenth-century mathematician

Nicolaus Bernoulli and was published by his brother Daniel in the St. Petersburg Academy Proceedings (1738; English trans.

1954); thus it's called the St. Petersburg Paradox)

A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The pot starts at 2 dollars and is

doubled every time a head appears. The first time a tail appears, the game ends and the player wins whatever is in the pot.

Thus the player wins 2 dollars if a tail appears on the first toss, 4 dollars if a head appears on the first toss and a tail on the

second, 8 dollars if a head appears on the first two tosses and a tail on the third, 16 dollars if a head appears on the first three

tosses and a tail on the fourth, and so on. In short, the player wins 2k dollars, where k equals number of tosses (k must be a

whole number and greater than zero). What would be a fair price to pay the casino for entering the game?

To answer this, one needs to consider what would be the average payout: with probability 1/2, the player wins 2 dollars; with

probability 1/4 the player wins 4 dollars; with probability 1/8 the player wins 8 dollars, and so on. The expected value is thus

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papakonstantinidis Page 84

They developed the axioms underlying utility theory, in a synthesis of economics and

probability, as Utility functions :

Independence of different utility functions (associated with the fact that utility functions are

random variables).

Completeness all outcomes are assigned a utility.

Transitivity if A is preferred to B, and B is preferred to C, then A is preferred to C.

Continuity of utility (if wealth is continuous).

However, the basic attribute of a utility function is that it an increasing function, everyone

would value more money over less money, so:

0)(' xu

. The fact that 0)(' xu means that there is non-satiation, i.e. the agent never becomes

completely satisfied and will always prefer more to less. In the example of the beggar and the

millionaire, we can see that as wealth increases, each additional £1 has a lower perceived

value. This is not surprising and is known as decreasing marginal utility, that is

0')'( xu

Expected utility theory The classical resolution of the paradox involved the explicit introduction of a utility function , an

expected utility hypothesis an and the presumption of diminishing marginal utility of money. In Daniel Bernoulli's own words:

The determination of the value of an item must not be based on the price, but rather on the utility it yields…. There is no doubt

that a gain of one thousand ducats is more significant to the pauper than to a rich man though both gain the same amount. A

common utility model, suggested by Bernoulli himself, is the logarithmic fumction U(w) = ln(w) (known as”log utility”) It is a

function of the gambler’s total wealth w, and the concept of diminishing marginal utility of money is built into it. The expected

utility hypothesis posits that a utility function exists whose expected net change is a good criterion for real people's behavior.

For each possible event, the change in utility ln(wealth after the event) - ln(wealth before the event) will be weighted by the

probability of that event occurring. Let c be the cost charged to enter the game. The expected utility of the lottery now

converges to a finite value:

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papakonstantinidis Page 85

The consumer's utility function ranks each package in the consumption set. If

the consumer strictly prefers x to y or is indifferent between them, .

When When authors begin to map

out the conceptual

landscape of a topic they

should err in favor of

including too many factors,

recognizing that over time

their ideas will be refined. It

is generally easier to delete

unnecessary or invalid ele-

ments than it is to justify

additions.

The 3win model answers to that question: I support that this study is on the

right side Of course, this study does not the total suggestion (there are a lot of

applications and constraints) We support that this work covers the max of

“isolated issues” of the suggestion: it has been attempted the mapping of all the

known variables and constraints (above reffered)

According to all these:

“win-win-win papakonstantinidis model” (Bargaining - Agency -Set- Efficiency Justice-Egalitarian-Socialchoice- Utilitarianism- Sharing Incompleteness-Recursion - Impossibility) is suggested as theory 28////

WHY This is probably the most

fruitful, but also the most

difficult avenue of theory

development. It commonly

involves borrowing a per-

spective from other fields,

which encourages altering

our metaphors and gestalts

in ways that challenge the

underlying rationales

supporting accepted

theories. This profound

challenge to our views of

human nature, group

development, organizational

transactions, and so forth,

generally precipitates a

broad reconceptualization of

affected theories.This aspect

of conceptual development

is particularly critical, and

generally overlooked.

Theories often are

challenged because their as-

sumptions have been proven

unrealistic (generally by

The answer is: There is a big gap in the “social welfare” field Theorists tried to

approach the “social welfare” by using the classical forms of discussion focusing to

" Social Exclusion” i.e the relations of individuals with the society, There is not a

global commonly accepted theory which to includes all the accepted until now i.e

all dispersed theoretical approaches, seemingly unrelated (for example, the

Justice Theory to the Godel’s Incompleteness theorem and Arrow’ Impossibility

Theorem to Pareto efficiency, or the ZFC Set Theory or the Agent-Principle

Theory

So, for example, the Game Theory and the “Bargaining Theory (Nash) were

registered in Mathematical and Statistical Sciences

This approach includes the two theories in Social Sciences as it considers as a

prerequisite that everything in the economy, society, environment fit the game of

"interaction" The “Bargaining Problem constitutes the core of this work

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papakonstantinidis Page 86

work imported from other

areas).

What Is a Legitimate, Value-Added Contribution to Theory Development?

question

Brief

description

Win-win-win papakonstantinidis model

What and how One way to

demonstrate

the value of a

proposed change

in a list of factors

is to identify how

this change

affects the

accepted

relationships

between the

variables (Hows).

Just as a list of

variables does

not constitute a

theory, so the ad-

dition of a new

variable to an

existing list

should not be

mistaken as a

theoretical

contribution.

Relationships,

not lists, are the

domain of theory

why This is probably

the most fruitful,

but also the most

difficult avenue

of theory

development. It

commonly

involves

borrowing a per-

spective from

other fields,

which

encourages al-

tering our

metaphors and

gestalts in ways

that challenge

the underlying

Because, the suggested theory

0),,('max**:arg

0),,('..max

),,(

zyxfUUUUainb

zyxfU

zyxfU

totalCOMMUNITYBA

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papakonstantinidis Page 87

rationales

supporting

accepted

theories. This

profound

challenge to our

views of human

nature, group

development,

organizational

transactions, and

so forth,

generally

precipitates a

broad

reconceptualizati

on of affected

theories

the Venn diagram on the multiplicative relation: intersection 2 cycles

(A,B) :

win-win-win equilibrium should be on the intersection of 3 cycles (the

“C” cycle represents the “C”- Community Factor (intersection of 3 cycles”:

ABC section.. multiplicative effect

The two-person bargaining problem is a problem of understanding how two

agents should cooperate when non-cooperation leads to Pareto inefficient

results.- (a) A two-person bargain problem consists of:

A feasibility set , a closed convex subset of , the elements of which are

interpreted as agreements. Set is convex because an agreement could take

the form of a correlated combination of other agreements. (b) A disagreement,

or threat, point , where and are the respective

payoffs to player 1 and player 2.

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papakonstantinidis Page 88

The problem is nontrivial if agreements in are better for both parties than the

disagreement. The goal of bargaining is to choose the feasible agreement

in that could result from negotiations.

Win-win-win papakonstantinidis model meets the NASH AXIOMS:

1. Invariant to affine transformations or Invariant to equivalent utility

representations

2. Pareto Optimality

3. Independence of irrelevant alternatives

4. Symmetry

Formal definition

Let be a game with players, where is the strategy set for

player , is the set of stradegy

profiles and is the payoff function

for . Let be a strategy profile of player and be a strategy

profile of all players except for player . When each

player chooses strategy resulting in strategy

profile then player obtains payoff .

Note that the payoff depends on the strategy profile chosen, i.e., on the strategy

chosen by player as well as the strategies chosen by all the other players. A

strategy profile is a Nash equilibrium (NE) if no unilateral deviation

in strategy by any single player is profitable for that player, that is

Let S denote a set ( eg collection or listing) of all possible states of the

environment known as the sample space or universe; a typical state is denoted as

s. For example:

• S={s 1, s 2}; success/failure, or low/high price.

• S={s 1, s 2,...,sn-1,s n}; list of units sold or offers received.

• S=[0, ∞ ); stock price or salary offer (continuous positive set space)

Expected payoffs: probabilities (von Neumann, 1944)160 A notation for

a lottery is as follows: if options A and B have probability p and

1 − p in the lottery, we write it as a linear combination:

160 Neumann John von & Morgenstern Oscar (1944) Theory of Games and Economic Behavior, published in 1944Bull. Amer. Math. Soc. 51(07): 498–504

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papakonstantinidis Page 89

More generally, for a lottery with many possible options:

where .

According to these, possible payoff of the “win-win-win papakonstantinidis

theory” forms “sets”( eg collection or listing of all the possible win-win-win

positions, weighting by probabilities set

In this work probabilities are introduced as parts of “sharing” (the total =100

n

c

B

A

CBA

yxU

yU

xU

ό

UUU

)100(

,

,

ΠΡΟΣΟΧΗ…ΣΤΙΣ ΣΕΛΙΔΕΣ

(ΤΕΛΕΥΤΑΙΕΣ

who,when,whe

re

Generally, it is

insufficient to

point out

limitations in

current concep-

tions of a

theory's range of

application. For

example,

discovering that

a mainstream

personnel

selection model

has low

predictive

validity in a

military setting

does not by itself

constitute a

theoretical

contribution.

What factors are considered in judging conceptual ideas, or what constitutes a publishable theory study?

question Win-win-win papakonstantinidis model

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papakonstantinidis Page 90

Brief description

WHAT'S NEW?

Does the idea make a significant,

value-added contribution to

current thinking? Scope tends to

reflect the level of theorizing

(general versus middle level),

while degree reflects the

radicalness of the proposal

The idea makes a significant value-added contribution to

current thinking, due to its suggested thinking

construction: It transfers the 2pole bargain into a 3-pole

bargain, with the Community as the third part So thus

the Community (the “C” factor) is included in the "new"

bargaining’s construction

So WHAT?

Will the theory likely change

the practice of organizational science

in this area? Are linkages to research

evident (either explicitly laid out, or

easily, reliably deduced)?

WHY SO?

Are the underlying logic and

supporting evidence compelling? Are

the author's assumptions explicit? Are

the author's views believable?

WELL DONE?

Does the idea reflect sea-

soned thinking, conveying

completeness and thoroughness? Are

multiple theoretical elements (What,

How, Why, When-Where-Who)

covered? Do the arguments reflect a

broad, current understanding of the

subject? If propositions are included,

are they used properly? Does the argu-

ment have any glaring logical flaws?

Done WELL? Is the idea well written? Does

it flow logically? Are the central ideas

easily accessed? Is it enjoyable to

read? Is the idea long enough to cover

the subject but short enough to be

interesting?

WHY NOW? Is this topic of contemporary

interest to scholars in this area? Will it

likely advance current discussions,

stimulate new discussions, or revitalize

old discussions?

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papakonstantinidis Page 91

SUGGESTION /CONTRIBUTION

Let me say that this paper meets the above necessity, suggesting a new methodological tool

helping to create “new” forms of thinking as well as new forms of human behavior, thus

helping in social conflict solution

Particularly, I tried to identify the "win-win-win" as a key tool for the approach to social

welfare by clicking on the incompatibility of five basic theorems that define it - each one of its

own side-either positive (justice theorem ) or negative (the impossibility theorem)

The suggested "win-win-win papakonstantinidis model”161,162 is built up on these

incompatibilities, in particular as regards the pairs" Pareto efficiency – Impossibility Theorem”

"paradox liberty (Amartya Sen) - Pareto Efficiency” , “Theorem of Justice –Pareto Efficiency”

and (the most important) “the Theorem of incompleteness-the Impossibility Theorem”

The win-win-win papakonstantinidis model is a methodological tool for conflict resolution,

especially in the case of decision making, or in forming "instant reflection winning strategies"

in the BARGAIN (which is the frame) The “win-win-win papakonstantinidis model” concerns

the strategic decision making in a number of fields and domains (biology, psychology,

management, marketing, history- especially in interpretation of historic events-laography,

ethnology, anthropogeography, philosophy, economy, sociology, pure math, communication,

public speech, diplomacy, and go on The reason so many regards thinking and research

fields lies in the very nature of the model, especially in its triple pole perception, which leads

us to see things from another, alternative approach, the triple view, whether in psychology or

interpretation of historical events or diplomacy, or communication, or MANAGEMENT

Special regard is given to regional and local development field both as a regional and social

sciences. It proves that building social capital at local level mainly depends on social trust

links among local people: Social cohesion based on social capital may be measured by the

diversification Rate (R *) from strict globalization rules: From this point of view, local people’s

intervention should be useful, so as to diversify these "rules" at local level adjusting them to

local identity, including communication code, customs, ethics, culture. The Win-win-win

methodology [Papakonstantinidis Model] should facilitate local people to "readjust" bargaining

161 Papakonstantinidis L.A(2002-August 14) “The win-win-win model” Euracademy Guide The Visby University –Gotland Sweden 162 G Spais-Papakonstantinidis L.A (2014)The value of the ‘triple pole’ approach in bargaining for vertical cooperative advertising and the research challenges for the evolution of this topic in the cooperative advertising literature- World Review of Entrepreneurship, Management and Sust. Development, Vol. 10, Nos. 2/3, 2014

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globalization rules locally, through a sensitization process: Community is defined as a discrete

spatial / cultural entity at its sensitization process' limit

The “win-win-win papakonstantinidis model” (2002, August, SW) may, thus, transform

individual winning –instant reflection –strategies (the win-win Nash Theory) in a NEW –three

poles-equilibrium point, including the COMMUNITY (Environmental Protection, Value Systems,

Ethic etc), which is the “absolute cooperation” limit point in the bargain between TWO

At least, “linguistic recursion” is been approached by the Pirahã linguistic idiom as a real

minimalist language, concerning the possibilities of “one-two-many” expression of people

remained isolated

APPLICATION:

The “P.A.C triple-pole circulation based on The Cournot-Theocharis Problem163

Reconsidered164

In 1959 Theocharis showed that with linear demand and constant marginal costs Cournot

equilibrium is destabilized when the competitors become more than three. With three

competitors the Cournot equilibrium point becomes neutrally stable, so, even then, any

perturbation throws the system into an endless oscillation. Theocharis's argument was in fact

proposed already in 1939 by Palander None of these authors considered the global dynamics

of the system, which necessarily becomes nonlinear when consideration is taken of the facts

that prices, supply quantities, and profits of active firms cannot be negative. In the present

paper we address the global dynamics.

APPLICATIONS: Rural Regions’ People-local Authorities-Consumers of R.T services (P.A.C)

CASE STUDY: The “People-Authorities-Consumers (PAC) triangular relations

▲ c.

Concluding,

the win-win-win papakonstantinidis model’s equilibrium does exist: It is when bargainers A,B

and the Community “C”, have equal probabilities to satisfy their needs|. The same conclusions

163 R. D. Theocharis (1960), “On the stability of the Cournot solution on the oligopoly problem,” Review of Economic Studies, vol. 27, pp. 133–134, 1960. 164José S. Cánovasa, Tönu Puub, Manuel Ruízc (2008) The Cournot-Theocharis Problem Reconsidered Chaos, Solitons &Fractals

Volume 37, Issue 4, August 2008, Pages 1025–1039

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are resulted from any other scientific domain (history, psychology, sociology, economics,

management, marketing ….

Since the New-classical School of Thought in Economics focusing on the “bargaining

equilibrium” (Nash Equilibrium) and the equimarginal principle (consumer choice) have been

restarted” by the game theory (exactly: the “non cooperative game theory”) “it seems that the

bargaining behavior is in the centre of our research From this point of view, “bargaining

behavior” is in focus: Maintainig the “Bargening Behavior” in the centre of our research

According to our conjecture (see at the “rainbow concept”) what it needs the modern economy

is a new “restarting”, based on game theory and its extensions

Now, there are two problems to be solved:

1. We must distinguish between “cardinal” and “ordinal” utility

a. “Cardinal utility” (Jeremy Bentham) concerns the inter-personal comparisons, thus

leading in an “objective size” which can be measured; that means: "all people we

have the same needs, the same preferences…and the only one to distinguish

concerns only the “quantity” It says us that the “A” took more bananas from "B" as

the result of the bargaining and so it will be happier than "B" In practice, this is

not the case. The "A" may prefer apple banana or suspect any fruit while B derive

satisfaction from eating bananas or no satisfaction In practice, this is not the case.

The "A" may prefer apple banana or suspect any fruit while B derive satisfaction

from eating bananas or no satisfaction

b. “Ordinal utility” (West-type form- Kant and others) In practice, each of us creates

a personal "satisfaction level in satisfaction lader" which is not comparable with

that of other people only by chance (eg "ice cream" is high on the personal level of

satisfaction of many people .. or even what forms "massive made ones

preferences "imposed" by the media So, the ordinal personal utility is transferred ,

via media in “cardinal”

2. We should note that people have a diffent attitude in a bargain due to their

psychological situation: in a bargain 2 main people types are met: the reckless

investor and the “risk aversion man/woman” Their psychology define the end of any

bargain: Risk aversion people require more and more guaranties to come to an

agreement: “Bargain operates in favor of those risk aversion people

3. At any case, the suggested equilibrium could be a social welfare solution: In the case

of “cardinal utility” it of course satisfies its role: it suggests equal shares for all the 3-

bargain parties (33-33-33) In the case of ordinal utility it is used to restrict the

bargaining power of each of them and at the same time provides the Community (the

“others” ) with more power for two different orientations: (a) for its role as :agent” of

its citizens (the Principles) and as an arbitrator in a dispute between two bargainers

▲

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METHODOLOGY

Part II

Methodology

Theoretical Building blocks

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There are 2 main questions to be answered

1. Does the social welfair exist

2. If yes, then give the theoretical background

NOTE

A. MAIN QUESTION: How could the bargaining problem contribute to social welfare? How

can I find the "new" equilibrium point, concerned the utility of A,B? Bargaining

problem as a part of "negotiation procedure, has been analyzed by the "game non-

cooperative theory (Nash, 1950) But in my mind it should be more fair and social,

thus contributing in "welfare economics" How, can I approach this?

1. comparatively, in our current globalized era,different than 1950's, the elements of

Time, Space, and Size, could be helpful variables, to evaluate the condition of each

and every bargaining, in its own context. A qualitative narrative analysis could be a

useful instrument to go after anthropological, phylosophical, as well as socio-

psychological and socio-cultural aspect of the matter. - Faranack Nader Benz

2. I would just include preference for fairness and social welfare in payoffs. For example

A and B are bargaining and their payoffs are x and y. You can add psychological

preferences to the payoffs like this: X = x + f1 , where f1 is the satisfaction player A

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gets when the outcomes of the bargaining are fair and social. Do the same for Y. Then

just solve for the equilibrium according to Nash (1950). Arthur Tarasov ·

3. Maurice Allais, théorie générale des surplus PUG (Grenoble, France) exchange till every

agent is satisfied. Prices are not given by mathematical models. No hypothesis on

convexity. Dominique Bouf

B. Evidence suggests that a "win-win-win" approach through the process of

"sensitization" creates the basis for a strong socialization through jointly tackling

common problems of a place a "Community" (village, city, region, state) The common

goal at the local level ("flag theme" according to the European terminology) joint

individuals through “team psychology”, allowing everyone / each to freely express his

/ her personality through the common target (Amartya Sen collective choice)165 which

is the development of their own place

C. Is there any strong argument, by which the "win-win-win papakonstantinidis model"

should be defined in terms of the "Principal-Agent" Theory?

Prof Yevgen Bogodistov thinks that the discussion concerns mediators. A mediator is

a principal, or agent. The third party could be understood as a principal, if it had

some power over the first and the second party (giving orders, paying money, etc.).

On the other hand the third party is not an agent - it cannot obey to the will of each

of other parties. The third party, however, comes into play through an invitation by

main parties. In this moment the main parties legitimize it: they give certain power,

for example, to support the decision or to sign the final contract. So, my personal

opinion is that a third party is rather a partner (co-princal) to both of the main parties.

But you ask a very interesting question: 1. how are these relationships regulated?

Probably, by a kind of mutual/ formal/informal contract

2. How is the cognitive level of complex relationships? I completely agree with you

that the more complex the relationship the more "points of view" each party has to

assess. So yes, in triadic relationships 3ach party has to think about its actions, and

actions and perceptions of actions by each other involved party. And probably even

more:

1. Two dimensions - actions and perception of actions

2. Three parties (at least)

Your point is, however, crucial - at the time of information processing the parties

should switch different roles -partner, agent, principal. Plus perception of actions as

partner, agent, and principal I assume that all these tasks are made for each dyad.

But it is important to differentiate between acting as a principal/agent/partner and

thinking from the point of view (aka taking roles) of them. Acting is usually more

powerful in research, but perception has a great influence on actions and on

psychological states afterward (e.g. cognitive dissonance theory).

165 Amartya Sen (1970) Collective Choice and Social Welfare - Holden-Day January 1st 1970

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We have based this work on contradictions between theories themselves or /and theorems,

taking into considerretion the “Russell’s paradox”: it describes a barber who is defined such

that he both shaves himself and does not shave himself. The barber is the "one who shaves

all those, and those only, who do not shave themselves." The question is, does the barber

shave himself?

Answering this question results in a contradiction. The barber cannot shave himself as he only

shaves those who do not shave themselves. As such, if he shaves himself he ceases to be a

barber. If the barber does not shave himself then he fits into the group of people who would

be shaved by the barber (and, so, as the barber he needs to shave himself)

“That contradiction [Russell's paradox] is extremely interesting. You can modify its form; some

forms of modification are valid and some are not. I once had a form suggested to me which

was not valid, namely the question whether the barber shaves himself or not. You can define

the barber as "one who shaves all those, and those only, who do not shave themselves." The

question is, does the barber shave himself? In this form the contradiction is not very difficult

to solve. But in our previous form I think it is clear that you can only get around it by

observing that the whole question whether a class is or is not a member of itself is nonsense,

i.e. that no class either is or is not a member of itself, and that it is not even true to say that,

because the whole form of words is just noise without meaning.”(Bertrand Russell,”The

Philosophy of Logical Atomism)166

In that frame, the question, now, is if “possible contradictions” should be examined inside or

outside the problem

There is an important difference between “being inside the problem”, from one and observing

and studying the problem, from the other:

In the second case we obtain a“mirror's cognition” as the graph below

166 Bertrand Russell (1872–1970) The term was first coined in a 1911 essay by Russell entitled "The Basis of Realism." However, it became widely known only when Russell gave a series of lectures in 1918 entitled "The Philosophy of Logical Atomism". Russell was much influenced by Ludwig Wittgenstein, as an introductory note explicitly acknowledges.

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You can see that the “candle flame” in the mirror perception (apparent source) is the opposite

from the light source

“Some attempted formalizations of thenaive set theory created by Georg Cantor led to a

contradiction” According to naive set theory, any definable collection is a set. Let R be the set

of all sets that are not members of themselves. If R is not a member of itself, then its

definition dictates that it must contain itself, and if it contains itself, then it contradicts its

own definition as the set of all sets that are not members of themselves. This contradiction is

Russell's paradox.

Symbolically:

Having a good starting point, the next step is to find and defined these theoretical

contradictions that concerne the "social welfare" and/or the policy planning's resulted

We have now to approach these contradictions, which will be analyzed in the Chapters II and III

To manipulate with Incompatibilities:

1. The impossibility theorem (1951 Kenneth Arrow: book: Social Choice and Individual

Values, as well as the Amartya Sen “liberal paradox”

2. the theorem of incompleteness (Kurt Gödel (1931)

3. the Rawls Theorem on Justice, 1958)- the veil of ignorance

4. the Nash Equilibrium in Nash “Non cooperative Game Theory 1951(annals of

Mathematics,1951 Vol. 54, No. 2 (Sep., 1951), pp. 286-295)

5. The “Pareto optimality in a 3D space according to

6. Caratheodory conjecture (umbilical points in a sphere), then the main issue in this

research concerns the possibility that a win-win-win communication should exist in

real terms,

7. The agency theory (Stiglitz Joseph 2001) An agency, in general terms, is the

relationship between two parties, where one is a principal and the other is an agent

who represents the principal in transactions with a third party as each of them to win :

]win-win-win equilibrium

8. the ZBC set theory (a selection of objectives)

9. the cognition by linguistic recursion (EVARETT mind recursion (one-many): Human

mind is able to make recursions)

The study aims to highlight the existence and importance of a tri-polar process approach of

scientific and practice - everyday thinking For this purpose develops individual objectives

which reaches through the "thought experiment": In spite of the perception that the test

applies only to materials organic elements, the "thought experiment" adopted in this study

appears to have visible effects on application Thought experiment is adopted by the follow

means:

“The common goal of a thought experiment is to explore the potential consequences of the

principle in question: "A thought experiment is a device with which one performs an

intentional, structured process of intellectual deliberation in order to speculate, within a

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specifiable problem domain, about potential consequents (or antecedents) for a designated

antecedent (or consequent)" (Bowers PM, Cokus SJ, Eisenberg D, Yeate 2004) p. 150)167.The

study goes on by Implicative lattice

We expect that this work is well laid out and logical methodology will provide a great

backbone for the entire research paper, allowed to us build an extremely strong results

section Having some –selective- influences from the Ancient Greek Philosophy (Socrates, Plato,

Aristotle Epicurus), as well as philosophies of the Enlightenment168 and the “Age of Reason”

(such as Locke, Hobbes, Hume Kant & alle)169 as well as from modern rationalist philosophy,

this work combines an empiricist approach with a rationalism that emphasized conceptual

clarity and deductive argument. In this frame the Socratic dialectic method has been adopted

in this work:

o First the prevailing view (thesis) is presented and defined.

o Then this thesis is criticized (antithesis), by the ontological arguments

o Finally, these two opposite perceptions are merged in a unique construction

(synthesis)

o NOTE: [any triple-pole conception, either the essential or methodological approach

has been adopted by this article]

According to the prime objective of the Study (feasibility of social welfare even under capitalist

production and marketing system) and the three main pillars of the methodology adopted by

it, definitions of five theorems and 4 theories are recognized, as domains of "positive

acceptance” (thesis, in ancient Greek philosophy)

The same definitions are examined under a critical view (antithesis) thus leading in their

rejection

Finally, a third completely new aspect (synthesis) raised -I hope- as a result of the merger of

two previous positions / views

Regarding methodological path, which has been selected and given preference over other

alternative methodological choices, methods from the classic David Hume’s scientific work, as

it is expressed by "Research on Human Understanding”170 and “Enquiry Concerning Human

167

Bowers PM, Cokus SJ, Eisenberg D, Yeates (2004) Use of logic relationship to decipher protein network organization

Science Dec 2004. 306(5705):2246-9 168 Stanford Encyclopedia of Philosophy: The Enlightenment is the period in the history of western thought and culture, stretching roughly from the mid-decades of the seventeenth century through the eighteenth century, characterized by dramatic revolutions in science, philosophy, society and politics; these revolutions swept away the medieval world-view and ushered in our modern western world. Enlightenment thought culminates historically in the political upheaval of the French Revolution, in which the traditional hierarchical political and social orders (the French monarchy, the privileges of the French nobility, the political power and authority of the Catholic Church) were violently destroyed and replaced by a political and social order informed by the Enlightenment ideals of freedom and equality for all, founded, ostensibly, upon principles of human reason. The Enlightenment begins with the scientific revolution of the sixteenth and seventeenth centuries. The rise of the new science progressively undermines not only the ancient geocentric conception of the cosmos, but, with it, the entire set of presuppositions that had served to constrain and guide philosophical inquiry. 169 Voltaire Nicolaus Copernicus (19 February 1473 – 24 May 1543), Tycho Brahe (b. 1546-1601) Johannes Kepler (b 1571 –

1630) Galileo Galilei (b. 1564 – 1642) Isaac Newton (b. 1643 – 1727) …The Philosophical Revolution or the Age of Reason Rene

Descartes 1596 – 1650 Benedict Spinoza 1632 – 1677 Francis Bacon 1561 – 1626 Thomas Hobbes 1588 – 167 John Locke 1632 –

1704 David Hume 1711 – 1776 Jean-Jacques Rousseau 1712 – 1778 Immanuel Kant 1724 – 1804 de Montesquieu January 1689

– 10 February 1755), Baccarat, Helvetius, Diderot, D' Alembert,..) 170

Hume David (1748) “Philosophical Essays Concerning Human Understanding” (1 ed.). London: A. Millar. Retrieved28

June 2014 via Google Books

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papakonstantinidis Page 100

Understanding”171 and Jeremy Bentham’s “An introduction to the principles of morals and

legislation”172 focused on:

o the importance of logic against custom and tradition and

o precision in the use of terms, have been adopted

so that other researchers can review the results by replicating the research and guaranteeing

the validity. By this necessity a completely accurate description of the equipment and the

techniques used for gathering the data have been planned and executed, providing at the

same time an explanation of how the raw data was compiled and analyzed. The followed

methodology allows the readers to make their own decision about the validity of the data, thus

any reader to understand how research data have been obtained, allowed them to evaluate the

quality of the results

Behavior’s Assumptions

1. Any decision making may be considered as the output of the behavioral trends in any

bargain, between two (2) (Papakonstantinidis, 2007)173.

2. Public involvement –especially in the development strategy /or/planning is achieved

by five (5) easy stages (steps), i.e information, sensitization, participation, involvement

and partnership, in its main version (Arnstein, 1969)174 This process influences the

behavior in the bargain.

3. There is interaction between behavior and bargain. There is no bargain without

behavior. There is no behavior without bargain (Papakonstantinidis, 2011)175

4. Each of the three poles behavioral interacts with other within the bargain and during

the bargain

5. All individuals are indifferent between any two probability distributions over social

states -Pareto efficiency (Pareto, 1916176; Stiglitz, 1987)177.

171 Hume David (1748) “Philosophical Essays Concerning Human Understanding” (1 ed.). London: A. Millar. Retrieved28 June 2014 via Google Books 172 Bentham, Jeremy (1780) Introduction to the Principles of Morals and Legislation- The First Edition of this work was privately printed in 1780 and first published in 1789. T second edition, 1823, chapter 17, 173

Papakonstantinidis (2007) Sustainable Development and Local Capacities in Rural Areas the ISA Congress’s Minutes, 2007

Jun 14 174 Arnstein, Sherry R. (1969)"A Ladder of Citizen Participation," JAIP, Vol. 35, No. 4, July 1969, pp. 216-224 175 Papakonstantinidis L.A -Spais, George S (2011) An Application of the Win-Win-Win Papakonstantinidis Model as an

Innovative Bargaining Solution Analysis in Cooperative Sales Promotion Campaigns

Proceedings of the 4th Annual Euromed Conference of the Euromed Academy of Businessp.p1724-1744

176 Pareto Vilfredo (1916). Trattato Di Sociologia Generale (4 volumes) G. Barbéra, 1916 177 Stiglitz Joseph E.(1987) The Causes And Consequences of the dependence of Quality on Price . Journal of Economic Literature, Vol. 25, No. 1 (Mar., 1987), pp. 1-48(American Economic Association) .Vol. XXV (March 1987), pp. 1-48

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papakonstantinidis Page 101

6. Conversion of a given behavior could be realized by using the same conflict rules that

push the PAC members in converging their behavior (Reynolds, 1999)178 In fact it is a NEW

behavior toward the absolute cooperation.

7. Conditions of Conflict behavior are developed in the frame of the "Instrumental

Rationality” in an environment of Common Knowledge of Rationality179.

8. “Sensitization” as a form of knowledge/information should be taught, thus influencing

the PAC 3-ple power poles (Papakonstantinidis, 1996, 1999, 2002, 2004180,

9. Behavioral analysis should be broached in close correlation with the suggested “win-

win-win papakonstantinidis model” and its usefulness in respect to local communities’

management and development (Herbert Simon 1955)181,

Starting from the “zero sum two players game” (John von Neumann- Oscar Morgenstern

1944)182 in the form of “win- lose” at any bargain, then was the John Forbs Nash who made

the difference, letting in both bargainers to win (win-win) But, for another time this bargain

was rather to the side of the winners (due to their bargaining force) than eliminating social

inequalities (the winner takes it all)

With this aim an hypothetical dipole bargain between 2 bargainers (*A,B) converted into 3-

pole by introducing the "Community" (the village, the town, the inhabitants of a country, a

continent, planet, after all) as a third pole in any bargain (win-win-win)

So the concept is to construct a theoretical-original-model so that it should respond better to

the conditions of "social welfare"

With this aim an hypothetical triple-pole bargain between 2 (A and B and the "Community"

included as the third pole) is a basis for scientific dialogue By the tem “Community” we can

178Reynolds, C. W. (1999) Steering Behaviors For Autonomous Characters, in the proceedings of Game Developers Conference 1999 held in San Jose, California Miller Freeman Game Group, San Francisco, California. Pages 763-782 179 Varoufakis Gianis (2007) “Game Theory” Gutenberg edition, Athens GR 2007 180 Papakonstantinidis L (1996) . The Sensitized Community 1st edition MAREL-NIKAS 2nd , 3rd and 4th editions, Gutenberg Ed (2009-2008) AND Papakonstantinidis L. (1999). “Local Sensitivity and the Bottom- up Approach: Methodological Tools for an Integrated, In-depended Development on Rural Areas in Greece” (L.E.A.D.E.R E.U Initiative Application in Greece)- 1999, ISA Review, RC-26 AND Papakonstantinidis, L. (2003). “Sensitization & the win-win-win model: An answer to Globalization’s Impact on Local Communities and Common Perceptions of the World Tendencies- Case Study : Community Redefinition- Tychero Evros” (2003 the ISA, RC-26 Review (vol 2003) AND Papakonstantinidis, L. (2004). “Sensitization and Involvement the Community: A Rural Tourism Application of the win-win-win Model” Review of Economic Sciences”-TEIEP, issue 6 (Piraeus- TEIEP Ed) AND Papakonstantinidis, L. (2004). “Sensitization as a form of knowledge creation and the Win-Win-Win Model…” Scientific Review of Applied Research, Vol VIII, No 2 /2003, pp 89-108, ISSN 1106-4110 AND Papakonstantinidis, L. (2004). Rural Tourism: The win-win-win Model” JOHAT /JENSEN India pp 30-47 AND Papakonstantinidis, L. (2005). Uj Iranyok a Regionalis Politikaban a Terulet-ter Mechatarozasa Haruomszintu Alkufolymatkent- A “Nuer-Nyer-Nyer Modell” Esettanulmany: A LEADER EU Kezdemenyezes Alkalmazasa Gorogorszagban (New trends in Regional Policy :Territory-Space Definition by a 3-level Bargaining Approach- The win-win-win model . Case study The LEADER EU Initiative Application in Greece- “Ter es Tarsadalom” (Journal of Space and Society) - Hungarian Academy of Sciences/Regional Studies Dpt - XIX enf 2005 iss 3-4pp 95-109 181. Simon Herbert A (1955) A Behavioral Model of Rational Choice The Quarterly Journal of Economics Vol. 69, No. 1. (Feb., 1955), pp. 99-118 182 John von Neumann- Oscar Morgenstern (1944) “theory of games and economic behavior” –PRINCETON University Press Edition

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imagine any common structure, i.e the village, the town, the inhabitants of a country, a

continent, planet, after all-

The point is that the third pole (the Community) will claim its own profits, in a future

negotiation It is about a "win-win-win" concept which is now the global requirement For

example, the first concrete example has to do with environmental protection Climate change

leaves no room to 2 competitors without considering the entire rest of the world Each

negotiation between 2 concerns the entire planet The how achieved in practice I think it can be

done with Laws, as long as there is the political will of Another Dimension It has to do with the

war see the two superpowers to compete by focusing on the war in the Middle East (Syria and

Iraq) But the agreement or disagreement affects millions of people in the two countries who

come as refugees to Europe

The recognition of the third pole in our daily life is connected with its social necessity

Without any imposition by dictatorial regimes, the 3-pole approach to bargaining, is necessary

and unavoidable if and only if humankind seeks survival solutions

In a “win-win-win” negotiation there is more possibility of achieving social welfare: This can

be proved by the math example below

On the other side we have 5 basic foundational and global known Theorems which are

incompatible So the concept here was to put them one against the other and seek "material" to

build the new

For example, the Incompleteness Theorem (Gödel) fades the Impossibility Theorem (K. Arrow)

and the Pareto Efficiency is basic for the Impossibility Theorem, but not for the “Justice

theorem (Rawls) But from these incompatibilities arises a necessity of completeness,

effectiveness, universal justice, a necessity of "umbilical points" freedom , economic

equilibrium The synthesis of all these lead to a situation utopia (romantic, idealistic) will

certainly not get, but from the other shows us a path of self-preservation and survival if the

goal is not suicidal

Besides, the proposed “win-win-win situation” has to face the market’s “information

asymmetry” and the “principal–agent problem” (also known as agency dilemma or theory of

agency) For this, the article lays out the “principal-agent problem” in order to make an wide

estimation on relation between "individual" and social (Community) interests Furthermore, he

“principal-agent” Theory help us to focus on the concept of “double thinking” bargaining

solution: one for him/her self (as “principles” and, at the same time as “representatives”

(agents) of the whole community see at “Social Contract (J,J Rousseau) 183

The Structure Sections, step by step

1. Accurate Description of materials and equipment used in the research

183 Jean Jacques Rousseau (1762) Du contrat social (ou Principes du droit politique) book Edité par Oxford at the Clarendon Press, London (1972)

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2. Explanation of how the samples were gathered, any randomization techniques and

how the samples were prepared

3. Explanation of how the measurements were made and what calculations were

performed upon the raw data

4. Describe the statistical techniques used upon the data

5. GENERAL NOTE: As it is known, that is the very basic structure of writing

methodology, and it will clarify all of the information, clear and direct, concise and

straight to the point

David Hume and Jeremy Bentham saw in him a model of one who emphasized the importance

of reason over custom and tradition and who insisted on precision in the use of terms. Hume's

influence was not so much on Bentham's method as on his account of the underlying

principles of psychological associationism and on his articulation of the principle of utility,

which was then still often annexed to theological views.

Bentham's analytical and empirical method is especially obvious when one looks at some of

his main criticisms of the law and of moral and political discourse in general. His principal

target was the presence of "fictions"—in particular, legal fictions. On his view, to consider any

part or aspect of a thing in abstraction from that thing is to run the risk of confusion or to

cause positive deceit. While, in some cases, such "fictional" terms as "relation," "right,"

"power," and "possession" were of some use, in many cases their original warrant had been

forgotten, so that they survived as the product of either prejudice or inattention. In those

cases where the terms could be "cashed out" in terms of the properties of real things, they

could continue to be used, but otherwise they were to be abandoned. Still, Bentham hoped to

eliminate legal fictions as far as possible from the law, including the legal fiction that there

was some original contract that explained why there was any law at all. He thought that, at the

very least, clarifications and justifications could be given that avoided the use of such terms.

For Bentham, morals and legislation can be described scientifically, but such a description

requires an account of human nature. Just as nature is explained through reference to the laws

of physics, so human behavior can be explained by reference to the two primary motives of

pleasure and pain; this is the theory of psychological hedonism. Bentham's analytical and

empirical method is especially obvious when one looks at some of his main criticisms of the

law and of moral and political discourse in general. His principal target was the presence of

"fictions"—in particular, legal fictions. On his view, to consider any part or aspect of a thing in

abstraction from that thing is to run the risk of confusion or to cause positive deceit. While, in

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some cases, such "fictional" terms as "relation," "right," "power," and "possession" were of

some use, in many cases their original warrant had been forgotten, so that they survived as

the product of either prejudice or inattention. In those cases where the terms could be "cashed

out" in terms of the properties of real things, they could continue to be used, but otherwise

they were to be abandoned. Still, Bentham hoped to eliminate legal fictions as far as possible

from the law, including the legal fiction that there was some original contract that explained

why there was any law at all. He thought that, at the very least, clarifications and justifications

could be given that avoided the use of such terms.

Finally, “synthesis” of that diametric opposite conceptions leads in the "new" (synthesis) that

results from their merge

Dialectic –that Socrates first taught-is the most famous methodological form, in modern

times: Hegel has adopted the Socratic dialectic and diffuses this in the “west” and from then

in the world: Georg Wilhelm Friedrich Hegel (1770-1831)184 was a holdover of Socrates in the

years of European Enlightenment, as adopted and extended the “dialectic” as a scientific

methodological tool

Hegel’s primary object185 in his dialectic is to establish the existence of a logical connection

between the various categories which are involved in the constitution of experience. He

teaches that this connection is of such a kind that any category, if scrutinized with sufficient

care and attention, is found to lead on to another, and to involve it, in such a manner that an

attempt to use the first of any subject while we refuse to use the second of the same subject

results in a contradiction. The category thus reached leads on in a similar way to a third, and

the process continues until at last we reach the goal of the dialectic in a category which

betrays no instability. If we examine the process in more detail, we shall find that it advances,

not directly, but by moving from side to side, like a ship tacking against an unfavorable wind.

The simplest and best known form of this advance, as it is to be found in the earlier

transitions of the logic, is as follows. The examination of a certain category leads us to the

conclusion that, if we predicate it of any subject, we are compelled by consistency to predicate

of the same subject the contrary of that category. This brings us to an absurdity, since the

predication of two contrary attributes of the same thing at the same time violates the law of

contradiction. On examining the two contrary predicates further, they are seen to be capable

of reconciliation in a higher category, which combines the contents of both of them, not

merely placed side by side; but absorbed into a wider idea, as moments or aspects of which

they can exist without contradiction. This idea of the synthesis of opposites is perhaps the

most characteristic in the whole of Hegel’s system. It is certainly one of the most Studies in

184 Hegel Georg Wilhelm Friedrich (1817) The Encyclopedia of the Philosophical Sciences in Outline (1817) (German: Enzyklopädie der philosophischen Wissenschaften im Grundrisse, 1817)

185 Hegel Georg Wilhelm Friedrich (1817Philosophy of Nature (Part Two of the Encyclopaedia of Philosophical Sciences), trans.

Michael John Petry, 3 vols., (London: George Allen and Unwin, 1970). Hegel's Philosophy of Nature, tr. A. V. Miller, 1970

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the Hegelian Dialectic186 difficult to explain. Indeed the only way of grasping what Hegel

meant by it is to observe in detail how he uses it, and in what manner the lower categories are

partly altered and partly preserved in the higher one, so that, while their opposition vanishes,

the significance of both is nevertheless to be found in the unity which follows. Since in this

way, and in this way only so far as we can see, two contrary categories can be simultaneously

true of a subject, and since we must hold these two to be simultaneously true, we arrive at the

conclusion that whenever we use the first category we shall be forced on to use the third,

since by it alone can the contradictions be removed, in which we should otherwise be involved.

This third category, however, when it in its turn is viewed as a single unity, similarly discloses

that its predication involves that of its contrary, and the Thesis and Antithesis thus opposed

have again to be resolved in a Synthesis. Nor can we rest anywhere in this alternate production

and removal of contradictions until we reach the end of the ladder of categories. It begins with

the category of Pure Being, the simplest idea of the human mind. It ends with the category

which Hegel declares to be the highest— the Idea which recognizes itself in all things187

1. According to the main objective ….

In this framework, the “principal-agent problem” is analyzed in order to yield useful

conclusions to be used as a basis for analyzing the "win-win-win papakonstantinidis" general

equilibrium And this, because the "problem of principal-agent" is a unique event in which the

person is asked to think twice: one for himself and one for his principal, thus forming a series

of other problems caused by the theory markets with asymmetric information "which in turn

leads to “adverse selection” ( the principal side) or to "moral hazard"(the agent side), due to

the “asymmetric information in the market It's with Stiglitz188, though, that information

asymmetry has reached mainstream acclaim, using a theory of market screening189, Through

Stiglitz's work, asymmetric information was placed into contained general equilibrium models

to describe negative externalities that price out the bottom of markets. For instance, the

uncertain health insurance premium needed for high-risk individuals causes all premiums to

rise, forcing low-risk individuals away from their preferred insurance policies.

2,1 AGENCY THEORY

In economic agency190, the problem is one of selecting a compensation system that will

produce behavior by the agent consistent with the principal’s preferences. Thus the focus is

on the nature of the incentive system and the contracting system that guides the distribution

186 Hegel Georg Wilhelm Friedrich (1817) Philosophy The Encyclopaedia Logic: Part 1 of the Encyclopaedia of Philosophical

Sciences, trans. T. F. Geraets, W. A. Suchting, and H. S. Harris (Indianapolis: Hackett, 1991). 187Taggart John McEllis McTaggart (J. M. E. McTaggart) ( (1922) “Studies in the Hegelian Dialectic” Cambridge University Press.

Second Edition (1922-First Edition was published in 1896)

188 Stiglitz Joseph E. (1975) The Theory of "Screening," Education, and the Distribution of Income- The American Economic Review Vol. 65, No. 3 (Jun., 1975), pp. 283-300 189 Market SCREENING Definition The process of discovering relevant information about a tradable asset in order to determine a fair price for the asset Primarily used to avoid creating an adverse transaction For example, an investor will conduct market screening to see if a company's operations support a stock price. 190 Ross, Stephen A. 1973. The economic theory of agency: The principal's problem. American Economic Review 62(2): 134-139.

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of those incentives, as well as the conditions of risk and information that condition the choices

of the actors191.

Origin of the Theory of Agency the pre-history

1. The first scholars to propose, explicitly, that a theory of agency be created, and to actually begin

its creation, were Stephen Ross and Barry Mitnick, independently and roughly concurrently.

2. Ross is responsible for the origin of the economic theory of agency, and Mitnick for the

institutional theory of agency, though the basic concepts underlying these approaches are

similar. Indeed, the approaches can be seen as complementary in their uses of similar concepts

under different assumptions. In short, Ross introduced the study of agency in terms of problems

of compensation contracting; agency was seen, in essence, as an incentives problem.

3. Mitnick introduced the now common insight that institutions form around agency, and evolve to

deal with agency, in response to the essential imperfection of agency relationships: Behavior

never occurs as it is preferred by the principal because it does not pay to make it perfect. But

society creates institutions that attend to these imperfections, managing or buffering them,

adapting to them, or becoming chronically distorted by them. Thus, to fully understand agency,

we need both streams -- to see the incentives as well as the institutional structures.

2.

There is a fine line between "legal" and "moral" representation (the "agency" side).The moral

representation from the general concept of morality (ethics) as developed through the

centuries It must be acknowledged that "We are part of a whole and not individual or separate

191 Mitnick, Barry M. 1974a. The theory of agency: The concept of fiduciary rationality and some consequences. Unpublished Ph.D. dissertation Department of Political Science, University of Pennsylvania Univ. Microfilms No. 74-22,881

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units" In this sense everyone is a potential "agent" of all the community interest (principle)

come from “market signaling and screening”192

SET THEORY; (BASED ON BOELEAN ALGEBEA)

Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis

of Logic (1847), and set forth more fully in his “An investigation of the Laws of

thought (1854)193

Metthodology followed in this work has adopted a

194

NOTE: In propositional logic195 and Boolean algebra,

1. De Morgan's laws are a pair of transformation rules that are both valid rules of

inference. They are named afterAugustus De Morgan, a 19th-century British

mathematician. The rules allow the expression of conjunctions and disjunctions purely

in terms of each other vianegation.

192 Stiglitz, Joseph and Andrew Weiss (1989) “Sorting out the Differences Between Screening and Signalling Models,” in Papers in Commemoration of the Economic Theory Seminar at Oxford University, edited by Michael Dempster, Oxford: Oxford University Press. 193 Boole George (2003) [1854] An Investigation of the Laws of Thought- Prometheus Books 194 See at Appendix (6) 195

Propositional calculus (also called propositional logic, sentential calculus, or sentential logic) is the branch of mathematical

logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components. Logical connectives are found in natural languages. In English for example, some examples are "and" (conjunction), "or" (disjunction), "not” (negation) and "if" (but only when used to denote material conditional).

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The rules can be expressed in English as:

The negation of a conjunction is the disjunction of the negations.

The negation of a disjunction is the conjunction of the negations.

or informally as:

)"....()....(.."........)"......("

)"....()......(......)..("

BnotandAnotassametheisBorAnot

also

BnotorBnotassametheisBAnot

The rules can be expressed in formal language with two propositions P and Qas:

and

where:

is the negation logic operator (NOT),

is the conjunction logic operator (AND),

is the disjunction logic operator (OR),

is a metalogical symbol meaning "can be replaced in a logical proofwith".

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Example:

2. Idempotence is the property of certain operations in mathematics and computer

science,that can be applied multiple times without changing the result beyond the

initial application. The concept of idempotence arises in a number of places in

abstract algebra (in particular, in the theory of projectors and closure operators) and

functional programming (in which it is connected to the property of referential

transparency). The term was introduced by Benjamin Peirce in the context of elements

of algebras that remain invariant when raised to a positive integer power, and literally

means "(the quality of having) the same power", from idem + potence (same + power).

There are several meanings of idempotence, depending on what the concept is

applied to: A unary operation (or function) is idempotent if, whenever it is applied

twice to any value, it gives the same result as if it were applied once; i.e., ƒ(ƒ(x)) ≡ ƒ(x).

For example, the absolute value function, where abs(abs(x)) ≡ abs(x).

Given a binary operation, an idempotent element (or simply an "idempotent") for the operation

is a value for which the operation, when given that value for both of its operands, gives that

value as the result. For example, the number 1 is an idempotent of multiplication: 1 × 1 = 1.

A binary operation is called idempotent if all elements are idempotent elements with respect

to the operation. In other words, whenever it is applied to two equal values, it gives that value

as the result. For example, the function giving the maximum value of two equal values is

idempotent: max (x, x)

3. In mathematics, a binary operation is commutative if changing the order of the

operands does not change the result. It is a fundamental property of many binary

operations, and many mathematical proofs depend on it. Most familiar as the name of

the property that says "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be

used in more advanced settings

4. Distributive: The distributive property tells us how to solve equations in the form of

a(b + c) The distributive property is sometimes called the distributive law of

multiplication and division. In abstract algebra and formal logic, the distributive

property of binary operations generalizes the distributive law from elementary

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algebra. In propositional logic, distribution refers to two valid rules of replacement.

The rules allow one to reformulate conjunctions and disjunctions within logical proofs

5. Law of identity, principle of logic stating that an object is the same as itself

A∪∅=AA∪∅=A

I can understand this one. AA union nothing is still AA. In the same way

that 1+01+0 is still 11.

However, it goes on to say:

A∪U=U

6. In set theory, a complement of a set A refers to things not in (that is, things outside

of) A. The relative complement of A with respect to a set B is the set of elements in B

but not in A. When all sets under consideration are considered to be subsets of a

given set U, the absolute complement of A is the set of all elements in U but not in A.

The relative complement of A (left circle) in B (right circle):

This paper has adopted the methodological tools of logic arising from the above properties of

set AND NETWORKING theory

CHAPTER 5

From the generalization to specialization

NETWORKING

and

UMPILICAL POINT on a sphere: the domain of the “win-win-win papakonstantinidis model’s definition

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INTRODUCTION

The main points of the Chapter V are:

Title of the points.. answering in:

1 the network of human relationships what

2 the network of “reactive” individual choices when

3 the network of the “instant reflection winning strategies how

4 The domain of the networking function* where

Starting from Pareto optimality and Nash Equilibrium in the NCG (No Cooperative Game) Theory, the

concept is to formulate a “new” equilibrium among three independent bargainers(A-B-C), each of whom,

may claim its own profit In addition the "C" (community) player must claim profit for all people, including

the A-B bargainers TABLE

Pareto Optimality (1906)196

Essentially, Pareto optimality describes a state of affairs in which resources are distributed such that it is

not possible to improve a single individual without also causing at least one other individual to become

worse off than before the change. It provides those studying economics with a certain perspective and

criteria for judging the efficiency of a distribution system. Additionally, this way of looking at economic

efficiency and income distribution helped Pareto and other contemporary economists develop

microeconomics as a field and discipline of study. Related to the idea of Pareto optimality is that of a

Pareto improvement.

A Pareto improvement is a term used when looking at a distribution of goods within a system from the

perspective of Pareto optimality.

A Pareto improvement is said to have taken place if a change is made in the distribution of goods or

resources that results in at least one individual being better off than before the change while not making

any other individual worse.

196 E-P Dept Dept Advice specialists http://www.economyprofessor.com/pareto-optimality-1906

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Another way of describing Pareto optimality is to describe any state as Pareto optimal when no Pareto

improvement is possible. This effectively means that it is impossible to improve the condition of any

single individual without harming the condition of another individual.

NETWORKING

Network theory197 is the study of graphs as a representation of either symmetric relations or, more

generally, of asymmetric relations between discrete objects. Network theory is a part of graph theory It

has applications in many disciplines

Network theory198 is the study of complex interacting systems that can be represented as graphs

equipped with extra structure. A graph is a bunch of vertices connected by edges:

Generally, networking may be seen as a function (the networking function)

),,,,,,,( enlpnsotpecbcadvnfPnet , where,

nodes(n), arcs (a), degree (odd-even) of vertices (dv), betweenness centrality (bc), eccentric(ec), tactical

positioning(tp), strong orientation (so), the Extent to which a Node Lies on a Path to other Nodes (enlpn)199

NETWORKS IN ECONOMICS:

the world economic net200

197 Newman, M.E.J (2010). Networks: An Introduction. Oxford University Press 2010 198 Baez, John C. (ed.) (1994) Knots and quantum gravity Oxford: Clarendon Press (imprint: Oxford University Press) 199 Papakonstantinidis L.A (2015)“The win-win-win papakonstantinidis model-Proposal on welfare economics

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Suppose we have a population of agents of two kinds: 'aggressive' (A) and 'cooperative' (C). Their

dynamics might be described by this reaction network: People use ‘network theory’ to mean the study of

large graphs, and how they change with time.

This is from a paper on the “network of global corporate control” which analyzed ownership links between 600,000 companies.

Reaction networks are also implicit in evolutionary game theory, a topic important in biology and

economics. For example, suppose we have a population of agents of two kinds: ‘aggressive’ (A) and

‘cooperative’ (C). Their dynamics might be described by this reaction network:

,,......... CONSTANTSsomefor

CCCCC

CA

AAAa

The idea is that aggressive agents sometimes destroy the agents they meet, while cooperative ones

sometimes reproduce.

We could elaborate this example indefinitely by introducing more kinds of agents: for example, agents

with different strategies, locations, or resources

More formally, to give a reaction network we start with any finite collection of species

kAAA ,..,. 21

We define a complex to be a linear combination of species with natural number coefficients, e.g.

4312 AAA

We define a reaction network to be a graph with:

200 Baez John (2015) Network Theory Azimouth Project December 22, 2015

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o vertices labeled by complexes

o edges labeled with arrows and also positive rate constants.

A reaction network gives an evolutionary game with stochastic dynamics. The idea is to write down201 a

vector whose components are the probabilities that the species present are described by any

given complex. Then evolve according to the master equation:

)1...(

Hdt

d

:.........

,............,,..........

soanotherturnscomplexone

whichatrateticprobabilisthedescribeentrieswhosematrixisH

Hdt

d

Where

.................... becameswhichatrateticprobabilistheisH

History

Euler's solution of the “The Seven Bridges of Königsberg problem”202 is considered to be the first true

proof in the theory of networks First, Euler pointed out that the choice of route inside each land mass is

irrelevant. The only important feature of a route is the sequence of bridges crossed. This allowed him to

reformulate the problem in abstract terms (laying the foundations of graph theory), eliminating all

features except the list of land masses and the bridges connecting them. In modern terms, one replaces

each land mass with an abstract "vertex" or node, and each bridge with an abstract connection, an "edge”

which only serves to record which pair of vertices (land masses) is connected by that bridge. The resulting

mathematical structure is called a graph. Next, Euler observed that (except at the endpoints of the walk),

whenever one enters a vertex by a bridge, one leaves the vertex by a bridge. In other words, during any

walk in the graph, the number of times one enters a non-terminal vertex equals the number of times one

201 Baez John (2015) Network Theory Azimouth Project December 22, 2015

202The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonard Euler in

1736 laid the foundations of GRAPG THEORY and prefigured the idea of topology The city of The Seven Bridges of

Königsbergin Prussia (now, Kalinegrad Russia ) was set on both sides of the Pregel River, and included two large islands which

were connected to each other and the mainland by seven bridges. The problem was to devise a walk through the city that

would cross each bridge once and only once, with the provisos that: the islands could only be reached by the bridges and every

bridge once accessed must be crossed to its other end. The starting and ending points of the walk need not be the same. The

difficulty was the development of a technique of analysis and of subsequent tests that established this assertion with

mathematical rigor.

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leaves it. Now, if every bridge has been traversed exactly once, it follows that, for each land mass (except

for the ones chosen for the start and finish), the number of bridges touching that land mass must

be even203 (half of them, in the particular traversal, will be traversed "toward" the landmass; the other half,

"away" from it). However, all four of the land masses in the original problem are touched by an odd

number of bridges (one is touched by 5 bridges, and each of the other three is touched by 3). Since, at

most, two land masses can serve as the endpoints of a putative walk, the proposition of a walk traversing

each bridge once leads to a contradiction. In modern language, Euler shows that the possibility of a walk

through a graph, traversing each edge exactly once, depends on the degrees of the nodes. The degree of

a node is the number of edges touching it. Euler's argument shows that a necessary condition for the walk

of the desired form is that the graph be connected and have exactly zero or two nodes of odd degree.

Besides, we take into consideration the use of some tools from network theory to describe the strategy of

football teams204. Using passing data made available by FIFA during the 2010 World Cup, we construct for

each team a weighted and directed network in which nodes correspond to players and arrows to passes.

The resulting network or graph provides a direct visual inspection of a team’s strategy, from which we can

identify play pattern, determine hot-spots on the play and localize potential weaknesses. Using different

centrality measures, we can also determine the relative importance of each player in the game, the

‘popularity’ of a player, and the effect of removing players from the game.

Network optimization

Network problems that involve finding an optimal way of doing something are studied under the name

combinatorial optimization. Examples include network flow, shortest path problem, transport problem,

transshipment problem, location problem, matching problem, assignment problem, packing problem,

routing problem, Critical Path Analysis

203the sets of even and odd numbers can be defined as following Even Odd 204Pena Javier López & Touchette Hugo (2012) “A network theory analysis of football strategies” July 2, 2012. arXiv:1206.6904v1 [math.CO] 28 Jun 2012

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Social Network analysis

Visualization of social network analysis:

Social Network Analysis examines the structure of relationships between social entities. These entities are

often persons, but may also be groups, organizations, nation states, web sites, scholarly publications

Since the 1970s, the empirical study of networks has played a central role in social science, and many of

the mathematical and statistical tools used for studying networks have been first developed in sociology

Amongst many other applications, social network analysis has been used to understand the diffusion of

innovations, news and rumors. Similarly, it has been used to examine the spread of both diseases

and health-related behaviors. It has also been applied to the study of markets, where it has been used to

examine the role of trust in exchange relationships and of social mechanisms in setting prices. Similarly, it

has been used to study recruitment into political movements and social organizations. It has also been

used to conceptualize scientific disagreements as well as academic prestige. More recently, network

analysis (and its close cousin traffic analysis) has gained a significant use in military intelligence, for

uncovering insurgent networks of both hierarchical and leaderless nature.

Centrality measures: Information about the relative importance of nodes and edges in a graph can be

obtained through centrality measures, widely used in disciplines like sociology For example eigenvector

centrality uses the eigenvectors of the adjacency matrix corresponding to a network, to determine nodes

that tend to be frequently visited. Formally established measures of centrality are degree centrality, sub-

graph centrality closeness centrality, betweenness centrality, eigenvectors centrality, The purpose or

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objective of analysis generally determines the type of centrality measure to be used. For example, if one is

interested in dynamics on networks or the robustness of a network to node/link removal, often the

dynamical importance of a node is the most relevant centrality measure.

Network optimization

Network problems that involve finding an optimal way of doing something are studied under the name

combinatorial optimization. Examples include network flow, shortest path problem, transport problem,

transshipment problem, location problem, matching problem, assignment problem, packing problem,

routing problem, Critical Path Analysis and PERT (Program Evaluation & Review Technique).

Euler approached this problem by collapsing areas of land separated by the river into points, which he

labeled with capital letters. Modern graph theorists call these vertices, and have gone on to represent

them and bridges graphically.

For Konigsberg, let us represent land with red dots and bridges with black curves, or arcs:

Thus, in its stripped down version, the seven bridges problem looks like this:

The problem now becomes one of drawing this picture without retracing any line and without picking your

pencil up off the paper. Consider this: all four of the vertices in the above picture have an odd number of

arcs connected to them. Take one of these vertices205, say one of the ones with three arcs connected to it.

Say you're going along, trying to trace the above figure out without picking up your pencil. The first time

you get to this vertex, you can leave by another arc. But the next time you arrive, you can't. So you'd

better be through drawing the figure when you get there! Alternatively, you could start at that vertex, and

then arrive and leave later. But then you can't come back. Thus every vertex with an odd number of arcs

attached to it has to be either the beginning or the end of your pencil-path. So you can only have up to

two 'odd' vertices! Thus it is impossible to draw the above picture in one pencil stroke without retracing.

The Generalization to Graph Theory: Euler went on to generalize this mode of thinking, laying a

foundation for graph theory. Using modern vocabulary, we make the following definitions and prove a

theorem:

Definition: A network is a figure made up of points (vertices) connected by non-intersecting curves (arcs).

205 N. L. Biggs, E. K. Lloyd and R. J. Wilson(1976), Graph Theory 1736–1936, Clarendon Press, Oxford, 1976, 8–9,

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Definition: A vertex is called odd if it has an odd number of arcs leading to it, otherwise it is called even.

Definition: An Euler path206 is a continuous path that passes through every arc once and only once.

Theorem: If a network has more than two odd vertices, it does not have an Euler path.

Euler also proved this:

Theorem: If a network has two or zero odd vertices, it has at least one Euler path. In particular, if a

network has exactly two odd vertices, then its Euler paths can only start on one of the odd vertices, and

end on the other.

Euler stated the rules in two theorems:

Euler's Theorem 1

o If a graph has any verticies of odd degree, then it cannot have an Euler Circuit.

o If a graph has all even verticies, then it has at least one Euler Circuit - usually more.

Euler's Theorem 2

If a graph has more than 2 verticies of odd degree, then if cannot have an Euler Path, and

If a graph is connected and has exactley 2 verticies of odd degree, then it has at least one Euler path. This

path must start at one of the odd-degree vertecies and end at the other.

Eulerian Path

The Königsberg Bridges graph. This graph is not Eulerian, therefore, a solution does not exist.

Every vertex of this graph has an even degree therefore this is an Eulerian graph. Following the edges in

alphabetical order gives an Eulerian circuit/cycle.

206C. L. Mallows, N. J. A. Sloane (1975). "Two-graphs, switching classes and Euler graphs are equal in number" SIAM Journal on Applied Mathematics 28 (4): 876–880.

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In graph theory, an Eulerian trail (or Eulerian path) is a trail in a graph which visits everyedge exactly once.

Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail which starts and ends on the same vertex.

They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg

problem in 1736. Mathematically the problem can be stated like this:

Given the graph in the image, is it possible to construct a path (or a cycle, i.e. a path starting and ending

on the same vertex) which visits each edge exactly once?

Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the

graph have an even degree, and stated without proof that connected graphs with all vertices of even

degree have an Eulerian circuit. The first complete proof 207of this latter claim was published

posthumously in 1873 by Carl Hierholzer208

The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an

Eulerian circuit, and the other is a graph with every vertex of even degree. These definitions coincide for

connected graphs

For the existence of Eulerian trails it is necessary that zero or two vertices have an odd degree; this means

the Königsberg graph is not Eulerian. If there are no vertices of odd degree, all Eulerian trails are circuits.

If there are exactly two vertices of odd degree, all Eulerian trails start at one of them and end at the other.

A graph that has an Eulerian trail but not an Eulerian circuit is called semi-Eulerian.

An Eulerian trail or Euler walk in an undirected graph is a walk that uses each edge exactly once. If such a

walk exists, the graph is called traversable or semi-Eulerian

207 N. L. Biggs, E. K. Lloyd and R. J(1976). Wilson, Graph Theory 1736–1936, Clarendon Press, Oxford, 1976, 8–9 208 Hierholzer Carl -Chr. Wiener (1873). "Ueber die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren". Mathematische Annalen (in German) 6: 30–32 proved that a graph has an Eulerian cycle if and only if it is connected and every vertex has an even degree (excluding the starting and terminal vertices). This result had been given, without proof, by Leonhard Euler in 1736. Hierholzer apparently explained his proof, just before his premature death in 1871, to a colleague who then arranged for its posthumous publication which appeared in 1873

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An Eulerian cycle Eulerian circuit or Euler tour in an undirected graph is a cycle that uses each edge

exactly once. If such a cycle exists, the graph is called Eulerian or unicursal The term "Eulerian graph" is

also sometimes used in a weaker sense to denote a graph where every vertex has even degree. For finite

connected graphs the two definitions are equivalent, while a possibly unconnected graph is Eulerian in the

weaker sense if and only if each connected component has an Eulerian cycle.

For directed graphs, "path" has to be replaced with directed path and "cycle" with directed cycle.

The definition and properties of Eulerian trails, cycles and graphs are valid for multi-graphs as well.

An Eulerian orientation of an undirected graph G is an assignment of a direction to each edge of G such

that, at each vertex v, the indegree of v equals the out degree of v. Such an orientation exists for any

undirected graph in which every vertex has even degree, and may be found by constructing an Euler tour

in each connected component of G and then orienting the edges according to the tour Every Eulerian

orientation of a connected graph is a strong orientation, an orientation that makes the resulting directed

graph strongly connected. Properties: An undirected graph has an Eulerian cycle if and only if every vertex

has even degree, and all of its vertices with nonzero degree belong to a single connected component.

An undirected graph can be decomposed into edge-disjoint cycles if and only if all of its vertices have

even degree. So, a graph has an Eulerian cycle if and only if it can be decomposed into edge-disjoint

cycles and its nonzero-degree vertices belong to a single connected component.

An undirected graph has an Eulerian trail if and only if exactly two vertices have odd degree, and if all of

its vertices with nonzero degree belong to a single connected component.

A directed graph has an Eulerian cycle if and only if every vertex has equal in degree and out degree, and

all of its vertices with nonzero degree belong to a single strongly connected component. Equivalently, a

directed graph has an Eulerian cycle if and only if it can be decomposed into edge-disjoint directed cycles

and all of its vertices with nonzero degree belong to a single strongly connected component.

A directed graph has an Eulerian trail if and only if at most one vertex has (out-degree) − (in-degree) = 1,

at most one vertex has (in-degree) − (out-degree) = 1, every other vertex has equal in-degree and out-

degree, and all of its vertices with nonzero degree belong to a single connected component of the

underlying undirected graph.

The asymptote formula for the number of Eulerian circuits in the complete graph209:

APPLICATIONS

209 Mackay, B.D. and Robinson, R.W.,(1998) “Asymptotic Enumeration of Eulerian Circuits in the Complete Graph”, Combin. Prob. Comput., 1998, pp. 437-449.

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SOCCER

Using network theory to analyze the performance of soccer teams and players produces unique insights

into the strategy of the world’s best team All renowned football teams in history have displayed a

recognizable footprint in their game-play, which has always been thought of as something observed by

football experts rather than described by game statistics. To reveal this footprint, we use the passing

distribution of a team to construct a weighted and oriented network, with nodes corresponding to players

and weighted arrows to the number of successful passes between players. By attaching each node to the

tactical positioning of the team, we then obtain an immediate picture of the team’s style, which can

profitably be used to observe overused and underused areas of the pitch or to detect potential

performance problems between certain players. By computing certain network invariants, such as

centrality measures, we can also analyze a team’s performance as well as the contributions of each of its

players. These measures yield, as will be seen, a lot of useful information despite the relatively small size

(11 players) of passing networks

The case of Spain: Special case: World Cup 2010 South Africa Final: Spain – Netherlands (1-0)

Spain’s third major championship in a row, confirms the team as the best in the world and one of the

greatest in history. So what makes Spain so good? Fans, pundits and sports journalists all point to Spain’s

famous strategy of accurate quick-fire passing, known as the tiki-taka style210. It’s easy to spot and

fabulous to watch, as the game on Sunday proved. But it’s much harder to describe and define. That

looks set to change. Today, Javier Lopez Pena at University College London and Hugo Touchette at Queen

Mary University of London reveal an entirely new way to analyze and characterize the performance of

soccer teams and players using network theory. They say their approach produces a quantifiable

representation of a team’s style, identifies key individuals and highlights potential weaknesses. Their idea

is to think of each player as a node in a network and each pass as an edge that connects nodes. They then

distribute the nodes in a way that reflects the playing position of each player on the pitch.

210 Davies, Jed C. (25 July 2012)."The tiki taka handbook" Liverpool F.C. (Liverpool) Tiki-taka is a style of play in football characterised by short passing and movement, working the ball through various channels , and maintaining possession. The style is primarily associated with La Liga Club Barcelona from John Cruff’s tenure as manager Tiki-taka moves away from the traditional thinking of formations in football to a concept derived from zonal play

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The image above shows the resulting networks for the Netherlands (left) and Spain using data from the

knockout stages of the 2010 World Cup in South Africa. These teams contested the final which Spain

won211. A visual inspection of these networks immediately reveals some interesting insights into the

match. The thickness of the arrows represents the number of passes between nodes and it is immediately

clear that the Spanish team pass more often. This image captures 417 passes by the Spanish team versus

266 for the Netherlands. Key players also stand out by the number of passes they make and receive,

such as 16 (Sergio Busquets) and 8 (Xavi). However, this representation also allows a much more

sophisticated analysis using the standard tools of network science. For example, closeness centrality

measures how easy it is to reach a given node in the network. In footballing terms, it measures how well

connected a player is in the team. Busquets and Xavi have the highest scores in the Spanish team. Both

are better connected than the best connected Dutch player, 1 (Steckelenberg) the goal keeper. That the

goal keeper was the Netherland’s best connected player itself speaks volumes. Another notion is

betweenness centrality, which measures the extent to which a node lies on a path to other nodes. In

footballing terms, betweenness centrality measures how the ball flow between players depends on another

player. Players with a high betweenness centrality are crucial for keeping the momentum of the game

going. These players are important because removing them has a huge impact on the structure of the

network. So a single player with a high betweenness centrality is also a weakness, since the entire team is

vulnerable to an injury to this player or a red card. Spain’s number 11 Joan Capdevilla is the player with

by far the highest betweenness centrality in this match. He is clearly a target for passes from many

players, which he feeds mainly to 14 (Xabi Alonso). Then there is the famous Page Rank algorithm which

measure’s a player’s popularity, as judged by the number of passes he receives from other popular

players. It gives a rough idea of who is most likely to end up with the ball after a suitably large number of

passes. In this game it is Xavi There are clearly limitations to this approach. The data is an average over

several games so it fails to capture the dynamics of specific games. And the positions of the nodes are

also a vast generalization and taken only from a player’s nominal starting position. Pena and Touchette

say there are various ways in which this approach could be improved. They suggest adding another node

to represent the opponents goal and would record the number of shots. They also imagine using a similar

approach to measure the accuracy of passes by taking into account the probability of pass from one

player to another being successful. “The defensive strength of a team could also be incorporated in the

model by tracking passing interceptions and recovered balls,” say Pena and Touchette. Perhaps more

fascinating would be a way of collecting and analyzing the data in real time to produce a network-based

analysis of a game as it happens.

211 http://www.technologyreview.com/view...-soccer-teams/

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BARCELONA

Under the title “Barcelona’s tiki-taka style of play has revolutionized football. But has their secret weapon

been decoded?,” the BBC Journalist Philip Ball wrote at 18 November 2014 an interesting article about the

“Science behind success”, In particularly wrote: “Like many other top teams, Barcelona has decided that

football is now a “numbers game”, as writers Chris Anderson and David Sally212 have put it in their book of

that title. Managers and coaches are looking for advantage in the statistics of the game: who has possession

the most, which parts of the pitch do they cover, who passed to whom? Passing patterns: Studies like that

conducted for Barcelona go well beyond the traditional totting up of how many shots were on target and for

what proportion of the game each side had possession of the ball. Team coaches are interested in the

patterns and shapes of how the play unfolds. Armchair fans are already accustomed to visuals such as “heat

maps” showing the territory that individual players covered over the course of a game, or diagrams of the

web of passes that led to a goal. One of the outcomes of such analyses is that it explodes myths. It was

because Jose Mourinho knew that the statistical goal-scoring potential of corner kicks was negligible (if

anything, they leave a side exposed to counter-attack) that he was so baffled, when he came to manage

Chelsea in England, at why crowds got so excited when their team was awarded one. The Spanish

national team has adopted much the same tactic, often to devastating effect, and it has changed football into

a game that is less about bold and brilliant attacking manoeuvres designed to secure winning goals and

more about patience, avoiding mistakes, and ensuring that you don’t lose. But how different, really, is tiki-

taka? Even when football was about young children booting a rain-sodden lump of leather on a windswept

sea of mud, we were taught about the importance of passing. Are Barcelona just doing more of the same, but

better? That’s what Rodriguez and colleagues have set out to discover. They have analyzed footage of the

2012-13 games in the first divisions of Spain, Italy, England, France and Germany to find distinctive “motifs”

in the patterns of passing. There have been previous studies of pass networks in football, but these have

tended to concentrate on things like the passes between specific pairs of players. Rodriguez and colleagues

have looked more deeply into the nature of the networks, searching for what they call “flow

motifs”: extended sequences of consecutive passes between specific players. This concept of characterizing

different network structures using motifs or patterns of interconnection is one that has been

developed previously by scientists to study natural systems such as networks of genes, neurons and

organisms in food webs. Messi business: Having identified the prevalence of such motifs in a team’s pass

networks, the researchers compared the numbers with how often these sequences appeared in randomly

generated networks with the same general features (such as the same average number of links between

nodes). This meant studying hundreds of thousands of individual passes. Even at a glance, the statistics for

Barcelona stood apart from those of the other Spanish teams. For example, they used an ABAC motif (let’s

say, Xavi to Messi, back to Xavi, then to Neymar) significantly more often, and an ABCD motif significantly

less often. In other words, there was much more structure in Barcelona’s game: as the researchers say, “tiki-

taka does not consist of uncountable random passes but rather has a precise, finely constructed structure”.

Barcelona's uniqueness became even more clear when the researchers carried out a so-called “cluster

analysis”, which groups teams according to how often they use each of the five possible four-pass motifs

(ABAB, ABCA and so on). While all of the other Spanish teams fall into two clusters, Barcelona occupies is out

on its own. And this special identity remains when teams from other European countries are included – one

or two other sides, such as Turin, West Ham and Juventus, fall a little outside the single main cluster in which

all the other teams are now gathered but Barcelona stands distant and aloof from the rest of the European

crowd”.

212 Anderson Chris and Sally David (2013) “The Numbers Game-Why everything you know about Soccer is wrong” Penguin,

2013

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People’s Careers:

In a completely rational analysis, it appears that the careers and enhance a person passes through the

logic of networking and with the same logic with which the Euler: Path through "hubs" mobility over

arches, powerful stance, search opportunities, move on paths that lead to the next nodes node (n), arcs

(a), degree (odd-even) of vertices (dv), betweenness centrality (bc), eccentric (ec), tactical positioning (tp),

strong orientation (so), the Extent to which a Node Lies on a Path to other Nodes (enlpn) such as to

maximize the following function

),,,,,,,( enlpnsotpecbcadvnf

From the other hand,

Networking is a socioeconomic business activity213 by which groups of like-minded businesspeople

recognize, create, or act upon business opportunities214

In the second half of the twentieth century, U.S. advocates for workplace equity[who?] popularized the

term and concept of networking as part of a larger social-capital lexicon—which also includes terms such

as "glass ceiling", "role model", "mentoring", and "gatekeeper"—serving to identify and address the

problems barring non-dominant groups from professional success. Mainstream business literature

subsequently adopted the terms and concepts, promoting them as pathways to success for all career

climbers. Since the closing decades of the twentieth century, networking has become an accepted term

and concept in American society.[citation needed] People now invoke "networking" in relation to

everything from child-rearing to science to the business activities described here

A professional network service (or, in an internet context, simply professional network) is a type of social

network service (LIKENID etc) that is focused solely on interactions and relationships of a business nature

rather than including personal, non-business interactions

A professional network service is used by business individuals to establish and maintain professional

contacts and a way to either find work or get ahead in career as well as gain resources and opportunities

for networking. According to LinkedIn managing director Clifford Rosenberg in an interview by AAP in

2010, "this is really a call to action for professionals to re-address their use of social networks and begin

to reap as many rewards from networking professionally as they do personally." Businesses mostly depend

on resources and information outside company and in order to get what they need, they need to reach out

and professionally network to others, such as employees or clients as well as potential opportunities215

The History216 : In 1997, professional network services started up throughout the world and continue to

grow. The first recognizable site to combine all features, such as create profiles, add friends, and search

friends, was SixDegrees.com. According to Boyd and Ellison's article, "Social Network Sites: Definition,

History, and Scholarship", "from 1997 to 2001, a number of community tools began supporting various

combinations of profiles and publicly articulated Friends." Boyd and Ellison go on to say that the next

wave began with Ryze.com in 2001. It was introduced as a new way "to help people leverage their

business networks Once the firm has decided to utilize Social Media applications, it is worth checking that

all employees may actually access them." According to the SNCR "the convergence of Internet, mobile, and

social media has taken significant shape as professionals rely on anywhere access to information,

relationships and networks

213 Jessica E. Vascellaro (2007-08-28). "Social Networking Goes Professional" The Wall Street Journal. 214 Hubert Österle, Elgar Fleisch, Rainer Alt (2001), Business networking: shaping collaboration between enterprises (2, illustrated ed.), Springer, 215 AAP (2010-12-10) "Career rewards can flow from social media" The Daily Telegraph. 216 Danah M. Boyd; Nicole B. Ellison (2007). "Social Network Sites: Definition, History, and Scholarship". Blackwell Publishing Inc

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▲

People are part of the earth system, they live in Earth, they behave according the earth (and Universe217)

rules Of course, People is even more than “part” of the organic material: They are soul, mind, spirit, love

By the same logic which behaves (our nearest) universe also behaves Earth and also human relations must

behave The same forces (attraction or repulsion) in force in Nature data (many of them know) should

apply to human social, political and economic relations People evolve through adaptation structures and

forces that always tend to the balancing status of these forces

Communication-reaction-selection-decision: Humans communicate with each other, by many ways

It is argued that the "language" and especially "writing", for achieving their communication- were the

most important discovery and the brilliant achievement of mankind For this, only mankind has written

History No other living organism has "History" "Communication" and "interaction" are the necessary

conditions for Choice and Decision's function People bargain, thus producing "reaction" by unique way.

In the opposite, everyone would live a "monastic life" If people have no interaction, each-other there

would be no choice, nor the decision will not even needed But people negotiate (interact) within a given

space (the earth space) with a specific logic which determines the attraction-repulsion-conflict for

thousand years These "movements" of people (even act as separate units) take place a finite space, the

Earth . It is logical, therefore, be harmonized with the movements and the forces and the environment of

the Earth and other celestial bodies

That means that even if people have the self-destruction they have, also the ability of survival through

the attraction-repulsion forces In addition, people have the "adjustment” ability (and of course, the

"adjustment in psychology"Sarbin Theodore R (1940) 218 has adopted the Socratic Method, focusing on the

term “adjustment” having many and conflicted meanings. Based on the last sentence of Sarbin, we have to

see if the adjustment in Psychology would lead human behavior in un-equilibrium situations or not

Equilibrium is the stability factor in Universe, the planets' movement, the Earth etc

People live the fear of the out of control "risk" of a conflict inside a strict time – space’s environment The

question is “what kind of time-space? Borrowed from juristic by mechanics adapted to biology and finally

taking over by psychology, the history of the world “adjustment” is one of the accretion of meanings In its

juristic sense “the process of setting right or settling” Based on the last sentence of Sarbin, In this frame,

people adjust their behavior according to their physical environment ( nowadays, it happens rather the

opposite) We have to imagine that people living in "spherical space" have the ability to adjust their

"reaction/bargaining behavior" and choices" in "special forms" within their social and economic networks

According to this "concept" it seems reasonable to look for the "domain" in which the "bargain’s reaction"

is achieved in spherical forms (coming from the spherical space) This Chapter is dedicated to the "win-

win-win papakonstantinidis function" spherical domain (umbilics)

217 The Universe is all of time and space and its contents

218 Sarbin Theodore R. (2006) “Adjustment In Psychology”- Journal of Personality Volume 8, Issue 3, pages 240–249, 1st edition

March 1940

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/////////////////////////////////

I tried to identify the "win-win-win" as a key tool for the approach to social welfare by clicking

on the incompatibility of five basic theorems that define it - each one of its own side-either

positive (justice theorem ) or negative (the impossibility theorem)

The suggested "win-win-win papakonstantinidis model”219is built up on these

incompatibilities, in particular as regards the pairs" Pareto efficiency – Impossibility Theorem”

"paradox liberty (Amartya Sen) - Pareto Efficiency” , “Theorem of Justice –Pareto Efficiency”

and (the most important) “the Theorem of incompleteness-the Impossibility Theorem”

The win-win-win papakonstantinidis model is a methodological tool for conflict resolution,

especially in the case of decision making, or in forming "instant reflection winning strategies"

in the BARGAIN (which is the frame) The “win-win-win papakonstantinidis model” concerns

the strategic decision making in a number of fields and domains (biology, psychology,

management, marketing, history- especially in interpretation of historic events-laography,

ethnology, anthropogeography, philosophy, economy, sociology, pure math, communication,

public speech, diplomacy, and go on The reason so many regards thinking and research

Special regard is given to regional and local development field both as a regional and social

sciences. It proves that building social capital at local level mainly depends on social trust

links among local people: Social cohesion based on social capital may be measured by the

diversification Rate (R *) from strict globalization rules: From this point of view, local people’s

intervention should be useful, so as to diversify these "rules" at local level adjusting them to

local identity, including communication code, customs, ethics, culture. The Win-win-win

methodology [Papakonstantinidis Model] should facilitate local people to "readjust" bargaining

globalization rules locally, through a sensitization process: Community is defined as a discrete

spatial / cultural entity, as their people’s sensitization process' is going to its

limit………………………………………………………………………………………………………….

The “win-win-win papakonstantinidis model” (2002, August, SW) may, thus, transform

individual winning –instant reflection –strategies (the win-win Nash Theory) in a NEW –three

poles-equilibrium point, including the COMMUNITY (Environmental Protection, Value Systems,

Ethic etc), which is the “absolute cooperation” limit point in the bargain between TWO

219

Papakonstantinidis L.A(2002-August 14) “The win-win-win model” Euracademy Guide The Visby University-Gotland-SW

Work summarizing

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Since the game theory (exactly: the “non cooperative game theory”) saved the New-classical

School of Thought in Economics letting it to make a restart, focusing on the “bargaining

equilibrium” (Nash Equilibrium) and the equimarginal principle (consumer choice) it seems

that the bargaining behavior is in the centre of our research

Starting from the “zero sum two players game” (John von Neumann- Oscar Morgenstern

1944)220in the form of “win- lose” at any bargain, then was the John Forbs Nash who made the

difference, letting in both bargainers to win (win-win) But, for another time this bargain was

rather to the side of the winners (due to their bargaining force) than eliminating social

inequalities (the winner takes it all)

With this aim an hypothetical dipole bargain between 2 bargainers (*A,B) converted into 3-

pole by introducing the "Community" (the village, the town, the inhabitants of a country, a

continent, planet, after all) as a third pole in any bargain (win-win-win)

So the concept is to construct a theoretical-original-model so that it should respond better to

the conditions of "social welfare"

With this aim an hypothetical triple-pole bargain between 2 (A and B and the "Community"

included as the third pole) is a basis for scientific dialogue By the tem “Community” we can

imagine any common structure, i.e the village, the town, the inhabitants of a country, a

continent, planet, after all-

The point is that the third pole (the Community) will claim its own profits, in a future

negotiation It is about a "win-win-win" concept which is now the global requirement For

example, the first concrete example has to do with environmental protection Climate change

leaves no room to 2 competitors

fields lies in the very nature of the model, especially in its triple pole perception, which leads

us to see things from another, alternative approach, the triple view, whether in psychology or

any interpretation of historical past time events or/and diplomacy, or even communication, or

MANAGEMENT……………………………………… without considering the entire rest of the world

Each negotiation between 2 concerns the entire planet The how achieved in practice I think it

can be done with Laws, as long as there is the political will of Another Dimension It has to do

with the war see the two superpowers to compete by focusing on the war in the Middle East

(Syria and Iraq) But the agreement or disagreement affects millions of people in the two

countries who come as refugees to Europe

The recognition of the third pole in our daily life is connected with its social necessity

Without any imposition by dictatorial regimes, the 3-pole approach to bargaining, is necessary

and unavoidable if and only if humankind seeks survival solutions

In a “win-win-win” negotiation/deal there is more possibility of achieving social welfare: This

can be proved by the math example below On the other side we have 5 basic foundational and

220

John von Neumann- Oscar Morgenstern (1944) “theory of games and economic behavior” –PRINCETON-

University..Press..ed

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global known Theorems which are incompatible each-other So the concept here was to put

them one against the other and seek "material" to build the new

For example, the Incompleteness Theorem (Gödel) fades the Impossibility Theorem (K. Arrow)

and the Pareto Efficiency is basic for the Impossibility Theorem, but not for the “Justice

theorem (Rawls) But from these incompatibilities arises a necessity of completeness,

effectiveness, universal justice, a necessity of "umbilical points" freedom , economic

equilibrium The synthesis of all these lead to a situation utopia (romantic, idealistic) will

certainly not get, but shows us, from the other, a path of self-preservation and survival if the

goal is not suicidal

CONCEPT

and the Study Design

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The concept is to launch a pilot project focused on the emergence of a new equilibrium

between three negotiators A-B-C (including the Community, “C”) in a bargain between two. How can this happen?

This work started with a simplistic syllogism: Capitalism with its fundamental axioms of the

"free market" and "competition" has solved many problems but created more One of these is

the "social inequality" and the consequent absence of "social welfare"

The "bargain" and the subsequent “bargaining power” manifested in and by this are on the

basis of the capitalist system

In the bargain there are two (2) quite rational negotiators with totally opposite interests that

try to achieve an agreement (or even disagreement), pursuing each one to gain the greatest

individual (and not collective) profit

It seems to me, that the "social welfare"(the objective of a probable “social choice”) is

impossible within the capitalist system that has at its center the man who acts rationally and

always for his personal interests

It was very easy for Kenneth Arrow (1950)221 to prove the "impossibility” of Social Choice

(inside the capitalist system) in his homonymous theorem (which earned him the Nobel Prize

in Economics in 1972)

“Game Theory” [especially, the “Non-cooperative Game Theory”] has an important contribution

to restart the “New-classical economic school” due to its character, as a conflict game between

2: The theory of games222 is a mathematical discipline designed to treat rigorously the

question of optimal behavior of participants in games of strategy and to determine the

resulting equilibria. Thus, in games of strategy223 there is conflict of interest as well as

possible cooperation among the participants. There may be uncertainty for each participant

because the actions of others may not be known with certainty. Such situations, often of

extreme complexity, are found not only in games but also in business, politics, war, and other

social activities. Therefore, the theory serves to interpret both games themselves and social

phenomena with which certain games are strictly identical. The theory is normative in that it

aims at giving advice to each player about his optimal behavior; it is descriptive when viewed

as a model for analyzing empirically given occurrences. In analyzing games the theory does

not assume rational behavior; rather, it attempts to determine what “rational” can mean when

an individual is confronted with the problem of optimal behavior in games and equivalent

situations224.

In contrast, if it were possible to import third party (natural or legal person, company, state,

associations of states) to negotiation between two (2) then this "new" person should have a

dual character, to produce results:

(a) as the third member of the bargaining

221 Kenneth Arrow 1951, 2nd ed., 1963 Social Choice and Individual Values, Yale University Press 222Martin Shubik 1953 (with J. P. Mayberry and J. F. Nash), "A Comparison of Treatments of a Duopoly Situation," Econometrica 21(1), pp. 141-154. 223 Martin Shubik, 1999. Political Economy, Oligopoly And Experimental Games: The Selected Essays of Martin Shubik, 2 v., Edward Elgar. Description and several chapter-preview links: Part I Political Economy; Part II Oligopoly; Part III Gaming; Part IVGame Theory and Operations Research. 224 Martin Shubik (2015) Economic applications Encyclopedia. com

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(b) as the "entity -umbrella", or as an agent over the other two negotiators, claiming his share

of any agreement (or disagreement)

But why, the two original parts (A-B) must accept an entity, "C" (whatever it is), in a bargain

between them which do not come from the set of possible positions defined by the

competition of their individual interests?

This is the point, which the “win-win-win papakonstantinidis theory” has been based on

Generally, this point has the most important contribution in building the new perception

(step by step) that is suggested here

This central question is broken down into three sub-question, each of which follows another

in the order of priority that have been completed (and one question for its practical utility)

5. What is the real meaning of the term “social welfare”?

6. Can a theory or a model based on the incompatibilities other theorems and theories

be supported and interpreted?

7. Does exist the only one “win-win-win papakonstantinidis 3D equilibrium” or not?

8. If YES, then which is its practical utility? Are there examples on it?

Answer to those questions build up the suggested “win-win-win papakonstantinidis theory”

o The first sub-question is referred in the pure theoretical “moral” approach of the

"social welfare" thus building up the “philosophical side of the proposal: From

Socrates 470/469 – 399 BC, Plato 428/427 or 424/423 – 348/347 BC), Aristotle 384 –

322 BC) and Epicourus 341-270 BC till Hobbs, Hume, Kant and from them till Jeremy

Bentham225, John Stuart Mill226 John Rawls227 J.J Rousseau228, Kurt Friedrich

225 Bentham Jeremy [1907 (1789) ]An Introduction to the Principles of Morals and Legislation Oxford: Clarendon Press

Retrieved on 1 October 2012 from the Library of Economics and Liberty.

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Gödel229 (The Incompleteness Theorem) or even Russell (1872-1970) (Russell’s

Paradox230, or Bernoulli Petesbourg Paradox231 (barbers paradox), the agency theory

Stefen Ross232:”… The relationship of agency is one of the oldest and commonest

codified modes of social interaction. We will say that an agency relationship has arisen

between two (or more) parties when one, designated as the agent, acts for, on behalf

of, or as representative for the other, designated the principal, in a particular domain

of decision problems. Examples of agency are universal. Essentially all contractural

arrangements, as between employer and employee or the state and the governed, for

example, contain important elements of agency. In addition, without explicitly

studying the agency relationship, much of the economic literature on problems of

moral hazard (see K. J. Arrow) is concerned with problems raised by agency. In a

general equilibrium context the study of information flows (see J. Marschak and R.

Radner) or of financial intermediaries in monetary models is also an example of

agency theory. The canonical agency posed as follows. Assume that both the agent

and the principal possess state independent von Neumann-Morgenstern utility

functions, G(.) and U(.) respectively, and that they act so as to maximize their

expected utility. The problems of agency are really most interesting when seen as

involving choice under uncertainty and this is the view we will adopt. The agent may

choose an act, a CA, a feasible action space, and the random payoff from this act, w(a,

0), will depend on the random state of nature O(EQ the state space set), unknown to

the agent when a is chosen. By assumption the agent and the principal have agreed

upon a fee schedule f to be paid to the agent for his services. T he fee, f, is generally a

function of both the state of the world, 0, and the action, a, but we will assume that

the action can influence the parties and, hence, the fee only through its impact on the

payoff. T his permits us to write, (1) f = f(w(a,6);6). Two points deserve mention.

Obviously the choice of a fee schedule is the outcome of a bargaining problem or, in

large games, of a market process. Much of what we have to say is relevant for this

view but we will not treat the bargaining problem explicitly. Second, while it is

possible to conceive of the fee as being directly functionally dependent on the act, the

theory loses much of its interest, since without further conditions, such a fee can

always be chosen as a Dirac 8-function forcing a particular act (see S. Ross). In some

226 Mill, John Stuart (1863). Utilitarianism (1 ed.). London: Parker, Son & Bourn, West Strand. Retrieved 6 June 2015 via

Google Books 227

Rawls John (1971) “A Theory of Justice” Harvard University Press USA, 1971 first edition 228 Rousseau Jean-Jacque (1762) Du contrat social ou Principes du droit politique; (Of the Social Contract, or Principles of Political Right) Publication,. Amsterdam, février-mars 1762, Marc Michel Rey, etc

229 Gödel Kurt Friedrich (1931),"Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme

I" Monatshefte für Mathematik und Physik 38: 173–98 (in English "On Formally Undecidable Propositions of "Principia

Mathematica" and Related Systems")

230 Russell Bertrand 1903. The Principles of Mathematics Cambridge University Press

231 Bernoulli, Daniel, 1954 [1738], “Exposition of a New Theory on the Measurement of Risk Econometrica, 22: 23–36 232Ross, Stephen A. 1973. The economic theory of agency: The principal's problem. American Economic Review 62(2): 134-139.

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sense, then, we are assuming that only the payoff is operational and we will take this

point up below. Now, the agent will choose an act, a, so as to (2) max E{G[f(w(a, 0);

0)]}, a 0 where the agent takes the expectation over his subjectively held probability

distribution. The solution to the agent's problem involves the choice of an optimal act,

ao, conditional on the particular fee schedule, i.e., ao=a((f)), where a(.) is a mapping

from the space of fee schedules into A. If the principal has complete information

about the fee to act mapping, a((f)), he will now choose a fee so as to max El

U[wv(a((f)), 0) (3 (f) e (3) - f(w(a((f)), 0); 0)] where the expectation is taken over the

principal's subjective probability distribution over states of nature. If the principal is

not fully informed about a(.), then a(X) will be a random function from his point of

view….” The problems of agency are really most interesting when seen as involving

choice under uncertainty and this is the view we will adopt. The agent may choose an

act, a CA, a feasible action space, and the random payoff from (and Stiglitz Joseph233)

the SET Cantor Theory, and the “until now” bibliography has been used (sometimes

with the same words as to support my argumentation:

o Set theory is the branch of MATHEMATICAL LOGIC that studies SETS which informally

are collections of objects. Although any type of object can be collected into a set, set

theory is applied most often to objects that are relevant to mathematics. The language

of set theory can be used in the definitions of nearly all MATHEMATICAL OBJECTS

o In MATHEMATICS the Cantor set is a set of points lying on a single LINE SEGMANT that

has a number of remarkable and deep properties (1883)

The second sub-question: Does be existed the only one “win-win-win papakonstantinidis 3D

equilibrium” or not?

d. Win-win-win equilibrium: The limit of convergence’s processes of different functions

e. Is a set formed by the Axioms?

Informal and formal axiom systems

One big reason for the expressed disconnect is that Gödel’s theorems are about formal axiom

systems of a kind that play no role in daily mathematical work. Informal axiom systems for

various kinds of structures are of course ubiquitous in practice, viz. axioms for groups, rings,

fields, vector spaces, topological spaces, Hilbert spaces, etc., etc.; these axioms and their

basic consequences are so familiar it is rarely necessary to appeal to them explicitly, but they

serve to define one’s subject matter. They are to be contrasted with foundational axiom

systems for the “mother” structures--the natural numbers (Peano) and the real numbers

(Dedekind)--on the one hand, and for the general concepts of set and function (Zermelo-

Fraenkel) used throughout mathematics, on the other. Mathematicians may make explicit

appeal to the principle of induction for the natural numbers or the least upper bound principle

233 Stiglitz, Joseph E. and all (1969) Readings in the modern theory of economic growthCambridge, Massachusetts: The M.I.T. Press

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for the real numbers or the axiom of choice for sets, but reference to foundational axiom

systems in practice hardly goes beyond that.

One informal statement of the basic Peano axioms for the natural numbers is that they

concern a structure (N, 0, s) where 0 is in N, the successor function s is a unary one-one map

from N into N which does not have 0 in its range, and the Induction Principle is satisfied in the

following form: (IP) for any property P(x), if P(0) holds and if for all x in N, P(x) implies P(s(x))

then for all x in N, P(x) holds.

METHODOLOGY

To manipulate with Incompatibilities, by the utility theory:

10. The impossibility theorem (1951 Kenneth Arrow: book: Social Choice and Individual

Values, as well as the Amartya Sen “liberal paradox”

11. the theorem of incompleteness (Kurt Gödel (1931)

12. the Rawls Theorem on Justice, 1958)- the veil of ignorance

13. the Nash Equilibrium in Nash “Non cooperative Game Theory 1951(annals of

Mathematics,1951 Vol. 54, No. 2 (Sep., 1951), pp. 286-295)

14. The “Pareto optimality in a 3D space according to

15. Caratheodory conjecture (umbilical points in a sphere), then the main issue in this

research concerns the possibility that a win-win-win communication should exist in

real terms,

16. The agency theory (Stiglitz Joseph 2001) An agency, in general terms, is the

relationship between two parties, where one is a principal and the other is an agent

who represents the principal in transactions with a third party as each of them to win :

]win-win-win equilibrium

17. the ZBC set theory (a selection of objectives)

18. the cognition by linguistic recursion (EVARETT mind recursion (one-many): Human

mind is able to make recursions)

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The study aims to highlight the existence and importance of a tri-polar process approach of

scientific and practice - everyday thinking For this purpose develops individual objectives

which reaches through the "thought experiment": In spite of the perception that the test

applies only to materials organic elements, the "thought experiment" adopted in this study

appears to have visible effects on application Thought experiment is adopted by the follow

means:

“The common goal of a thought experiment is to explore the potential consequences of the

principle in question: "A thought experiment is a device with which one performs an

intentional, structured process of intellectual deliberation in order to speculate, within a

specifiable problem domain, about potential consequents (or antecedents) for a designated

antecedent (or consequent)" (Bowers PM, Cokus SJ, Eisenberg D, Yeate 2004) p. 150)234.The

study goes on by Implicative lattice

We expect that this work is well laid out and logical methodology will provide a great

backbone for the entire research paper, allowed to us build an extremely strong results

section Having some –selective- influences from the Ancient Greek Philosophy (Socrates, Plato,

Aristotle Epicurus), as well as philosophies of the Enlightenment235 and the “Age of Reason”

(such as Locke, Hobbes, Hume Kant & alle)236 as well as from modern rationalist philosophy,

this work combines an empiricist approach with a rationalism that emphasized conceptual

clarity and deductive argument. In this frame the Socratic dialectic method has been adopted

in this work:

o First the prevailing view (thesis) is presented and defined.

o Then this thesis is criticized (antithesis), by the ontological arguments

o Finally, these two opposite perceptions are merged in a unique construction

(synthesis)

o NOTE: [any triple-pole conception, either the essential or methodological approach

has been adopted by this article]

According to the prime objective of the Study (feasibility of social welfare even under capitalist

production and marketing system) and the three main pillars of the methodology adopted by

it, definitions of five theorems and 4 theories are recognized, as domains of "positive

acceptance” (thesis, in ancient Greek philosophy)

The same definitions are examined under a critical view (antithesis) thus leading in their

rejection Finally, a third completely new aspect (synthesis) raised -I hope- as a result of the

merger of two previous positions / views

234

Bowers PM, Cokus SJ, Eisenberg D, Yeates (2004) Use of logic relationship to decipher protein network organization

Science Dec 2004. 306(5705):2246-9 235 Stanford Encyclopedia of Philosophy: The Enlightenment is the period in the history of western thought and culture, stretching roughly from the mid-decades of the seventeenth century through the eighteenth century, characterized by dramatic revolutions in science, philosophy, society and politics; these revolutions swept away the medieval world-view and ushered in our modern western world. Enlightenment thought culminates historically in the political upheaval of the French Revolution, in which the traditional hierarchical political and social orders (the French monarchy, the privileges of the French nobility, the political power and authority of the Catholic Church) were violently destroyed and replaced by a political and social order informed by the Enlightenment ideals of freedom and equality for all, founded, ostensibly, upon principles of human reason. The Enlightenment begins with the scientific revolution of the sixteenth and seventeenth centuries. The rise of the new science progressively undermines not only the ancient geocentric conception of the cosmos, but, with it, the entire set of presuppositions that had served to constrain and guide philosophical inquiry. 236 Voltaire Nicolaus Copernicus (19 February 1473 – 24 May 1543), Tycho Brahe (b. 1546-1601) Johannes Kepler (b 1571 –

1630) Galileo Galilei (b. 1564 – 1642) Isaac Newton (b. 1643 – 1727) …The Philosophical Revolution or the Age of Reason Rene

Descartes 1596 – 1650 Benedict Spinoza 1632 – 1677 Francis Bacon 1561 – 1626 Thomas Hobbes 1588 – 167 John Locke 1632 –

1704 David Hume 1711 – 1776 Jean-Jacques Rousseau 1712 – 1778 Immanuel Kant 1724 – 1804 de Montesquieu January 1689

– 10 February 1755), Baccarat, Helvetius, Diderot, D' Alembert,..)

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Regarding methodological path, which has been selected and given preference over other

alternative methodological choices, methods from the classic David Hume’s scientific work, as

it is expressed by "Research on Human Understanding”237 and “Enquiry Concerning Human

Understanding”238 and Jeremy Bentham’s “An introduction to the principles of morals and

legislation”239 focused on:

o the importance of logic against custom and tradition and

o precision in the use of terms, have been adopted

so that other researchers can review the results by replicating the research and guaranteeing

the validity. By this necessity a completely accurate description of the equipment and the

techniques used for gathering the data have been planned and executed, providing at the

same time an explanation of how the raw data was compiled and analyzed. The followed

methodology allows the readers to make their own decision about the validity of the data, thus

any reader to understand how research data have been obtained, allowed them to evaluate the

quality of the results

▲

METHODOLOGY: MAIN ISSUES

CHAPTER V

The chapter V is dedicated in TEN (10) basic issues:

237 Hume David (1748) “Philosophical Essays Concerning Human Understanding” (1 ed.). London: A. Millar. Retrieved28 June 2014 via Google Books 238 Hume David (1748) “Philosophical Essays Concerning Human Understanding” (1 ed.). London: A. Millar. Retrieved28 June 2014 via Google Books 239 Bentham, Jeremy (1780) Introduction to the Principles of Morals and Legislation- The First Edition of this work was privately printed in 1780 and first published in 1789. T second edition, 1823, chapter 17,

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papakonstantinidis Page 137

1. "win-win-win" introduction: The "Impossibility Theorem" (Kenneth Arrow) and the Decision Making process :

labeling of the decisions of individuals as they choose whether or not to become activists in one of two (hypothetic)

political parties and the "Voting Problem"

2. Presentations of “networking” that focuses on analysis against aggressive vs cooperative behavior

3. Pareto Efficiency

4. utility function

5. Game Theory an overall view

6. Bargaining Problem overview

7. Bargaining with Altruism

8. The feasible region the definition of the domain of the basic "win-win-win" utility equation

9. win-win-win as bargaining concept

10. Umbilical Points (generally) – the Caratheodory ’s Conjecture

▲

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN” IN THE CURRENT BIBLIOGRAPHY

ACCORDING TO THE EXISTING THEORY

1

Does social

welfare

exist?

DECISION

MAKING:

the decisions of

individuals as

they choose

whether or not

to become

activists in one

Kenneth Arrow: The (famous) “Impossibility Theorem240

"If we exclude the possibility of interpersonal comparisons of

utility, then the only methods of passing from individual tastes to

social preferences which will be satisfactory and which will be

defined for a wide range of sets of individual orderings are either

imposed or dictatorial”

GENERAL IMPOSSIBILITY THEOREM:

It is impossible to formulate a social preference ordering that

satisfies all of the following conditions:

1. Non-dictatorship: The preferences of an individual

should not become the group ranking without

“win-win-win” is a “decision making methodological tool It tries to

approach issues as

How do rational citizens decide how and whether to vote in two-candidate (or two-party) elections?; What spatial positions would rational candidates choose to offer citizens?; and What position(s), if any, would win and hence become the social choice?

Answers on that questions are very useful for understanding the real

problem in its dimensions

We support that a “win-win-win” situation (equilibrium point) is feasible

through the time

From fluent bibliography, we note:

The Ken Arrow’s “Impossibility Theorem”(1950) has been the

inspiration/incentive for me to study alternative ideas of Social Welfare

240 Arrow, K.J. (1950). "A Difficulty in the Concept of Social Welfare" Journal of Political Economy 58 (4): 328–346

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papakonstantinidis Page 138

of two political

parties.

and

Voting Problem

and

Feasible Region

for win-win-win

Equilibrium?

considering the preferences of others.

2. Individual Sovereignty: each individual should be able to

order the choices in any way and indicate ties

3. Unanimity: If every individual prefers one choice to

another, then the group ranking should do the same

4. Freedom From Irrelevant Alternatives: If a choice is

removed, then the others' order should not change

5. Uniqueness of Group Rank: The method should yield the

same result whenever applied to a set of preferences.

The group ranking should be transitive.

NOTE:

In a capitalist democracy there are essentially two methods by which social choices can be made: voting, typically used to make "political" decisions, and the market mechanism, typically used to make "economic" decisions. In the emerging democracies with mixed economic systems, Great Britain, France, and Scandinavia, the same two modes of making social choices prevail, though more scope is given to the method of voting and to decisions based directly or indirectly on it and less to the rule of the price mechanism. Elsewhere in the world, and even in smaller social units within the democracies, the social decisions are sometimes made by single individuals or small groups and sometimes (more and more rarely in this modern world) by a widely encompassing set of traditional rules for making the social choice in any given situation, e.g., a religious code.

The theorem has implications for welfare economics and theories

of justice It was extended by Amartya Sen to the liberal paradox

which argued that given a status of "Minimal Liberty " there was no

way to obtain Pareto Optimality, nor to avoid the problem of social

choice of neutral but unequal results.

An example of this would be to have the following choices to divide

a cake between three people. Let us call them A, B and C.

Choice 1: A gets nothing, B and C get half each.

Choice 2: B gets nothing, A and C get half each.

Choice 3: C gets nothing, A and B get half each.

Choice 4: divide the cake equally.

Thus, if each person votes to get as much cake as possible, choice 4

would be third from the top in everyone's list, and would in any

direct choice lose 2 to 1 against an unequal distribution. Since all of

these choices are Pareto-optimal – no one's welfare can be

improved without reducing the welfare of others – choice 4 would

not be chosen, since there would always be other preferred choices.

and even more, in a 3D space

Also, Prof. Tovey Craig (2010) gave me material to examine main issues

based on the probability of majority rule instability in the 2D Euclidean

model From this point of view, the ideas about “voting” or even the

political activism the spatial model of electoral competition, ,gave me

some ideas of examining the "decision making from different sides

That is very useful of my work, as I had to compare “nodes” (voters) in

relation with their decisions

Also, Aldrich J. (1983) “A Downsian Spatial Model with Party Activism..”,

has provided me with the main “question” as it concerns to "the decision

making" or even more, "the question concerned if the co-decision is a

state feasible and if so, what is the action event's field

Also Bossert W. and Tan G 1995 “An arbitration game and the egalitarian bargaining solution”) presented a simple arbitration procedure which is a multi-stage variant of Nash's demand game. In the absence of discounting, all Nash equilibria of the game yield the egalitarian solution in the first stage. The crucial feature of arbitration procedure is that, in the case of

incompatible demands, the game is allowed to continue and the player

who demands the higher gain over the disagreement point is penalized by

restricting her or his feasible demands in the following stage.

That is very useful for my work, by an alternative concept or point of view:

▲

Arrow supports wit math argumentation, that voting can be regarded as a

method of arriving at social choices derived from the preferences of

individuals. It is impossible to formulate a social preference ordering that

satisfies all of the following conditions:

We have to repeat the “hypothetic example of the “social experiment”

1. Non-dictatorship: The preferences of an individual should not

become the group ranking without considering the preferences

of others.

2. Individual Sovereignty: each individual should be able to order

the choices in any way and indicate ties

3. Unanimity: If every individual prefers one choice to another,

then the group ranking should do the same

4. Freedom From Irrelevant Alternatives: If a choice is removed,

then the others' order should not change

5. Uniqueness of Group Rank: The method should yield the same

result whenever applied to a set of preferences. The group

ranking should be transitive.

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papakonstantinidis Page 139

[we base the proposed “win-win-win papakonstantinidis model” on

the "incompatibilities" of those main theories]

1. The Impossibility Theorem (Kenneth Arrow)

2. Theory of Justice (John Rawls)

3. Liberal Paradox/ Minimal Liberty (Amartya Sen)

4. Pareto Optimality (Vilfredo Pareto)

5. the incompleteness theorem ( Kurt Gödel)241

6. networking (Euler)

7. game theory (non-cooperative)

8. bargaining theory (John Forbs Nash)

9. win-win-win theory (LP)- the “3bargainers model”

ARROW

Prof Arrow (born 1921) [Nobel Prize in Economics, 1972) argued in his (famous) paper (1950). "A Difficulty in the Concept of Social Welfare" Journal of Political Economy 58 (4): 328–346 the following concept: “…The last two methods of social choice, dictatorship and convention, have in their formal structure a certain definiteness absent from voting or the market mechanism. In an ideal dictatorship, there is but one will involved in choice; in an ideal society ruled by convention, there is but the divine will or perhaps, by assumption, a common will of all individuals concerning social decisions, so that in either case no conflict of individual wills is involved. The methods of voting and of the market, on the other hand, are methods of amalgamating the tastes of many individuals in the making of social choices. The methods of dictatorship and convention are, or can be, rational in the sense that any individual can be rational in his choice. Can such consistency be attributed to collective modes f choice where the wills of many people are involved? It should be emphasized here that the present study is concerned with the formal aspects of the foregoing question. That is, we ask if it is formally to construct a procedure passing a set individual tastes to a pattern of social decision-making, of social decision-making, the procedure in question being required to certain natural conditions. An illustration of the problem is the following well-known "paradox of voting'" Suppose there is a community consisting of three voters and this community must choose among three alternative modes of social action (e.g., disarmament, cold war, or hot war). It is expected that choices of this type have to be made repeatedly,

natural way of arriving at the collective preference scale would be to say

that one alternative is preferred to another if a majority of the Community

prefer the first alternative to the second, i.e., would choose the first over

the second if those were the only two alternatives

Let CandBA ....., be the three alternatives

and 3....2,1 and the three individuals.

Suppose individual)....,.....(

.................1

CtoAthereforeand

CtoBandBtoAprefers

Individual)..........(......

..........2

AtoBthereforeandAtoCand

CtoBprefers

and

Individual BtoCthereforeandBtoAand

AtoCprefers

..........(.......

..........3

Then majorityCtoBprefersmajorityaand

BtoAprefers

..............

........

We may therefore say that the community

CtoBandBtoAprefers ................

If the community is to be regarded as behaving rationally, we are forced to say that

CtopreferedisA .........

. But, in fact, a majority of the community

AtoCprefers ......... 268

So the method just outlined for passing from individual to collective tastes

fails to satisfy the condition of rationality as we ordinarily understand it.

Can we find other methods of aggregating individual tastes which imply

rational behavior on the part of the Community and which will be

satisfactory in other ways?

WIN-WIN-WIN

There are, at least, a general objection and three ways of controversial

skepticism:

241 This theorem is one of the most important proven in the twentieth century. Here are a few brief selections that will help you start to understand it. Gödel’s original paper “On Formally Undecidable Propositions” 14. Walter Bossert and Guofu Tan (1995) An arbitration game and the egalitarian bargaining solution* Soc Choice Welfare (1995) 268

. Samuelson, Paul (1947) Foundations of Economic Analysis (Cambridge, Mass.: Harvard University Press, , chap. viii;

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but sometimes not all of the three alternatives will be available. In analogy with the usual utility analysis of the individual consumer under conditions of constant wants and variable price-income situations, rational behavior on the part of the Community would mean that the Community orders the three alternatives according to its collective preferences once for all and then chooses in any given case that alternative among those actually available which stands highest on this list.

A natural way of arriving at the collective preference scale would be

to say that one alternative is preferred to another if a majority of

the Community prefer the first alternative to the second, i.e., would

choose the first over the second if those were the only two

alternatives

Let CandBA ....., be the three alternatives

and 3....2,1 and the three individuals.

Suppose individual)....,.....(

.................1

CtoAthereforeand

CtoBandBtoAprefers

Individual

)..........(......

..........2

AtoBthereforeandAtoCand

CtoBprefersand

Individual

BtoCthereforeandBtoAand

AtoCprefers

..........(.......

..........3

Then majority

CtoBprefersmajorityaand

BtoAprefers

..............

........

We may therefore say that the community

CtoBandBtoAprefers ................

If the community is to be regarded as behaving rationally, we are forced to say that

CtopreferedisA .........

. But, in fact, a majority of the community

AtoCprefers ......... 242

So the method just outlined for passing from individual to collective

GENERAL OBJECTION:

We can imagine the political "game" as "bargaining game"

The same "relationship" that binds politicians and voters each other,

applies to negotiation between 2 seeking to maximize their personal

satisfaction (everyone, as he feels this personal satisfaction)

In the case of three negotiators (or three voters, for 2 political parties, Community orders the three alternatives according to its collective preferences once for all and then chooses in any given case that alternative among those actually available which stands highest on this list.

BUT

…………………

In the suggested “win-win-win bargaining system” we introduce the

“third party,, in a bargain between two, i.e A-B and the Community-the

“C” Factor

However, this is not enough

We saw in the “Impossibility Theorem” (Arrows) that in a "meeting" of

three, cannot be formed "collectivity", unless alternative options

But if the Community should be seen as the third pole of the bargain,

then it could play a double role in each infinitesimal form of

"bargaining" and so the question acquires new interest-see scheme-

In the scheme above, we tried to “introduce” the above concept in colors :

Let the big square, be the “bargain” and let red-blue in the diagonal be

bargainers (A-B) or their strategies with payoffs,

Now, we have to present the other diagonal squares “deep blue-white”

By these squares we suggest to “color” the role of the Community in a

bargain (any bargain) between two

Deep blue expresses the “red-blue” synthesis, which is true

But the most important, is “white” with which we color the “extra role” of

the Community: A synthesis of the opponent interests towards the

agreement, characterized by more equality - justice - solidarity - efficiency

242

. Samuelson, Paul (1947) Foundations of Economic Analysis (Cambridge, Mass.: Harvard University Press, , chap. viii;

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papakonstantinidis Page 141

tastes fails to satisfy the condition of rationality as we ordinarily

understand it. Can we find other methods of aggregating individual

tastes which imply rational behavior on the part of the Community

and which will be satisfactory in other ways? If we adopt the

traditional identification of rationality with maximization of some

sort, then the problem of achieving a social maximum derived from

individual desires is precisely the problem which has been central to

the field of welfare economics.4 However, the search for a clear

definition of optimum social welfare has been plagued by the

difficulties of interpersonal comparisons. The emphasis, as is well

known, has shifted to a weaker definition of optimum, namely, the

determination of all social states such that no individual can be

made better off without making someone worse off. As Professors

Bergson, Lange, and Samuelson have argued, though, the weaker

definition cannot be used as a guide to social policy; the second type

of welfare economics is only important as a preliminary to the

determination of a genuine social maximum in the full sense. E.g.,

under the usual assumptions, if there is an excise tax imposed on

one commodity in the initial situation, it can be argued that the

removal of the tax accompanied by a suitable redistribution of

income and direct tax burdens will improve the position of all

individuals in the society. But there are, in general, many re-

distributions which will accomplish this end, and society must have

some criterion for choosing among them before it can make any

change at all. Further, there is no reason for confining the range of

possible social actions to those which will injure no one as compared

with the initial situation, unless the status quo is to be sanctified on

ethical grounds. All we can really say is that society ought to abolish

the excise tax and make some redistribution of income and tax

burdens; but this is no prescription for action unless there is some

principle by which society can make its choice among attainable in-

come distributions, i.e., a social indifference map.

Voting can be regarded as a method of arriving at social choices

derived from the preferences of individuals. Another such method of

more specifically economic content is the compensation principle, as

proposed by Mr. Kaldor: in a choice between two alternative

and self-organization : Indeed the white color is the synthesis of all

rainbow’s colors

Thus Community (the rest of population except the two bargainers (A-B)

has a double role, in any bargain between two

a. The third (maybe invisible) bargainer in a bargain between two

b. The “synthesis” and the responsibility of forming step-by step

the agreement

In the suggested “win-win-win papakonstantinidis model” introduces us to

a number of 3-pole approaches, as for example the “model of partisan

activists (which is our last objective)269

Youth activism is youth engagement in community organizing for social

change: Social change refers to an alteration in the social order of

a society. Social change may include changes in nature, social institutions,

social behaviors, or social relations. Youth activists fight for a better world!

Youth participation in social change focuses more on issue-oriented

activism than traditional partisan or electoral politics270Youth have taken

lead roles in public protests and advocacy around anti-war activism, anti-

crime and government corruption271 anti-government censorship,

expanded educational access, and public transportation access.

Technology and the use of digital media has changed the way youth

participate in activism globally, and youth are more active in media than

older generations Social media

This reversal of traditional activism "partisans" in "Thematic activism" is a

very important consequence of changing daily life and patterns through

technology that has entered our lives

However,

The main influence of “New Technologies” has been in our

communication and the “Social Networking” as well as in the way that

people (mainly young people) perceive the "New Age"

Facebook/twitter has become a tool for youth to not only gather

information, but broadcast events and activities, participate in activist

groups, and get in contact with other activist. Twitter although it is used to

provide links to activism, is not regarded to be as useful because of the

limitation of 140 characters. Twitter has also been used to spread

awareness of social issues by using hashtags

Hashtag/instagram: A hashtag is a type of label or metadata tag used

on social network and micro-blogging services which makes it easier for

269 Joel Paddock (1997) “Political Culture and the Partisan Style of State Party Activists Publius Oxford University Press Vol. 27, No. 3 (Summer, 1997), pp. 127-132 270 Bonvillani, Andrea; et al. (2008). "Juventud y política en la Argentina (1968-2008): Hacia la construcción de un estado del arte" Revista Argentina de Sociología 6 (11): 44–73. 271

Gordon, H.R. (2010) “We fight to win: Inequality and the Politics of Youth Activism”. Rutgers, NJ: Rutgers U Press

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economic states χ and y, if there is a method of paying

compensations under state χ such that everybody can be made

better off in the state resulting from making the compensations

under χ than they are in state y, then χ should be chosen in

preference to y, even if the compensation is not actually paid.

Apart from the ethical difficulties in the acceptance of this principle,

there is a formal difficulty which was pointed out by Professor

Scitovszky: it is possible that simultaneously χ should be preferred to

y and y be preferred to x. Just as in the case of majority voting, this

method of aggregating individual preferences may lead to a pattern

of social choice which is not a linear ordering of the social

alternatives. Note that in both cases the paradox need not occur; all

that is said is that there are preference patterns which, if held by the

individual members of the society, will give rise to an inconsistent

pattern of social choice. Unless the trouble-breeding individual

preference patterns can be ruled out by a priori assumption, both

majority voting and the compensation principle must be regarded as

unsatisfactory techniques for the determination of social

preferences…”

Preference and indifference are relations between alternatives. Instead of working with two relations, it will be slightly more convenient to use a single relation, "preferred or indifferent." The statement,

xRybysymbolizedwill

ytotindifferenorpreferredisx

......

............."

" The letter R , by itself, will be the name of the relation and

will stand for a knowledge of all pairs such that xRy

Now, we have, for any pair of alternatives x and y either

that x

is preferred to y or y to x or that the two are indifferent.

That is, we have assumed that any two alternatives are comparable. But this assumption may be written symbolically, The statement

ytotindifferenisxreadisxIy ...........:....

." I t is clear that IandP ..,, so defined, correspond to the

users to find messages with a specific theme or content Users create and

use hashtags by placing the hash character (or number sign) # in front of

a word or un-spaced phrase, either in the main text of a message or at the

end. Searching for that hashtag will then present each message that has

been tagged with it.

For example, on the photo-sharing service Instagram the hashtag # blue

sky allows users to find images that have been tagged as containing the sky

and#cannes2014 is a popular tag for images from the2014 Cannes Film

Festival Hashtags can be used to collect public opinion on events and

ideas at the local, corporate, or world level. For example, searching Twitter

for #worldcup2014 returns many tweets from individuals around the

globe about the 2014 FIFA World Cup

Sign of Hashtag

As it concerns of the new-new trends of communication/marketing, it must For the very latest communication / marketing forms will have to look at very recent and remarkable scientific papers that are written exactly as these changes communication standards happen Just these very recent trends, they run thinking particularly of young people addressed the form of “win-win-win bargain”: It is estimated that in the coming decades, social networking will facilitate forms of collaboration, self-organization, as young people will redefine Values and Standards, as well the huge opportunity of direct communication will be accompanied by new forms PERCEPTION One of the trends of what today we call "consumers" is the "salmon" which Professor Dr. Papakonstantinidis Stavros and alle approach Indeed, From the very recently published excellent work of (1) Stavros Papakonstantinidis,(2) Athanasios Poulis, Prokopis Theodoridis (2016 Jan) titled “R U #SoLoMo Ready?” Consumers and Brands in the Digital Era”272 we found an excellent description on today’s consumer’s trends :

272 (1) Prof.Papakonstantinidis Stavros,(2) Poulis Athanasios, Theodoridis Prokopis (2016 Jan) “R U #SoLoMo Ready?” Consumers and Brands in the Digital Era” First published in 2016 by Business Expert Press, LLC PAPAKONSTANTINIDIS LEONIDAS A.(2013), INVOLVING COMMUNITIES IN RURAL TOURISM: A “WIN-WIN-WIN PAPAKONSTANTINIDIS MODEL” METHODOLOGICAL APPROACH CASE STUDIES : WOMEN RURAL TOURISM COOPERATIVES REPORTS 108 COMMUNITIES AS A PART OF SUSTAINABLE RURAL TOURISM – SUCCESS FACTOR OR INEVITABLE BURDEN? PROCEEDINGS OF THE COMMUNITY TOURISM CONFERENCE, 10TH – 11TH SEPTEMBER 2013 IN KOTKA, FINLAND EDITOR: UNIVERSITY OF HELSINKI RURALIA INSTITUTE

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ordinary notions of preference and indifference, respectively

The statement ytopreferredisxreadisxPy ...............

The statement ytotindifferenisxreadisxIy ..........".....

It is clear that IandP .... so defined, correspond to the ordinary

notions of preference and indifference, respectively.

Axiom

yRxorxRyeitheryandxallForAxiom ..,..................:1...

xRzimply

yRzandxRyzandyxallForAxiom

..

....,......,........2..

AND

xPzthenyRzandxPyIff

yPzorxRyeitheryandxallFore

xIzthenyIzandxIyIfd

xPzthenyPzandxPyIfc

xRythenxPyIfb

xRxxallfora

Lemma

..............

......................

..............

...............

............

,...........

:

The example of voting

In short, the theorem states that no rank-order voting system can be

designed that always satisfies these three "fairness" criteria:

If every voter prefers alternative X over alternative Y,

then the group prefers X over Y.

If every voter's preference between X and Y remains

unchanged, then the group's preference between X and Y will

also remain unchanged (even if voters' preferences between

other pairs like X and Z, Y and Z, or Z and W change).

There is no "dictator": no single voter possesses the

power to always determine the group's preference.

“…Today’s consumers can check into a store with the use of a geolocation service (Foursquare), redeem an offer that is available, and share their comment on that platform. Then immediately they can post an update on their Facebook timeline, referencing the retailer’s page. SoLoMo consumers have three basic characteristics: SOcial media engagement, LOcal findability, and smart-phone MObility marketing that is SOcial-LOcal- MOtivation The authors write in their scientific work Social networks are the “activities, practices, and behaviors among communities of people who gather online to share information, knowledge, and opinions using conversational networks. Conversational networks are web-based applications that make it possible to create and easily transmit content in the form of words, pictures, videos and audios” Social networking sites like Facebook, Twitter, and Instagram are growing rapidly as channels of human communication allowing brands and consumers to engage in public discussions. As consumers are using social media as their main source of information, communication, and entertainment, marketers will be finding a fruitful environment full of opportunities….”

Keeping in mind that the one long-term goal is to develop a "three actor"

spatial model (i.e., one with candidates, citizens, and activists), the model

of partisan activists I propose to be parallel, with the usual spatial model

of elections as closely as possible. The connections between the model of

activists and the electoral model, is very important argument for the win-

win-win (the Community included) model: The relation (A-B-Community)

in the bargain, has a number of similarities with “candidates-citizens-

activists. Besides, it is the same relation “PAC” in the “local development

scientific field” (People(Local), Authorities (Local) and Consumers of the

“rural tourism” services273 Also, the triangular relation “teacher-student-

parents” in the case of “Educational crisis”274

Activism consists of efforts to promote, impede, or direct social, political,

economic, or environmental change, or stasis with the desire to make

improvements in society and to correct social injustice. Forms of activism

range from writing letters to newspapers or to politicians, political

campaigning, economic activism such as boycotts or preferentially

patronizing businesses, rallies, street marches, strikers, sit-ins, and hunger

strikes One can also express activism through different forms of art. Daily

acts of protest such as not buying clothes from a certain clothing company

because they exploit workers is another form of activism275 Still, it is

important to note that there might be some fairly straightforward

connections between the two models (the model of partisan activists AND

the electoral model) . The principal conclusions that the author tried to

reach here are that the distribution of activists in the two parties will be

relatively cohesive within each party, relately divergent between parties,

and generally in stable equilibrium. Researchers showed that if partisan

activists are distributed n ways rather like those derived here, candidates

who might want to converge to each other (and the policy center) to win

the general election might need to diverge along the line of party cleavage

to obtain the support of partisan activists in order to receive the

nomination in the first place. In effect, I answer in this article the question

273

274

275

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papakonstantinidis Page 144

From the other side, the Downsian or spatial model of voting under Euclidean or quadratic concave preferences is a widely used model of group choice and has found extensive empirical application as well, particularly in 2 dimensions The spatial model of electoral competition proposed by Downs in 1957 has generated a great deal of subsequent analysis. There has been accumulation of knowledge about these sorts of models. Throughout this development, there has been virtually unwavering attention to a closely intertwined set of questions243:

a) How do rational citizens decide how and whether to vote in two-candidate (or two-party) elections?;

b) What spatial positions would rational candidates choose to offer citizens?; and

c) c) What position(s), if any, would win and hence become the social choice?

The questions I ask concern political parties and actual or potential activists in one or the other of the two parties. Specifically, given a two-party system:

a. Who is more or less likely to become involved with a political party, and in which party are they likely to be active?

b. What are the consequences of these choices; that is, how are the partisan activists distributed across the space? Are these distributions stable and enduring? and

d) What consequences might the answers to questions (a) and (b) have for parties, policies, and elections in the short and long runs? In this article, I propose a model to answer questions (a) and (b). In the concluding section (and more briefly below), I will suggest some of the ways in which question (c) might be explored and answered.

a "three actor" spatial model (i.e., one with candidates, citizens, and activists), The model of partisan activists he proposed was parallel the usual spatial model of elections as closely as possible. The connections between the model of activists and the electoral model will not be made here. Still, it is important to note that there might be some fairly straightforward connections between the two models statement (Kenneth Arrow,1950)244: The need to

aggregate preferences occurs in many disciplines: in welfare

economics where one attempts to find an economic outcome which

would be acceptable and stable; in decision theory, where a person

has to make a rational choice based on several criteria; and most

naturally in voting systems which are mechanisms for extracting a

decision from a multitude of voters' preferences.

The framework for Arrow's theorem assumes that we need to

extract a preference order on a given set of options (outcomes).

Each individual in the society (or equivalently, each decision

of why partisan activists might be distributed as these authors assumed

them to be.

Preparing the world for a new "level of consciousness"?

The answer is rather complicated:

The current literature on concepts such as "social justice", equality, equal

distribution, shows a wide range of authors-researchers who insists on a

process of "preparing" for a new consciousness. Religion is not a matter, or

"conspiracy" but a matter of pure logic: The world cannot survive in the

form it has today. Huge burden of our natural environment, climatic

changes huge scale, huge movements "immigrants" and refugees from

their land and their accumulation in the "major centers" huge economic

losses, wars etc.

I tried to approach the main issue, from different scientific fields (math,

economics, marginal economics, sociology, psychology, history, laography

science of law, game theory, bargaining theory …

Let’s start:

ACTIVISM has a meaningful importance for the “win-win-win model” It is

its core, and, at the same time, it is the win-win-win model' in terms of

its practical application

THE CONTRIBUTION OF "WIN-WIN-WIN" IN KNOWLEDGE FIELD

KNOWLEDGE-BEHAVIOR SYNTHESIS:

According to Spais (Spais 2012)276 the win-win-win papakonstantinidis

model is a methodological tool for conflict resolution, especially in the case

of decision-making, or in forming "instant reflection winning strategies" in

the bargain (which is the frame

From the other, “sensitization" may be concerned as an information, thus

changed the 3 parts’ imperfect information, into a complete information

as Harsanyi's conditional probabilities claims. It is a hard process in the

bargain, which smoothes the angles of conflict or the payoffs/utilities

(according to Nash) The "third win" may be an umbrella, which conjoins

different "dipolar relationships" Especially, in the local management

context, it must be understood that the existence of a "distinguishable

entity", depends upon the degree of understanding and sensitization of

243

Aldrich John H.(1983) A Downsian Spatial Model with Party Activism The American Political Science Review Vol. 77, No. 4

(Dec., 1983), pp. 974-990, published by American Political Science Association 21 Papakonstantinidis L.A (2010) “Applying the Win-Win-Win Model in School Management Crisis: The Greek Case” (RC26)-Book of Proceedings I.S.A XVII ISA World Congress of Sociology Sociology on the Move Gothenburg, Sweden (2010/July, 11-17) 244

Arrow, K.J. (1950). "A Difficulty in the Concept of Social Welfare" Journal of Political Economy 58 (4): 328–346

276 GS Spais (2012) An integral bargaining solution analysis for vertical cooperative sales promotion campaigns based on the

win-win-win papakonstantinidis model” Journal of Applied Business Research (JABR) 28 (3), 359-384

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papakonstantinidis Page 145

criterion) gives a particular order of preferences on the set of

outcomes. We are searching for a ranked voting system, called

a social welfare function (preference aggregation rule), which

transforms the set of preferences (profile of preferences) into a

single global societal preference order. The theorem considers the

following properties, assumed to be reasonable requirements of a

fair voting method:

Non-dictatorship

The social welfare function should account for the wishes of multiple

voters. It cannot simply mimic the preferences of a single voter.

Unrestricted domain245

(or universality) For any set of individual voter preferences, the

social welfare function should yield a unique and complete ranking

of societal choices. Thus:

It must do so in a manner that results in a complete

ranking of preferences for society.

It must deterministically provide the same ranking

each time voters' preferences are presented the

same way.

Independence of irrelevant alternatives (IIA)

The social preference between x and y should depend only on the

individual preferences between x and y (Pair wise) In dependence).

More generally, changes in individuals' rankings

of irrelevant alternatives (ones outside a certain subset) should have

no impact on the societal ranking of the subset. For example, the

introduction of a third candidate to a two-candidate election should

not affect the outcome of the election unless the third candidate

wins. (See Remarks below.)

Positive association of social and individual values

knowing better the other polar (Spais, Papakonstantinidis and

Papakonstantinidis, 2009). For the needs of the study, I adjust the

conceptualization, in order to deal with local management and

development decisions The win-win-win perception is based on the

assumptions of information accessibility and diffusion that characterize the

modern globalized societies as well as the complexity in the decision-

making values that the "third win" (the "C" factor) could unlock a series of

obstacles (Spais, Papakonstantinidis and Papakonstantinidis, 2009).

Another idea, is that the individual three-by-two, (although doubts) must

take into consideration at each time that there is the third distinguishable

part (Spais, 2012) in the bargain, based on behaviorist analysis through

the "neural networks". Resent literature on behavioral analysis, provides

us with the relation between knowledge and behavior So, an overview is

attempt (Papakonstantinidis, 2004)277, as to find the relation between

“knowledge transfer and knowledge creation”, in the frame of the

“Modern Innovation Theory- M.I.T” (Fischer M.M, 2006 Nonaka and

others) Behavior thus may resulted from this knowledge types’ synthesis,

as the table below

Table 3: Knowledge Creation and Transfer- Types of Behavior

Papakonstantinidis, 2003

SOCIAL CAPITAL- SENSITIZATION278

Type of

Knowledge-1

Type of

Knowledge-2

Synthesis Resulted

Behavior

tacit tacit Sympathe

tic

Socialization

tacit codified Conceptu

al

Externalization

codified tacit Procedura

l

Internalization

codified codified Systemic Networking

sympathetic systemic Conceptu

al

Sensitization

systemic systemic Procedura

l

Strategic

245 I’ve based the win-win-win in an unrestricted domain: we can imagine the “umbilical points of a sphere to form a new domain of bargaining function 277

278 Papakonstantinidis LA(2003) “Sensitization as a form of knowledge creation and the Win-Win-Win Model…”

ΕΠΙΣΤΗΜΟΝΙΚΗ ΕΠΕΤΗΡΙΔΑ ΕΦΑΡΜΟΣΜΕΝΗΣ ΕΡΕΥΝΑΣ (Περιοδική Επιστημονική Έκδοση του ΤΕΙ Πειραιά) Vol VIII, No 2 /2003, pp 89-108, ISSN 1106-4110

1. Papakonstantinidis LA(2004) “Sensitization and Involving the Community. A Rural Development Application of the Win-Win-Win Model” ΕΠΙΘΕΩΡΗΣΗ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ (Περιοδική έκδοση ΤΕΙ Ηπείρου –αναγνώριση…) τεύχος 6/2004 pp 177-192

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papakonstantinidis Page 146

(or monotonicity) If any individual modifies his or her preference

order by promoting a certain option, then the societal preference

order should respond only by promoting that same option or not

changing, never by placing it lower than before. An individual should

not be able to hurt an option by ranking it higher.

Non-imposition

(or citizen sovereignty) Every possible societal preference order

should be achievable by some set of individual preference orders.

This means that the social welfare function is surjective: It has an

unrestricted target space.

Arrow's theorem says that if the decision-making body has at least

two members and at least three options to decide among, then it is

impossible to design a social welfare function that satisfies all these

conditions at once.

A later (1963) version of Arrow's theorem can be obtained by

replacing the monotonicity and non-imposition criteria with:

Pareto efficiency

(or unanimity) If every individual prefers a certain option to another,

then so must the resulting societal preference order. This, again, is a

demand that the social welfare function will be minimally sensitive

to the preference profile.

The later version of this theorem is stronger—has weaker

conditions—since monotonicity, non-imposition, and independence

of irrelevant alternatives together imply Pareto efficiency, whereas

Pareto efficiency and independence of irrelevant alternatives

together do not imply monotonicity. (Incidentally, Pareto efficiency

on its own implies non-imposition.)

▲

Alternative Dispute Resolution (ADR; known in some countries, such

as Australia246 as external dispute resolution) includes dispute

«Sensitization» is a complex but useful methodological approach,

providing - in the starting phase - local people with the «community

consensus», creating the conditions of a sustainable local development. In

other words, «sensitization» may be a fundamental local endogenous

conception under which local people learn to be active members of the

community, making their own skills and abilities valuable to their

community’s development procedure

Sensitization is a process, as well as a way of thinking –a philosophy-

motivating local people towards a common goal and providing them with

new forms of an alternative behaviour, with respect to their own place

«identity» : In fact, sensitization introduces a psychological reform : it let

people change their perception, about the «market community»

The objective is to prove that the rationalization of the «Integrated

Endogenous Local Development» could prove to be a valuable policy

means, under the proposed methodological procedure of Sensitizing Local

People, toward their common development goal, based on their own

forces. «Sensitization». as a useful methodological approach -a

philosophy- may be the fundamental conception for building the social

capital at local level, by making valuable the local people’s «intrinsic

inclinations» , under a new value system, and human communication.

The rationalization of the «Integrated Endogenous Local Development»

could prove to be a valuable policy means, under the proposed

methodological procedure of «Sensitizing Local People» towards their

common development goal. In this starting phase, «social capital», i.e the

ability of local agencies to joint up their own forces, so that to co-operate,

in a collective and efficient way, could prove to be the key-point for the

development procedure, if it was possible to be developed through a

«sensitized bottom-up approach».

Some ideas, in our life should not to be marketed : Social capital could

involve non –market “terms” as “self-respect”, “trustfulness” etc

«Community» should be concerned as «a big family», inside and at the

same time, as an enterprise in its habitants’ relations with other places or

communities, for survival

The ‘concept” of “big family” let the community operate under a spirit of

«human communication», human values, and respect to their own place’s

tradition and culture, or to the «community identity»

We try to highlight to those sides of the integrated local development

procedure, which could be improved, if they could be combined with the

social capital, at local level, under the «sensitization» methodology,

providing an innovative «bottom-up» approach, motivating local people

to be active, in planning and applying «their own ideas» for their

2. Papakonstantinidis LA(2005) Social Capital at Local Level-Methodology proposed : Sensitization «The Sensitized

Community»- Book of Proceedings ISA (RC 26) 3. Papakonstantinidis LA (2004) Sensitization & the win-win-win model: An answer to Globalization’s Impact on Local

Communities and Common Perceptions of the World Tendencies- Case Study: Community Redefinition- Tychero Evros” – ISA European Congress (I.S.A) – RC 26 (Sociotechnics and Sociological Practice) Central Theme: “Social Capital and Transformations in the Age of Globalization”, .Molyvos, Lesvos Isle, 11-14 Ιουνίου 2004.

246 Australian Securities and Investments Commission

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papakonstantinidis Page 147

resolution processes and techniques that act as a means for

disagreeing parties to come to an agreement short of litigation. It is

a collective term for the ways that parties can settle disputes, with

(or without) the help of a third party.

ADR is the closest statute to “win-win-win” In fact, the Community’s “win” is double 1. is the third pole of seeking the enforcement of "own" interest AND 2 is the arbitrator ensures equality and justice in the A-B bargain But who ensures the A-B opposite this third part of the deal (Community); The answer is one and unique: The Republic, the democratic regime thus meeting to the origins of the “win-win-win” Despite historic resistance to ADR by many popular parties and their advocates, ADR has gained widespread acceptance among both the general public and the legal profession in recent years. In fact, some courts now require some parties to resort to ADR of some type, usually mediation, before permitting the parties' cases to be tried (indeed the European Mediation Directive (2008)expressly contemplates so-called "compulsory" mediation; this means that attendance is compulsory, not that settlement must be reached through mediation). Additionally, parties to Merger and acquisition transactions are increasingly turning to ADR to resolve post-acquisition disputes The rising popularity of ADR can be explained by the increasing caseload of traditional courts, the perception that ADR imposes fewer costs than litigation, a preference for confidentiality, and the desire of some parties to have greater control over the selection of the individual or individuals who will decide their dispute247Some of the senior judiciary in certain jurisdictions (of which England and Wales is one) are strongly in favor of this (ADR) use of mediation to settle disputes Prof .Tovey Craig(2010) studied the “Instability in two dimensions’248: Especially he concerns on the classic instability theorems of Euclidean voting theory definitively that treats all cases except that of an even number of voters in 2 dimensions. For that case, all that has been known is that the set of stable configurations is neither measure zero nor measure one. It has been shown from other researchers, that the probability of equilibrium is 0 in three or more dimensions, and in two dimensions when the number of voters is odd. To be more precise, the set of

configurations for which equilibrium exists is measure 0 for these

cases. In contrast, one dimension always admits of an equilibrium249

The case of 2 dimensions with an even number of voters has never been resolved. All that is known is that the set of configurations for which equilibrium exists, and the set for which equilibrium does not exist, both have positive measure. (The first fact can be established

community development. A “sensitized community” is less depended on

the outside decision making centre.

«Sensitization» - as the upper- limit of the sensitization procedure- is been

approached, step by step, especially :

Establishing the «bottom-up approach» in planning development at local level

Analyzing local people «intrinsic inclinations» in respect with a «system value»

Creating a «team psychology» among local people

Creating a «Central Theme» -a «flag»- for motivating local people The proposed procedure may be useful, especially in small rural-isolated-

areas

Indeed, small rural less developed areas are experienced by «poor cycles»,

due to the world existing system, which reproduces dependencies

especially those of a «centre-periphery system». All crucial final decisions

for their development, are made by the centre From this point of view,

benefits addressed to those poor areas are absorbed by the centre.

Besides, the small-and poor- rural areas are burdened by the «negatives»

of «free market» operation.

The presented Model , “The S.H.I.E.L.D Model”, from the initial letters of

«Sensitized Harmonic, Integrated Endogenous Local Development»

(PAPAKONSTANTINIDIS) may provide a «shield» against the «negatives»

coming from the «free market» mechanisms’ operation. It is based on the

endogenous cooperation, which may improve the rural local places’

competitiveness, in the world market. «S.H.I.E.L.D Model» describes an

alternative form of cooperation, in which, «common place» is the «main

point» («spatial discrimination», instead of «classes discrimination» of the

Marxian theory) Based on «hidden local abilities» -the intrinsic

inclinations- human communication (which is easier in the place with a

small population size), more degrees of «free choices» and less degrees of

psychological pressure and more harmony between biological-

psychological-working rhythms, the presented (for the first time) Model

«tries» to make the Endogenous Local Force, «valuable» and useful, in the

maximum, under the operation form, of an integrated strategic local Plan.

At the same time, S.H.I.E.L.D Model «suggests» different ways by which

local people could be more «happy» , with more degrees of «free choices»

and biological-psychological «harmony», during the development

procedure (in the stage of planning, as well as in the stage of realizing the

development, at local level)

to restore the local problem in the scientific dialogue, under the prism of

globalization impact on “community”; it highlights the contemporary

dynamics of social capital in the frame of “territory-community”

redefinition, due to globalization phenomenon; social transformations

such as labour mobility, lack of free time, emotional instability, rapidly

high tech changes provide us with the necessary material to deal with the

247 Totaro, Gianna., "Avoid court at all costs" The Australian Financial Review Nov. 14 2008. (April 19, 2010) 248. Tovey Craig A (2010): The probability of majority rule instability in the 2D Euclidean model with an even numbers of voters

Oct 2010 · Social Choice and Welfare (Keywords Spatial voting-Equilibrium-Stability-Euclidean preferences-Majority rule) 249 Tovey Craig (2010)”The probability of majority rule instability in the 2D euclidean model with an even number of Voters” SOCIAL CHOICE AND WELFARE · OCTOBER 2010-Preprint submitted to Social Choice and Welfare February 14, 2010 Papakonstantinidis, L. A. (2004a). Sensitization and involving the community. A Rural Development Application of the Win-Win-Win Model” Scientific Review of Economic Sciences, 6, 177-192.

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by considering 12 n points at the vertices

of a regular polygon on 12 n vertices, and one point at

the polygon's center. The center point is an equilibrium, and small

perturbations of the n2 points do not disturb the equilibrium.

The second fact is established by considering n2 points at the

vertices of

a regular gonn 2 No equilibrium exists, and

nonexistence is unaffected by small perturbations of the n2

points.) In the D2 Euclidean spatial model of voting, n

voter ideal points are located in 2 and voters prefer policies (points) closer to their ideal points under the Euclidean norm. An equilibrium point is one that cannot be dislodged by majority vote.

That is,y

is an equilibrium point if there does not existx

such that strictly more than 2

n of the ideal points are closer to

x than to

y , under the Euclidean norm.

.Besides,

Aldrich John H. (1983)250 examined an individual "calculus of

participation" that is similar to the spatial interpretation of the

"calculus of voting." This calculus is then generalized by examining

conditions that may hold for aggregate activism probabilities, and

the relationship between the two forms is investigated. Some results

are then presented which concern the distributions of activists in

the two parties.

Also, from a quite different point of view, population genetics is a

quantitative of evolutionary biology that is concerned with the

evolution of genetic variation in a population over time. The

locations of the genome which exhibit genetic variation are called

loci (sing. locus), and the variations at these loci are called alleles.

For example, a locus could be a single nucleotide of DNA, with the

set of alleles being the four possible DNA nucleotides. The

distribution of the alleles in a population fluctuates over time due to

the biological processes of mating, mutation, recombination and

natural selection, among other things. The most basic model of

population evolution, the Wright-Fisher model describes the alleles

at a single locus of a population of size N as evolving in discrete

generations, where the alleles in each generation are generated by

community problem as a “market problem” in a global environment; it

provides us with the incentive to find out ways of therapy, or even ways

as to involve the community –as a reaction to globalization phenomenon-

in the bargaining problem; that is the paper contribution, in terms of

sensitizing the community people

From this point of view sensitization, based on knowledge transfer and

knowledge creation in the community may be proved to be a useful

methodological tool and a creative approach to conflict resolution, based

on Nash “no-cooperative game” theory.

It particular, we focuses on the “sensitization process” – a form of

knowledge creation- as the reaction to a given information, which

influences the socioeconomic behavior and therefore, the pure individual

strategies, leading them to a converge. It may be concerned as an

extension to Nash “non cooperative game” theory (win-win model)

according to which, both parties involved in a negotiation may formulate

winning strategies. Community involvement may be seen as a three-way

negotiation.

Taking part in such a negotiation each member of the community should

ask him/her self three questions: “what is the best for me?” “what is the

best for me and for the other?” and “what is the best for me, for the other

and for the Community?” ( as the third, “invisible” part in the bargain).

As individual strategies are going to be converged, then a solid basis may be created for a real cooperation between the members of the community thus maximizing the socioeconomic profit for all the involved parties in a negotiation (win-win-win) the conflict between a single economic system (Globalization) and a

fragmented cultural and political world, creates tendencies on social

capital contemporary dynamics; globalization is marketed by the tension

between global economic and technological interdependence and social

interconnectedness , on the one hand, and cultural fragmentation and

political division on the other (Alberto Martinelli, 2003, p. 293) [Martinelli,

A. 2003, 'Markets, Governments, Communities and Global Governance',

International Sociology, vol.18,n.4, jube 2003:291-324]279.

The world can be conceptualized as a single system but world society does

not exist yet, since there is no normative consensus reflected in commonly

accepted institutions at the world level; and therefore global integration

and governance should not be taken for granted. Globalization s one of the

most distinctive features of the temporary dynamics of capital; this is

especially distinguished in the case of social capital; it has been defined in

many complementary ways as “time-space compression” (Harvey, 1989),

“action of distance” (Giddens, 1990) “accelerated interdependence”

(Ohmae, 1990) and “networking” (Castells, 1998) It can be defined

(Alberto Martinelli, 2003, p. 294) “as a set of related processes that

interconnect individuals, groups, communities, states, markets,

corporations and international governmental and non-governmental

organizations in complex webs of social relations; and, more synthetically,

as the growth of networks of worldwide interdependence .The impressive

literature on globalization can be arranged in a conceptual space with

reference to three mayor axes, i.e “Hyper-globalization vs sceptics” (wich

focuses on degree of novelity of globalization and its impact on nation-

states; “Neo-liberals vs neo-Marxist and radicals (focused on balance of

250 Aldrich John H.(1983) A Downsian Spatial Model with Party Activism Author(s): Source: The American Political Science Review, Vol. 77, No. 4 (Dec., 1983), pp. 974-990

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randomly sampling parent alleles from the previous generation

while giving them an opportunity to mutate.251

ACTIVISM:

I found a an activist's guide to making signs, giving speeches, and

convincing others they should support your cause (Effective

Information Distribution for Activists by the Rad Cat Press August

8, 2013)252

Human Psychology and Reception of Information:

KNOWLEDGE

• New knowledge sticks best to already existing

knowledge. When presenting information, relate it to

commonly known concepts, beliefs, pop-culture, or

images.

• The brain remembers sexual, silly, or humorous

information better than it does other types.

• Different people learn better with different senses. This is

explained later in 'Giving a Presentation.'

APPEAL EMOTIONALLY TO PEOPLE

People are often selfish when dealing with strangers They care a

whole lot about themselves, their friends, and their family, and not a

whole lot about you and your movement (any activist movement)

This is why it is essential that while trying to convince a person to

support your movement, that you connect it to their wants and

needs in some way. How does it impact them, their health, money,

land and loved ones?

A common assumption activists make is that their strong emotions

toward a cause will be shared by everyone else. They believe this to

the extent that they think yelling or aggressively attacking others will

win allies. What these activists forget is that it took themselves a

very long time to arrive at their current set of beliefs. Perhaps it was

growing up in a certain environment such as the forest or city.

Perhaps it was being the black sheep within a family. Perhaps it was

positive-negative globalization impact and its western hegemonic

character on the world; “Homogenization vs heterogeneity and

hybridization (which focuses on the cultural dimension of globalization)

More than one types of a place’s “carrying capacity” (physical, economic,

social, environmental, psychological) explain the “insist” of a place, to

accept people and human activities, beyond the equilibrium point

providing the place with a satisfied level of “quality of life”. Rural places

have the “advantage” of operating below the point: Small size of

population, low infrastructure, human relations, based on more “free

time” and a harmony between physical and technical environment.

(Papakonstantinidis, 1997 : The S.H.I.E.L.D Model”)Usually, rural places are

isolated and depended on decision-making centers. In most of cases, these

centers are interested for maximizing their economic profit, than building

the rural development procedure (Samir Amin, 1971: 189).From the one

hand, one could measure a number of rural development negatives, but

“rural space” is a real “field” of “policy intervention”, through motivating

the “endogenous” human forces locally. But how?

The answer is:Through Sensitizing Local People [ Papakonstantinidis, ISA,

1999 –01)

By the term “sustainable development”, in general, we mean the total of

local

interventions that ensure that the non-renewable natural resources of a

place are not used up. The most characteristic definition is given by the

“Brundtland Committee” report which states that

“Sustainable development is the development that satisfies the needs

of the present without minimizing the ability of the future

generations to satisfy their own” (WCED 1987:2-10). Also:

“Sustainable development is the development which meets the needs

of the present generation, without compromising future generations

to meet their own needs” (Swarbrook J. 1999 : 17)280

Even though the sense of sustainability is very old, in our

days this term has acquired a more general mental meaning in order

to cover the social, sociological, psychological and, particularly, the

cultural aspects of the wearing out of the resources of “admission

279

251 Bhaska Anand(2012) “Approximate sampling formulas under the coalescent with finite-alleles models of mutation” - University of California, Berkeley A thesis submitted in partial satisfaction of the requirements for the degree of Master of Arts Dr.Papakonstantinidis Leonidas Dimitropoulos Anastos(2012) “The win-win-win Papakonstantinidis model -A behavioral

analysis in dynamical systems The Non Instrumental Rationality Paradox Case-study: Hellenic Benefactors” ISBEFA –

International Scientific Press

Candace West; Don H. Zimmerman (1987) “Doing Gender”- Gender and Society, Vol. 1, No. 2. (Jun., 1987), pp. 125-151 252

Effective Information Distribution for Activists by the Rad Cat Press August 8, 2013) 280 Swarbrook J.( 1999) Sustainable tourism management- Wallingford CABI Publishing

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papakonstantinidis Page 150

facing oppression growing up. Whatever it was, realize that

convincing people that your movement is worth their time is an

involved task and takes time.

NON-VIOLENT COMMUNICATION

Yelling, or speaking violently, rarely, if ever, convinces a person that

they are wrong in an argument. Try your best to call people in, not

out. Positive reinforcement is more effective than negative

reinforcement. It is counter-intuitive, but rewarding a person for

good behavior gives them a reason to exhibit a new behavior,

whereas punishing someone for a bad behavior does nothing

toward showing them an alternative. A person who enters into an

argument with you in anger or violence should first be mediated

with. Your goal is to calm them down by openly listening to their

needs without reacting in argument, criticism, or judgment. Ask

questions. You can state your side once they have calmed down.

If you do need to call a person out, do so speaking from your needs

and observable facts, not with guilt, humiliation, shame, blame,

coercion, or threats.

Questions are good because it shows that you want to understand

the other person and makes it less likely they will go into a

staunchly defensive mode of speaking. Many times people are

unaware of how their actions impact others, and just need a friendly

wake up call. Those who ignore or mock your desire for change

probably will not alter their behavior. It may be best to not waste

your time on these individuals.

To approach the activists’ behavior must be distance oneself, from both of those activists whose behavior may be predicated on their potential for changing the party materially and the careerist, whose cost-benefit calculations are so vastly different. Activists here are partisans because they desire to see the party realize its goals; they want to support the party, not change it. In additional it is assumed that activists contribute to only one party, not to both simultaneously. Finally, the decision to become an activist is a potentially long-term commitment, a "standing decision." To be sure, the decision to become involved in a specific campaign will depend upon the particular set of candidates standing for election at that particular time and place253. But, the "partisan" part of the decision emphasizes that the "standing decision" depends on where and for what the party stands. The Riker-Ordeshook calculus254 is more obviously relevant in this setting. Since they show that no rational citizen would vote for the less preferred candidate, their calculus swings on the turnout decision, leading to their famous

equation: CDPBR where R = "Reward" for

areas” (WTO 1995).

What is generally acceptable is that the examination and

evaluation of the conditions of sustainable development requires the

consideration of the economic, social and ecological systems within a

unified analysis framework at the same time.

The new approach of sustainable development is based on the need

for convergence of the environmental development policies and

combines three individual pursuits :

The efficiency of economy

Social equity and justice

Environmental protection

The search for the relation between local management and sustainable

development follows four different approaches [ Swarbrook]:

The socioeconomic environment, given by the constraints of the

“new economy”, in a more complicated outlook (complementary and

multifold basis).

The “integration of activities”, in the concept of sustainable local

development, where viability focuses on the preservation-extension

of local activities, under an integrated form, in the long run.

The environmental, in the sense of ecologically sustainable local

development, where viability focuses on the used natural resources.

The cultural, in the sense of a cultural sustainable local development,

i.e tradition, the ethic, the climate conditions of the local population

[Friedman-Weaver: 92 ]

The local resources are not renewable (human & cultural resources &

environment).

The “socioeconomic environment” in the framework of a “new economy”

system defines the wide-range targets of a local management

intervention, towards local people welfare [Agnes Gannon: 111]281 :

- the self-feeding local development activities

- the preserving of the non-renewable natural resources

- the safekeeping of the natural and human environment

- the safekeeping/reproduction of the cultural being

- the preserving of the sociological and psychological tissue

- the safekeeping of the natural-cultural individuality

253 John H. Aldrich(1983) “A Downsian Spatial Model with Party Activism” The American Political Science Review, Vol. 77, No. 4 (Dec., 1983), pp. 974-990 254 William H. Riker and Peter C. Ordeshook(1968) A Theory of the Calculus of Voting The American Political Science Review

Vol. 62, No. 1 (Mar., 1968), pp. 25-42

Riccardo Petrell (2001) Capitalismo Blu. La predazione della vita. Verona: Stampato in proprio. Università del Bene Comune,

Ass. Monastero del Bene Comune, 2011.

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voting instead of abstaining, P = (Subjective) probability that one's vote will ''count,'" B = Differential benefits from seeing the preferred candidate elected, D = "Citizen duty" (or positive rewards associated with voting, independent of the outcome), and C = Costs of voting.

BEHAVIOR255 Behavior modeling

Behavior modeling James E Mazur (2005) suggests two different theories about punishment is the negative law of effect/ matching law (Rachlin & Herrnstein, 1969) and the avoidance theory of punishment (e.g., Dinsmoor, 1954, 1977). The negative law of effect is simply the view that reinforcement and punishment have opposite effects on behavior: reinforcement strengthens behavior and punishment weakens behavior. The avoidance theory (Myerson and Sandra Hale 1984) of punishment takes a different approach. According to Herrnstein the matching law, choices are distributed according to rates of reinforcement for making those choices. An instance of this for two choices can be stated mathematically

as 21

1

RR

R

21

1

rr

r

where R1 and R2 are rates of response for two alternative responses, and r1 and r2 are rates of reinforcement for the same two responses. Similarly for the punishment, where the equation has opposite sign

Rational Behavior

Rational behavior for a consumer’ definition (Simon H. “1955).

Generally speaking, interaction behavior is an important indicator of the underlying relationship between individuals (Clark E Moustakas 1956) In a Model of rational behavior for a consumer (a typical games theory / bargaining application), we assume a consumer faces a choice of n commodities labeled 1,2,...,n each with a market price p1, p2,..., pn. The consumer is assumed to have a cardinal utility function U (cardinal in the sense that it assigns numerical values to utilities), depending on the amounts of commodities x1, x2,..., xn consumed. The model further assumes that the consumer has a budget M which is used to purchase a vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn). The problem of rational behavior in this model then becomes an optimization problem, that is:

),,....2,1(max xnxxU

subject to:

Mpixi

under the constrain xi , 0xi

}....2.1{ nxi

This model has been used in “general equilibrium theory, partculary to show the existence and “Pareto efficiency”256of economic equilibria

1.1 Social transformations impact on community due to Globalization Some “social transformations impact on the community” points are

accurate as:

“Globalization of economies without global rules may lead to a gap between market economy and human society” (Warlas, 1980) Indeed this gap is nowadays obvious, even if sizes are better than decades before, due to new technologies. But

“New technologies “attack” to “space” and “time” variables toward eliminating them’ (Riccardo Petrella, 2001)282

“State” substance trends to retreat, under the globalization of economies phenomenon “...each big city follows a global metropolitan strategy breaking down traditional links with its state operation...” (R. Petrella, 2001)

the meaning of “active citizens” who participate both in planning and achieving the development procedure may be rather an utopia, than a real situation [Papakonstantinidis, 2002 & 2003]

People have , nowadays much more than one choices, to meet their needs [ the “McDonalts syndrome” (Papakonstantinidis, 2000) ] as the result of a production –consumption far from meeting real needs- the “market society” (Zahareas, 1986)

During the globalization procedure, people more and more feel “placeless” without a real point of concern, as they are more and more depended on markets (T.Meyer, 2000)

“Space” “State”, “Regions” definitions nowadays may be

impossible under “placeless conditions”, due to “market economy”

followed by their dependencies on money market all over the world.

(Chomsky 1973283.[( Chomsky, Noam (1973), "Conditions on

Transformations", in Anderson and Kiparsky, A Festschrift for Morris

Halle, New York: Holt, Rinehart & Winston, pp. 232–286 ] Petrella

Riccardo, 2001284,[ Petrella Riccardo (2001) Il Manifesto dell'acqua. Il

diritto alla vita per tutti EGA-Edizioni Gruppo Abele. Collana Altri

saggi. Edizione: 2º, 2001]. Grougman, 2003 285) [ Crougman Paul

2003 The Great Unraveling: Losing Our Way in the New Century W.

W. Norton & Company. Retrieved 2010-01-12]

In the opposite, under those conditions, may be easier, the “territory-community” term to be defined, as “the political alternative position” to economies globalization phenomenon for the reasons of the lack of “global rules” or even a minimum of “bargaining ethic” (Marinoff 1999)

“Territory-community” , the first “family after” organizational unit, had not highlighted under now; it has been characterized in fluent literature [[ MacGaffey Jannet (1987), Robertson C. (1997), Osirim Mary J (2003), Katseli Luca (1979) House-Midamba B. and Ekechi F (1995), Kamitza R (1994) Horn Nancy (1994)] as the “informal sector” of the economy

Development trends in the last decades of the 20th century and early the

21st reflect two contrasting features: The first is sustained improvement

in the living conditions in many countries captured by declining mortality

rates, rising per capita incomes better nutrition, improved education

levels, a more impartial judicial and legal system and broader civil and

political freedom (at least before “September 11” event). It is being

281

255

Martinelli, A. 2003, 'Markets, Governments, Communities and Global Governance', International Sociology, vol.18,n.4, jube

2003:291-324.

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Interactive Behavior

Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect. “ A kind of groups action, having an impact output on status organizing processes in decision making in other groups whose members differ in external status (Berker J, Cohen, Zeldich 1972 Jun)257 or even,,, “the kind of action which describes conditions influencing the display of gender-related behavior is presented as a supplement to existent models of sex differences. (Deaux, Kay; Major 1987) A closely related term is interconnectivity which deals with the interactions of interactions within systems: combinations of many simple interactions can lead to surprising emergent phenomena. Interaction has different tailored meanings in various sciences Interaction behavior is an important indicator of the underlying relationship between individuals. On the basis of overt behavior we often make inferences and interpretations and arrive at an understanding of its meaning and significance for the individuals involved. This kind of knowledge is possible when we have accurate presentations and descriptions of observable behavior.

Bargaining Behavior

Bargain is defined as a form of energy (Papakonstantinidis, 2002, Aug) between two distinguishable entities with different expectations and controversial interests, where each part intends to sovereign. Another definition (Uchendu, Victor(1967) is “Bargaining or haggling is a type of negotiation in which the buyer and seller of a good or service dispute the price which will be paid and the exact nature of the transaction that will take place, and eventually come to an agreement Bargainers’ behaviour is shaped by many factors, but instrumental rationality may be the dominant criterion. At any case, recent literature provides us with the relation between knowledge and behavior.Practically, the social relationship “imitates” the survival conflict in Nature, which presupposes the distinguish entities separate acquired independent presence and action, in a whole “planet system” based on complementarity solidarity, and altruism This action is directed by the motive of gaining an individual profit. (Nash J.F Nasar & Kuhn, 2001) As for the tendency to conflict, it: refers to the tendency to competition (Spais, Papakonstantinidis and Papakonstantinidis, 2009) between the two parts of the bargain with different expectations and controversial interests, results from the combination: a. the case of the distinguishable entity, b. mistrust of each distinguishable entity and c. tendency to improvement. Based on the above, the motive of individual benefit leads with mathematic precision to the conflict, the tendency to sovereignty and from there to a competition climate, which is the corner stone of our economic system. The bargaining problem is about a two-person bargaining situation involves two individuals (Von Neumann and Morgenstern, 1947), who have the opportunity, either to be competitors to each other (win-lose), or to make coalitions, or even to create pure individual

increasingly recognized that development is about the quality of people’s

lives and expansion of their ability to shape their own futures. It involves

more equitable education and job opportunities, greater gender equality

better health and nutrition cleaner and more sustainable natural

environment (World Bank Report, 2000)

The second feature consists of setback to real terms of the development

due to wealth concentration, regional and local inequalities , the absolute

poverty in large parts of the planet, lack of food and medical care in these

parts, increasingly children mortality, increasingly economic migration

trends, dramatic climate changes, due to human activities, armed

conflicts, terms confusion: The last one consists what is nowadays called

“numbers against welfare”, due to different messages [ the “new-speak”

of our Information Age” ].

To start with “development” it is necessary to redefine it, in the frame of

the “New Age of Globalization and Information” conditions: Definitions

given during the industrial Age are not accepted in the post-industrial

period; what kind of development is needed, now? A higher per capita

income via economic growth should be an objective of the economic

policy, under the new conditions? How market should eliminate the

increasingly inequalities and / or restore environmental parameters? How

technological changes should contribute in a more equal wealth

distribution , or in a global welfare? These are some questions , or

challenges for the development planners. They have, firstly, to redefine

the “field” of their planning intervention policy For example, what “area”

is in the “New Age” ? The “cybern-space could be included? What a

regional area is? The expansion of big cities or the metropolitan centers

provides us with new data, about terms as “regional”, or “local” defined

during the industrial period. Terms as “territory”, “place”, “community”

“space” “spatial analysis” etc defined during the industrial period for the

specific needs of industrial development have no mean in the post-

industrial period Industrial Age provided us with a more clear terms

definitions “Space is defined by the relations between people who live in a

place” (Perroux 1955) But nowadays the “fictitious workers” for example

living in Tokyo offer their “job” in New York City, through the cyberspace.

These people are closer to “job” environment than home Besides

“economic dualism” in those cases must be excluded People in U.S,

usually offer their work in a different State from those where they live.

They take the plane every day, to go to their jobs. People usually spend

more and more hours per day in the “enterprise environment” than home

The have no “free time” They are used to concern job as home and home

as job, with impact on family life (Schor J,2001 ) It is therefore estimated

that a definition gap really exists. From this point of view, development

planners have to redefine fundamental terms as “territory-community” in

the frame of New Age conditions for development planning and policy.

From the other hand, a global society which derives its main profits from

282

283

284

285

257 Berger, Joseph, Bernard P. Cohen, and Moms Zelditch. Jr. 1972. "Status Characteristics and Social Interaction." American Sociological Review 37: 241-55

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strategies, based on bargainers’ instant reflection behavior (win-win) (Nash, 1950; Arrow and Debreu, 1954; Aumann, 1987; Crawford, 1997 Nash (1951) focused on payoff shares/utilities combination. Bargain may result in either agreement or disagreement (Nash, Nasar and Kuhn, 2001). Utility expresses the constraint or the “fear factor” of disagreement for the negotiator who desires negotiations to be led in agreement more than the other one. Who needs more, negotiation leading to an agreement expects more utility, but – probably has been a central research topic in economics for over five decades and has become an interesting issue in many fields in recent years.

Bargaining has been a central research topic in economics for over five decades and has become an interesting issue in many fields in recent years. Bargaining is the central mechanism employed to set the terms of a cooperation and/or exchange in order coordination and solution to be achieved between/among the parties. Consequently, there is growing interest in the literature from different fields that can help improve the effectiveness and efficiency of bargaining solutions analyses. Especially the two person bargaining problem is a problem of understanding how two agents should cooperate when non-cooperation leads to Pareto-inefficient results. It is in essence an equilibrium selection problem; Researchers can offer insights and frameworks to help policy-makers, managers and other protagonists It is obvious that win-win-win could introduce a “new concept of behavior which is closer to activism, than to “marketer’s patterns

MARKET PATTERNS258 Market Patterns describe the business and explain the general pattern of change of the particular market model indicating how this change is likely to impact business operations. Hypothesize the basic short-run and long-run behaviors of the model in the business you have chosen in a “market economy.” They have to provide support for your assumptions and conclusions. Researching the company, collect costs, revenue data, other data from the business or that you deem relevant. Explain how you would modify the data in order to make it relevant to decisions a manager must make. They have to explain the major factors that affect the degree of competitiveness in your business. Use the data to develop at least three (3) measures (e.g., productivity measures) to show how the

drugs, sex-fear , guns, commercialized childhood, sadism against children,

school transformation in a “directed amnesia” & values & esthetic &

ethic nihilism is going to its end (George Steigner, 1999 “Grammars of

Creation”). Social transformations are going in the frame of trends of

nihilism (zero trends) ; “there is not exist a global economy without global

rules” (Warlas, 1990); in his “Grammars of Creation” , Steigner introduces

the dilemma: “we need more answers, or questions? Maths and Physics

provide us with answers, but philosophy may be the only one which

provides us with “questions”; and nowadays we need more questions,

than answers...” People in the most developed countries try to escape to

astrology, even for political decisions making ; but history has run more

speed than predicted: If Winston Churchill was a horse -fighter , early the

20th century, then fifty years later had to use an hydrogen-bomb against

his enemies and fifty years later –early the 21st century we are called to

face the “assymetric war” in context with the “religious-fontamelism” born

by a two-poles conception, according to which people and ideas have

been concentrated in a two-poles system: the “axe of good” against the

“axe of devil”, black against white or the “ one-zero system” , by

eliminating the intermediate human and social perspective. Europe may

be proved rater unable to face their own political- territory problems (

Kossovo,Bosnia, etc).

concern job as home and home as job, with impact on family life (Schor

J,1998)286 It is therefore estimated that a definition gap really exists. From

this point of view, development planners have to redefine fundamental

terms as “territory-community” in the frame of New Age conditions for

development planning and policy.

From this point of view, having presenting “sensitization” as added tacit

knowledge, the example pre-assumes that there are three persons (as in

the win-win-win hypothesis) that competes each-other

A. the TWO (2) basic Gödel's incompleteness theorems (1931) Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete

B. The peer-pressure/Grameen Bank successful experiment in Bangladesh

C. The institution of arbitrator in relation with the Democratic Regime of west type’s societies ((under state control by Independent Authorities)

Precisely, A. FIRST To deal with the TWO (2) basic Gödel's incompleteness

theorems (1931) : Gödel's incompleteness theorems are among the most important results in modern logic. These discoveries revolutionized the understanding of mathematics and logic, and had dramatic implications for the philosophy of mathematics. There have also been attempts to apply them in other fields of

258 “ECO 550 ASSIGNMENT 3 MARKET MODEL PATTERNS OF CHANGE”- HOMEWORK AND TUTORIALS- 23-01-2016

286 Schor Juliet (1998) The Overspent American: Upscaling, Downshifting and the New Consumer, June 1998. (New York: Basic Books). Paperback Edition. (New York: HarperCollins), 1999. Japanese edition (Tokyo: Iwanami Shobo), 2000. Video version entitled The Overspent American: Why We Want What We Don’t Need, produced by Media Education Foundation, September 2003. Chinese edition 2009.

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industry is evolving. They have also to provide evidence supporting your rationale. Research two of the business’ closest competitors to determine the pricing strategy for each business indicating how knowledge of this information may influence pricing decisions in your business. Provide support for your rationale. Recommend a pricing policy for the business you chose. Assess how your pricing policy maximizes profits for the business. Finally, the have to provide support for your rationale. Alternative Dispute Resolution:

ADR (Alternative Dispute Resolution) is generally classified into at

least four types: negotiation, mediation, collaborative law, and

arbitration (Sometimes a fifth type, conciliation, is included as well,

but for present purposes it can be regarded as a form of mediation

ADR can be used alongside existing legal systems such as “sharia”

courts within common law jurisdictions such as the UK.

ADR traditions vary somewhat by country and culture. There are

significant common elements which justify a main topic, and each

country or region's difference should be delegated to sub-pages.

Alternative Dispute Resolution is of two historic types. First,

methods for resolving disputes outside of the official judicial

mechanisms Second, informal methods attached to or pendant to

official judicial mechanisms. There are in addition free-standing and

or independent methods, such as mediation programs and ombuds

offices within organizations. The methods are similar, whether or

not they are pendant, and generally use similar tool or skill sets,

which are basically sub-sets of the skills of negotiation.

ADR includes informal tribunals, informal mediative processes,

formal tribunals and formal mediative processes. The classic formal

tribunal forms of ADR are arbitration (both binding and advisory or

non-binding) and private judges (either sitting alone, on panels or

over summary jury trials). The classic formal meditative process is

referral for mediation before a court appointed mediator or

mediation panel. Structured transformative mediation as used by

the U.S. Postal Service is a formal process. Classic informal methods

include social processes, referrals to non-formal authorities (such as

a respected member of a trade or social group) and intercession.

The major differences between formal and informal processes are

(a) pendency to a court procedure and (b) the possession or lack of a

formal structure for the application of the procedure.

For example, freeform negotiation is merely the use of the tools

philosophy, but the legitimacy of many such applications is much more controversial. The first incompleteness theorem: Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory. EXAMPLE: For each consistent formal theory T having the required small amount of number theory, the corresponding Gödel sentence G asserts: "G cannot be proved within the theory T". This interpretation of G leads to the following informal analysis If G were provable under the axioms and rules of inference of T, then T would have a theorem, G, which effectively contradicts itself, and thus the theory T would be inconsistent. This means that if the theory T is consistent then G cannot be proved within it, and so the theory T is incomplete. Moreover, the claim G makes about its own un-provability is correct. In this sense G is not only un-provable but true, and provability-within-the-theory-T is not the same as truth. The formal proof reveals exactly the hypotheses required for the theory T in order for the self-contradictory nature of G to lead to a genuine contradiction The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency. Given that the consistency of a system can be proven outside of the given formal system, Gödel says, The Second Incompleteness Theorem One big reason for the expressed disconnect is that Gödel’s theorems are about formal axiom systems of a kind that play no role in daily mathematical work.

See math prove next

B. SECOND: there are forms like the “peer pressure” introduced in

countries like Bangladesh GRAMEEN BANK Muhammad Yunus)

:“….There are several barriers to entry in the lending business in

developing countries, many of which have to do with the information

advantages that incumbent moneylenders have over potential entrants. To

begin, the local moneylender is intimately familiar with his clientele, and

this gives him a huge information advantage over a bank officer in

selecting reliable loan recipients.

At the same time, the moneylender is in a very good position to monitor

borrowers since he can check up on their activities daily.

Local moneylenders are also familiar with village customs and practices

and can offer useful business advice; they are also in a good position to

provide informal insurance to the loan recipients, too, since they know

when a nonperforming loan is caused by outside causes, like bad weather,

and when laziness is the cause.

Finally, moneylenders operate at a much smaller scale than Citibank does. Most of these loans are minuscule by Western standards, and Citibank just is not set up to handle tiny investments, even if they are potentially very profitable.

These factors -- selection costs, monitoring costs, local experience, insurance and inappropriate scale -- conspire to create a virtual monopoly for the moneylender. Even moneylenders from neighboring villages might find it hard to compete with someone who has an intimate knowledge of a particular village's inhabitants. The result is tens of thousands of tiny monopolies and many profitable projects that are never undertaken because of the high cost of borrowing.

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without any process. Negotiation within a labor arbitration setting is

the use of the tools within a highly formalized and controlled

setting.

Calling upon an organizational ombudsman's office is never, by

itself, a formal procedure. (Calling upon an organizational

ombudsman is always voluntary; by the International Ombudsman

Association Standards of Practice, no one can be compelled to use

an ombuds office.)

Organizational ombuds offices refer people to all conflict

management options in the organization: formal and informal,

rights-based and interest-based. But, in addition, in part because

they have no decision-making authority, ombuds offices can,

themselves, offer a wide spectrum of informal options.

An organizational ombudsman (OO) is a designated neutral or

impartial dispute resolution practitioner whose major function is to

provide independent, impartial, confidential and informal assistance

to managers and employees, clients and/or other stakeholders of a

corporation, university, non-governmental organization,

governmental agency or other entity. As an independent and neutral

employee, the organizational ombudsman ideally should have no

other role or duties. This is in order to maintain independence and

neutrality, and to prevent real or perceived conflicts of interest259.

Using an alternative dispute resolution (ADR) sensibility, an

organizational ombudsman provides options for people with

concerns, including whistleblowers, who seek to bring their concerns

forward safely and effectively. Additionally, an organizational

ombudsman offers coaching on ethics and other management

issues, provides mediation to facilitate conflict resolution, helps

enable safe upward feedback, assists those who feel harassed and

discriminated against. Overall, the organizational ombudsman helps

employees and managers navigate bureaucracy and deal with

concerns and complaints.

The organizational ombudsman role has evolved from at least two

sources: a) an evolution from the concept of the 'classical'

ombudsman and b) a spontaneous creation and re-invention——of

But there is hope. About 25 years ago Muhammad Yunus, a Bangladeshi economist trained in the United States, developed a lending model that managed to overcome these kinds of barriers. His business model for microcredit has been immensely successful, spawning imitators the world over.

Most of these lenders are nonprofits, but they are self-supporting nonprofits, which do not require subsidies or loan guarantees. There are even a few for-profit enterprises experimenting with the Yunus microcredit model.

Mr. Yunus put his plan into effect through an institution he called the Grameen Bank.

The critical feature of the program is that a candidate for a loan must form a group with four other people who are not family members. Two members of the group originally receive a loan, and if they do well, the others then receive loans.

The borrowers are encouraged to assist each other, and all loan disbursements and repayments are made publicly, in front of other groups. Loans are always for one year, at a fixed interest rate of 20 percent, and they are always for modest amounts: no more than a few hundred dollars

The borrowers use the loans to buy looms, chickens, cows and make other small capital investments. They start repaying the loan two weeks after getting it, and once they have repaid the initial loan, they are allowed to apply for new ones.

How does this business model solve the information problems described above? First, take the selection problem. The Grameen design provides strong incentive for good borrowers to join together, since they don't want to risk losing a loan because of one failure or troublemaker. The fact that they cannot join with other family members removes one sort of pressure to dilute group quality.

Second, the members of the group have an incentive to monitor one another's activities actively. They can provide advice, assistance, education and, if necessary, insurance. The group members themselves are in the best position to know whether a recipient is slacking off or has just had a run of bad luck, and they have great incentives to monitor their behavior in an honest and helpful way.

Third, all of this selection, monitoring, educating and insuring is done not by high-paid professionals, but by Bangladeshi peasants. The transactions costs of using groups are far, far lower than are the transactions costs for traditional bank loans.

There are other interesting economic angles. Over 90 percent of the borrowers are women. This isn't so much an ideological choice as a pragmatic one -- women turned out to be better credit risks. They were more tightly tied to the home and had fewer outside temptations, so they focused much more intently than did male borrowers on completing their projects.

All this seems to work. The bank says it has a repayment rate of 99 percent, and over 92 percent of the bank's shares are owned by the borrowers. Peer pressure can be an immensely strong force, and the Grameen Bank has figured out how to make it work in the cause of

259 Mary Rowe (2012) “Informality the Fourth Standard of Practice” Journal of the International Ombudsman Association Vol 5

Nr 1

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the idea of an internal, neutral conflict resolver——often by senior

managers who had never heard of the classical model.

Evolution from the classical model: the classical ombudsman

appeared in Sweden in the early 19th century as an independent

high-level public official responsible to the parliament or legislature

and appointed by constitutional or legislative provisions to monitor

the administrative activities of government. This model has been

copied and also adapted in many ways in many countries and

milieus.

The spontaneous creation model: the organizational ombudsman

role has also been regularly "re-invented" by employers who did not

know of the classical ombudsman but valued the importance of a

senior manager who is a neutral, independent, confidential and

informal problem-solver and systems change agent. Examples

appeared in the 1920s in the US and probably appeared here and

there in many cultures. In many organizations the organizational

ombudsman is seen as part of a complaint system or link to a

complaint system, but the office is intended to function, and to

appear to function, independently from all regular line and staff

management

This spectrum is often overlooked in contemporary discussions of

"ADR." "ADR" often refers to external conflict management options

that are important, but used only occasionally. An organizational

ombuds office typically offers many internal options that are used in

hundreds of cases a year. These options include:

delivering respect, for example, affirming the feelings of a

visitor, while staying explicitly neutral on the facts of a case,

active listening, serving as a sounding board,

providing and explaining information, one-on-one, for

example, about policies and rules, and about the context of a

economic development.

Experiments elsewhere haven't been uniformly successful. In some countries, the poverty stricken do not have enough group solidarity to provide the necessary discipline. In more urban settings, it may be difficult to find appropriate small-scale investments. But there are numerous successful operations inspired by the Grameen bank.

One program, Project Enterprise, runs a Grameen-type program for minority entrepreneurs in New York.

To answer the question posed in the first paragraph: Citibank and other Western banks are well aware of the Grameen model. In 1999 the Citigroup Foundation donated $1 million to the program.

Citibank, along with others, is currently experimenting with micro-lending in India and other developing countries. Multinational banks may yet find ways to break the moneylenders' monopolies and finance micro-investment in poor countries.

Access to capital is critical for economic development. Grameen and its many offspring, both nonprofit and for-profit, offer an exciting model for alleviating poverty287.

C. THIRD we introduce the concept of “arbitration game” which

has been analyzed by excellent researchers 288

ARBITRATION and the “win-win-win”: In a practical level,

“arbitration" has an incremental role in the "win-win-win

papakonstantinidis model" Indeed, the 3rd bargainer

(Community-the "C" factor ) could be recognized as an "neutral

arbitrator" in dispute between two (A-B) bargainers

In additional the "C" factor has an active overall role in a 2-

poles "bargain" due to its acceptance (its rules) by A-B

bargainers

ARBITRATION289

Hearing and determining of a dispute or the settling of differences

between parties by a person or persons chosen or agreed to by them

Bossert W.& Guofu T., .. presented (1995)their work titled

“An arbitration game and the egalitarian bargaining

solution” 290Journal of Economic Literature

Classification (Numbers: C72, C78)

287 Hal R. Varian (2001) In a model for lending in developing nations, a Bangladesh bank relies on peer pressure for collateral. New York Times; New York, N.Y.; Nov 22, 2001; 288

289 (Walter Bossert and Guofu Tan (1995) An arbitration game and the egalitarian bargaining solution* Soc Choice Welfare

(1995) Journal of Economic Literature Classification Numbers: C72, C78.

290 Bossert W.& Guofu T (1995) “An arbitration game and the egalitarian bargaining solution” Journal of Economic Literature Classification (Numbers: C72, C78)

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concern,

receiving vital information, one-on-one, for example,

from those reporting unacceptable or illegal behavior,

reframing issues,

helping to develop and evaluate new options for the

issues at hand,

offering the option of referrals to other resources, to

"key people" in the relevant department, and to managers and

compliance offices,

helping people help themselves to use a direct approach,

for example, helping people collect and analyze their own

information, helping people to draft a letter about their issues,

coaching and role-playing,

offering shuttle diplomacy, for example, helping

employees and managers to think through proposals that may

resolve a dispute, facilitating discussions,

offering mediation inside the organization,

"looking into" a problem informally,

facilitating a generic approach to an individual problem,

for example instigating or offering training on a given issue,

finding ways to promulgate an existing policy,

identifying and communicating throughout the

organization about "new issues,"

identifying and communicating about patterns of issues,

working for systems change, for example, suggesting new

policies, or procedures,

Informal referral to a co-worker known to help people work out

issues is an informal procedure. Co-worker interventions are usually

informal.

Conceptualizing ADR in this way makes it easy to avoid confusing

tools and methods (does negotiation once a lawsuit is filed cease to

be ADR? If it is a tool, then the question is the wrong question) (is

mediation ADR unless a court orders it? If you look at court orders

and similar things as formalism, then the answer is clear: court

annexed mediation is merely a formal ADR process).

Bargaining:

They analyzed simple arbitration procedure which is a multi-

stage variant of Nash's demand game. In the absence of

discounting, all Nash equilibria of the game yield the

egalitarian solution in the first stage. The crucial feature of

their arbitration procedure is that, in the case of incompatible

demands, the game is allowed to continue and the player who

demands the higher gain over the disagreement point is penalized

by restricting her or his feasible demands in the following

stage. Suitable modifications of the arbitration game yield the

lexicographic extension of the egalitarian solution, resp. the

proportional solutions.

The arbitration game is considered that it is a multi-stage

variant of Nash's demand game. The first stage is the same as in

Nash's demand game, but the game continues in the case of

incompatible demands. The player who demands the higher gain over

the disagreement point is penalized in the second stage. In

particular, the disagreement point is moved by guaranteeing the

player with the lower demand her or his demanded utility, and the

resulting new ideal point provides - as before - the upper bound

for the players' demands. This restriction seems to be reasonable

and plausible in order to penalize the player who asked for "too

much" in the case of incompatible demands. The game continues

until either the game stops after a finite number of stages or

there is "perpetual incompatibility," in which case the

disagreement outcome is implemented. We show that in the absence

of discounting all Nash equilibria of the arbitration game lead

to the egalitarian bargaining solution in the first stage.

Since a buyer will seek to deduct any shortfall from the purchase price,

calculating the true-up can be particularly contentious.

Earn-out provisions are often used by buyers to finance deals that require

less cash up front.

An earn-out is a contingent element of the purchase price that is

determined post-closing based on a target's performance against

contractually defined benchmarks.

The structure of an earn-out, however, creates disputes over control,

business decisions, and accounting practices.

SO, it a few basic strategies that can help private equity firms mitigate the

risk of post-acquisition disputes are outlined.

Thorough due diligence should be conducted at each stage of the

acquisition, with particular scrutiny on the seller's interim balance sheet.

Companies should agree on the accounting policies and methods that the

deal is based on. For example, the parties should explicitly discuss target

working capital and how it will be calculated prior to signing the merger

agreement.

Further, buyers should retain a copy of all the accounting records that

could be used to resolve a dispute.

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There are many problems, of a bargaining set

As we know, A t w o - p e r s o n b a r g a in in g p r o b le m is a pair

2..),..,( RSwheredS is the feasible set of utility

vectors and

2Rd

is the disagreement point.

The problem ),( dS is c o m p r e h e n s iv e ( s t r i c t ly

c o m p r e h e n s iv e ) if and only if, for all

yzthatsuchSzand

SydyxandSxRyx

.........(

.........., 2

dxwithSxiii

nsiveiscomprehedSii

convexandcompactisSi

thatsuch

dSproblemsBARGAININGofsettheisR

..,...)..(

,),,)..((

........)...(

,,

).....(............

The set of strictly comprehensive bargaining problems is denoted

byR , that is,

R the subset of R that is obtained if

comprehensiveness is strengthened to strict comprehensiveness in

condition ( i i ) above.

The id e a l p o in t of a bargaining problem

.2,1...,max).(

....)..,(.),(

idxSxxdSa

bydefinedisdSaRdS

ii

A b a r g a in in g s o lu t io n is a function

RdSallfor

SdSFthatsuchRRF

),(..

..),(,.....: 2

The egalitarian solution

The complexity and compressed time frame of most acquisitions

precludes private equity firms from foreseeing and preempting all

potential issues.

If disputes emerge, buyers should evaluate potential resolution tools

based on the type of dispute and the dollar amount under consideration.

The mediator conducts “shuttle diplomacy” between the two parties until

a settlement is reached.

Arbitration can represent the best path to an informed ruling in complex

cases that can be misunderstood by juries.

Arbitration is often used for disputes involving more substantial claims

that relate to such issues as benefit of the bargain, fraud, and

representations and warranties.

For claims that arise from accounting-related disputes, such as working-

capital true-ups and earn-outs, companies may opt to retain a neutral

accounting arbiter to adjudicate the dispute.

It is suggested that alternative dispute resolution can be used to

prevent disputes advancing to litigation.

Mediation is used as a means to avoid more costly litigation. In this non-

binding process, the companies agree on a judge, an attorney or an

accountant to help them reach a settlement.

The mediator conducts “shuttle diplomacy” between the two parties until

a settlement is reached.

Arbitration can represent the best path to an informed ruling in complex

cases that can be misunderstood by juries. Hearing and determining of a

dispute or the settling of differences between parties by a person or

persons chosen or agreed to by them

Does an arbitration game ensure an egalitarian bargaining solution?

The question is if an "arbitration game" could ensure that we will have more justice, equity, and more social welfare.. i need someone to prove (in math language) that an equilibrium point (the optimum egalitarian point) exists on not exists

ANSWER: Not unless the index of power is a uniform distribution and the bargaining solution is a Walrasian equilibrium. This happens with probability zero. Mohamed El-Hodiri, 2016, 02, 15 University of Kansas

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papakonstantinidis Page 159

xythatsuchSynot

anddxdxthatsuchSx

POINTuniquethebedSERdSallfor

letingbydefinedisKalaiE

..............

............

........),(,),....

..,..)..1977,..(

2211

▲

A generalization of the egalitarian solution is the class of proportional (or weighted egalitarian) solution:

),(,,),..

)1977,)...(.......(

dSERdSFor

KalaiRawithE

a

a

is defined as the unique point Sx such that

xythatsuchSynot

anddxadx

...........

..)..( 2211

Clearly, 1a leads to the egalitarian solution.

The relationship between axiomatic bargaining solutions and equilibria of strategic models has first been studied by Nash (1953) in his pioneering paper. He considers a strategic model of bargaining that supports his axiomatic solution, namely, the Nash (1950) bargaining solution. His game consists of a single stage in which the two players simultaneously announce "demands" in terms of utilities. If these demands are compatible given the set of feasible utility vectors, then each player receives the amount he or she demanded; otherwise the disagreement event occurs. This game has many Nash equilibria. In order to refine the set of equilibria, Nash further considers a perturbed demand game and shows that if the disagreement outcome is excluded, the only equilibrium that is robust with respect to certain perturbations in the structure of the game yields the Nash bargaining solution. The refinement used by Nash bears some similarity to Selten's (1975) "trembling hand"260 perfection. Nash's demand game has been extended and modified in other contributions. For example, Binmore (1987) has proposed a bargaining game of alternating offers and shown that the Nash bargaining solution is the limit of the unique subgame- perfect equilibrium of his game as the probability of the negotiation process breaking down approaches zero. Carlsson (1991) has studied a variation of the perturbed demand game by assuming that the players make errors in choosing their actions in the bargaining process. He shows that the equilibrium outcome converges to the Nash solution when errors go to zero. Osborne and Rubinstein (1990, Ch. 4) have provided more detailed discussions on these extensions. The purpose of all these studies is to examine the strategic foundations of cooperative bargaining solutions. In most

//////////////////////////////////////

▲

KENNETH ARROW

BRIEF REVIEW

THE MAIN QUESTION: How do rational citizens decide how and whether to vote in two-candidate (or two-party) elections?;

Arrow supports wit h math argumentation, that voting can be regarded as

a method of arriving at social choices derived from the preferences of

individuals. It is impossible to formulate a social preference ordering that

satisfies all of the following conditions:

We have to repeat the “hypothetic example of the “social experiment”

1. Non-dictatorship: The preferences of an individual should not

become the group ranking without considering the preferences

of others.

2. Individual Sovereignty: each individual should be able to order

the choices in any way and indicate ties

3. Unanimity: If every individual prefers one choice to another,

then the group ranking should do the same

4. Freedom From Irrelevant Alternatives: If a choice is removed,

then the others' order should not change

5. Uniqueness of Group Rank: The method should yield the same

result whenever applied to a set of preferences. The group

ranking should be transitive.

Let CandBA ....., be the three alternatives [a triple “bargain”

and 3....2,1 and the three individuals.

260Selten , R. (1975) A reexamination of the perfectness concept for equilibrium points in extensive games. International Journal

of Game Theory 4:25-55.

Cohen, D. K & Ball, D. L.. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes and L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey Bass.

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cases, justifications of the Nash solution are obtained. Another interesting cooperative bargaining solution is the egalitarian solution developed by Kalai (1977) and Myerson (1977). Without using Nash's axiom of independence of scale of utility they have provided alternative axioms under which interpersonal comparisons of utility must be possible. These axioms lead to the proportional solution and, in a symmetric bargaining situation, the egalitarian solution. One of the main axioms in this approach is a monotonicity axiom with respect to expansions of the feasible set. An alternative is a condition that involves a step-by-step negotiation process. This axiom imposes an invariance condition under decomposition of the bargaining process into several stages. As Kalai and Myerson pointed out, step-by-step negotiation has at least two advantages. First, it makes it easier to implement a solution since the negotiation can be broken up into several stages. Second, the players do not have incentives to change the order of the negotiations. This process is likely to be observed in actual negotiations.-see below

▲

TREMPLING HAND (SELTEN)261

In GAME THEORY trembling hand perfect equilibrium is a

refinement of Nash equilibrium due to R. Selten A trembling hand

perfect equilibrium is an equilibrium that takes the possibility of off-

the-equilibrium play into account by assuming that the players,

through a "slip of the hand" or tremble, may choose unintended

strategies, albeit with negligible probability.

The game represented in the following normal form matrix has two

pure strategy Nash equilibria

namely RightDownandLeftUp ,....,

However, only LU , is trembling-hand perfect.

Left Right

Up 1,1 2.0

Down 0,2 2,2

Trembling Hand perfect equilibrium

Suppose individual)....,.....(

.................1

CtoAthereforeand

CtoBandBtoAprefers

Individual)..........(......

..........2

AtoBthereforeandAtoCand

CtoBprefers

and

Individual BtoCthereforeandBtoAand

AtoCprefers

..........(.......

..........3

Then majorityCtoBprefersmajorityaand

BtoAprefers

..............

........

We may therefore say that the community

CtoBandBtoAprefers ................

If the community is to be regarded as behaving rationally, we are forced to say that

CtopreferedisA .........

. But, in fact, a majority of the community

AtoCprefers ......... 291

If the community is to be regarded as behaving rationally, we are forced to say that

CtopreferedisA .........

. But, in fact, a majority of the community

AtoCprefers ......... 292

The base of this reasoning is the “ranking” coming from people thinking

rationally

Today, in the 21st century, conditions are quite different from those of the 50's This differentiation is due-among others-mainly to the reversal of perception that we had to communicate between us The tremendous

261Selten R. (1975) A reexamination of the perfectness concept for equilibrium points in extensive games. International Journal

of Game Theory 4:25-55. 291

. Samuelson, Paul (1947) Foundations of Economic Analysis (Cambridge, Mass.: Harvard University Press, , chap. viii; 292

. Samuelson, Paul (1947) Foundations of Economic Analysis (Cambridge, Mass.: Harvard University Press, , chap. viii;

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papakonstantinidis Page 161

Assume player 1 is playing a mixed strategy

10..)..,1( for

Player 2's expected payoff from playing L is:

12)1(1

Player 2's expected payoff from playing the strategy R is:

22)1(0

For small values of player 2 maximizes his expected payoff

by placing a minimal weight on R and maximal weight on L

. By symmetry, player1 should place a minimal weight on D if

player 2 is playing the mixed strategy ),1(

Hence LU , is trembling-hand perfect.

However, similar analysis fails for the strategy profile RD,

Assume player 2 is playing a mixed strategy )1,(

Player 1's expected payoff from playing U is:

2)1(21

Player 1's expected payoff from playing D is:

22)1(2)(0

For all positive values of , player 1 maximizes his expected

payoff by placing a minimal weight on D and maximal weight on

U Hence RD, is not trembling-hand perfect because

player 2 (and, by symmetry, player1 maximizes his expected

payoff by deviating most often to L if there is a small chance of error

in the behavior of player 1

IOA

In the 1970’s and early 1980’s, organizational ombuds (O,O)

recognized three basic pillars of their (O,O) profession:

o independence,

o Confidentiality

speed of electronic computers create a new perceptions landscape and "strategies" even under rationality conditions Decisions are very fast taken and in addition, the COMPUTERS give more alternatives than those set -a rigorous cohesive scientific approach, such as the "Theorem impossible" Another reason is that in parallel with the evolution of the world, mathematics evolved even faster, creating a new field "evidentiary process" Already since 1831 Gödel had prepared the scientific community to accept alternatively, either the completeness or consistency .. He proved that they cannot apply both “cohesion” and “completeness” Based on this, if you accept the coherence of "Theorem Impossible" then it must be admitted simultaneously, the "incompleteness" of this theorem So, if you accept the "completeness" then-according to Gödel, you cannot accept the "consistency" of this Theorem Let us first sketch the main intuition for the proof, without going into detail and of course without claiming to be exact. The formulae of a formal system (we will restrict ourselves to the PM here) can be viewed syntactically as finite sequences of the basic symbols (variables, logical constants, and parentheses or separators), and it is easy to define precisely which sequences of the basic symbols are syntactically correct formulae and which are not. Similarly, proofs are formally nothing else than finite sequences of formulae (with specific definable properties). Of course, it is irrelevant for meta-mathematical observations what signs are taken for basic symbols, and so we will chose natural numbers for them. Hence, a formula is a finite sequence of natural numbers, and a proof schema is a finite sequence of finite sequences of natural numbers. The meta-mathematical concepts (theorems) hereby become concepts (theorems) about natural numbers, which makes them (at least partially) expressible in the symbols of the system PM. In particular, one can show that the concepts \formula", \proof schema", \provable formula" are all expressible within the system PM, i.e. one can, for example, come up with a formula

)(vF of PM that has one free variable v (whose type is sequence of

numbers) such that the semantic interpretation of

formulaprovableaisvisvF ........:)..(

We follow Prof Kenneth Arrow, until the point of the three (3) simple

different and separate parties in a bargain, or rational alternative choices

But, (in short)

The “new’ concept that is introduced now, is the “one more” than 3

parties in a bargain:

We can imagine the political “game” as a “bargaining game” From this

point of view, the example pre-assumes that there are three persons (as in

the win-win-win hypothesis) that competes each-other

The Community’s role in a bargain ),(( fSG between A-B is double:

The role of the third party of a bargain between two, which claims its own

“profit”

AND

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papakonstantinidis Page 162

o Neutrality (impartiality).

Informality was recognized as a fourth principle, or pillar of

practice, somewhat later. This happened relatively slowly, over at

least often years, after the first three pillars were widely adopted.

This article briefly describes that process. The article asserts that

informality is an essential principle for the profession as practiced

today — as essential as independence, confidentiality and

neutrality. Without informality, the other three principles of OO

practice could not function in today’s legal climate, and many

managers would find OOs to be interfering with their authority.

Informality permits OOs to offer a very wide variety of informal

options, to all cohorts, and across all organizational boundaries

Aldrich John H. Mc Ginnis Michael D.(1989) A model of party constraints on optimal candidate positions Mathematical and

Computer Modelling Volume 12, Issues 4–5, 1989, Pages 437-450

Decision making is not a very simple concept: it depends mainly

on262

/////////////////////////////////

Second, it is not under consideration some other forms of social

solidarity as for example “social economy”

But “political elections” is a game, a spatial model of electoral

competition. A model of political parties is developed and a general

theorem about the existence of distinct Nash equilibria distributions

of party activists is proven. Candidates are assumed to acquire

resources from the party and its activists and through the

candidate's own campaign organization to assist in their campaign

efforts, and they are assumed to value both winning and policy

outcomes. We then explore the formal properties of this more

general model, especially examining the impact of party-based

resources and of candidate policy preferences on the optimal

location of candidates. We show, in particular, that such positions

will, in general, be divergent, and yet there will be regular

differentiation between the nominees of the two political parties263.

There is a close relation between “political elections” and

“citizenship” and liberal democracy:

Will Kymlicka and Wayne Norman264 note that advanced

democracies can “become difficult to govern, even unstable”

without strong citizenship qualities If so, examining citizenship on

the global periphery would seem to be of particular urgency, given

weak states’ propensity for in-governability and instability.

The role of the arbitrator in a bargain A-B

The Community's double role (as the third bargainer and as arbitrator . i.e

as bargainer and agent of the rest 2i of Community’s population it is

estimated that ensures a bargain with more justice egalitarianism and

more efficiency

But,

who checks, the community?

who controls the controller and arbitrator between the two bargainers?

The answer is, the “Liberal Democracy”, or, simply “ Democracy"

In a "Free Community" people sacrify a part of their "freedom", in order

to obtain another freedom, the "political freedom" which enjoy in a new

Community, the "Political Community"

That means it is run by the people for the people. Citizens in our democracy have rights. For example, we have the right to speak freely, to practice our religion, to vote, and so on. Citizens in a democracy also have responsibilities. One of these responsibilities is to choose our leaders. Another is to keep informed about what is going on with our government. It is also the responsibility of citizens to help make their community and neighborhood good places in which to live.

A democracy needs active citizens in order to work. There are many ways to take part in a democracy. This booklet will deal with three ways to be an active citizen. These three ways are:

Voting

Communicating with Elected Officials

Volunteering

Liberal democracy (bourgeois democracy or) is called a representative

democracy which is based on the principles of political liberalism. This is

the predominant type of democracy after the First World War and was

formed mainly in the 19th century. Foundation of liberal democracy is a

constitution that provides for separation of powers to independent bodies

and guarantee certain individual rights for its citizens, in particular in order

to limit state intervention capabilities in their life. The classical liberal

democracies usually contrasted with the popular democracies,

participatory democracy and direct democracy, while historically an

262

Aldrich John H. Mc Ginnis Michael D.(1989) A model of party constraints on optimal candidate positions Mathematical

and Computer Modelling Volume 12, Issues 4–5, 1989, Pages 437-450 263 Gannon Agnes (1994) Rural tourism as a factor in rural community economic development for economies in transition.

Journal of Sustainable Tourism, 2(1), 51-60 JOURNAL OF SUSTAINABLE TOURISM 2(1-2):51-60 · JANUARY 1994 Stanford Encyclopedia of Philosophy( http://plato.stanford.edu/entries/citizenship/) 264Will Kymlicka & Wayne Norman (1994) Return of the citizen: A survey of recent work on citizenship theory Ethics 104

(2):352-381 (1994)

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papakonstantinidis Page 163

Mason writes,”..If vigorous notions of citizenship are typically

associated with strong states, it seems intuitive that these same

citizenship attributes would be feebler in weak and failing states.

Still, given the tremendous variation among states, as well as the

multiple theories of citizenship, it is not clear what dimension or

type of citizenship may be associated with overall state weakness.

Many weak states may have insubstantial notions of citizenship as a

consequence of incomplete nation-building projects – this may

dominate explanations of weak citizenship among certain African

nations. Some weaker states may be wracked by the divided and

competing loyalties common in plural societies. Multiple ethnicities

in Yugoslavia and the Soviet Union, for example, exemplify how this

can pose an obstacle to the formation or maintenance of a strong

sense of citizenship and a unified national identity. In Latin America

it is not uncommon to find developing states that are incapable or

unwilling to fulfill basic obligations to its citizens, undermining

society’s loyalty, sense of weakness, and patriotism that characterize

a strong citizenry. In extreme cases of violent internal conflict or

security emergencies, the citizen-state bond may be ruptured

almost entirely. Still others states are challenged by having a

transnational population that has been permanently dispersed by

war or other internal calamity, making the construction of a

citizenship project extremely problematic. Lebanon might be

illustrative of this last dynamic.

What does citizenship look like in relatively weak states, and weak

democracies in particular? Is the idea of the citizenry and the

relation between state and society the same in weak states, only

less developed, or are there operative fundamentally different

definitions of what it means to be a citizen? Are weaker notions of

citizenship necessarily one of the markers of weak and failing states?

If so, what is the causal relation between the two? How relevant are

current theoretical debates to our understanding of the concept of

citizenship in the developing world?

Mason reviewed the principal strains of citizenship theory and the

current theoretical debates, on “Citizenship Classification and

Theory” The conceptual disarray surrounding the concept of

citizenship is familiar territory. She sums it up this way: “There is no

notion more central in politics than citizenship, [yet] none more

variable in history, or contested in theory.” We are all citizens of

somewhere (except for that fellow in The Piano who had the

misfortune of being born on an trans-Atlantic steamer in the

1920’s), but we do not share the same rights and obligations as

citizens. The citizen emerged from democratic philosophy and

practices, and yet citizenship bonds in non-democratic states may be

as strong, or stronger, than in modern democracies. An individual

can be a citizen of more than one country at the same time, yet only

enjoy the rights of a citizen in one of those political communities.

Many comply with the formal political and civic duties of being a

evolution of the constitutional monarchy.

Indeed, the "Liberal –west type- Democracy” provides theoretical-let us

say-- the possibility of reward or punishment / penalty to those who

manage the processes by which the "third win" is fulfilled with the dual

mission : the third player, and the "arbitrator ensure equality, justice, self-

organization and the effectiveness of the" collective "decision

The last, fulfilled through the reward or punishment that is the people (the

Community as a whole) with their vote in elections every 4 or 5 years

Amid the Enlightenment, first the American and then the French

Revolution, was liberal under the request of the abolition of the monarchy

and governance from political representatives, elected by a portion of the

people voting. These representatives could express competing interests

and perceptions within society through their attachment to different

political parties. Shaping this system, the founders of the US state explicitly

rejected direct democracy as an option, believing that it would lead to the

predominance of the most populous lower social classes or in chaotic

disarray and shaped the representative democracy naming the new

constitution "republican" and not "democratic" to refer to the Roman

state of the Hellenistic period

Dimensions of citizenship293

Definitions

The concept of citizenship is composed of three main elements or

dimensions (Cohen 1999)294 The first is citizenship as legal status, defined

by civil, political and social rights. Here, the citizen is the legal person free

to act according to the law and having the right to claim the law's

protection. It need not mean that the citizen takes part in the law's

formulation, nor does it require that rights be uniform between citizens.

The second considers citizens specifically as political agents, actively

participating in a society's political institutions. The third refers to

citizenship as membership in a political community that furnishes a distinct

source of identity.

In many ways, the identity dimension is the least straightforward of the

three. Authors tend to include under this heading many different things

related to identity, both individual and collective, and social

integration.[5] Arguably, this is inescapable since citizens' subjective sense

293

STANFORD ENCYCLOPAIDIA OF PHILOSOPHY 294

Cohen, D. K. and Ball, D. L.(1999). Developing practice, developing practitioners: Toward a practice-based theory of

professional education. In G. Sykes and L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey Bass. 51 Carens (2000), “Culture, Citizenship and Community, A Contextual Exploration of Justice as Evenhandedness”, Oxford University Inc, New York

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citizen, yet feel a stronger sense of association with and loyalty to

another type of community. In short, what does it mean to be a

citizen?

In broad strokes, citizenship can be understood in four distinct, yet

overlapping, ways In its least problematic form it is a legal category

related to formal membership in a

Conflated with what is popularly understood as nationality, this

definition of citizenship identifies the political community to which

an individual belongs. This attribution was historically assigned by

virtue of being born in a particular territorial designation, jus soli, or

as the result of a parent’s nationality, jus sanguinis. Just as territorial

boundaries sharply demarcate state sovereignty, so nationality laws

establish strict criteria for distinguishing between citizens and aliens.

Although massive waves of global migration have called for new

citizenship rules, the “politics of citizenship” in receptor states in the

North is such that rigorous legislation related to naturalization, that

determines inclusion in and exclusion from the state, is maintained

This legal definition of citizenship reflects a world order that

privileges the state as the primary political unit, denying, in most

cases, the possibility of citizenship status deriving from non-political

criteria, such as ethnicity or religion, in sub-national or transnational

communities.

Related to this legal definition is the view of citizenship as identity.

This citizenship-as-identity perspective, however, distinguishes

formal membership in a state from an individual’s sense of

association, belonging, and loyalty to a particular community

(Kymlicka and Norman 1995). The collective consciousness

traditionally rooted in culturally homogenous ethno-national

communities has steadily evolved into a modern national identity

based on association with a state organization. Still, for many

individuals a civic national identity associated with the modern

nation-state exists alongside the persistence of national identities

deeply rooted in pre-political cultural associations. But regardless of

the origin, citizenship-as-identity becomes a common denominator

that supersedes competing identifications, embodies collective

allegiance to the political community, and fosters patriotism to the

nation-state, its myths and its symbols (Miller 2000).

A third interpretation of citizenship is as a status, derived from an

individual’s possession of a set of rights and obligations with relation

to the state. This rights-based notion of citizenship has its origins in

the emergence of the modern nation state and the social contract.

The French Revolution marks a turning point in the development of

citizenship models, where for the first time the conception of

citizenship came to mean the rights of citizens against the

absolutism of the monarch, the arbitrariness of state power, and the

legal and political privileges of aristocratic society (Castle and

of belonging, sometimes called the “psychological” dimension of

citizenship (Carens 2000)295 necessarily affects the strength of the political

community's collective identity. If enough citizens display a robust sense of

belonging to the same political community, social cohesion is obviously

strengthened. However, since many other factors can impede or

encourage it, social integration should be seen as an important goal (or

problem that citizenship aims to achieve (or resolve), rather than as one of

its elements. As we will see, one crucial test for any conception of

citizenship is whether or not it can be said to contribute to social

integration.

Relations between the three dimensions are complex: the rights a citizen

enjoys will partly define the range of available political activities while

explaining how citizenship can be a source of identity by strengthening her

sense of self-respect (Rawls 1972)296. A strong civic identity can itself

motivate citizens to participate actively in their society's political life. That

distinct groups within a state do not share the same sense of identity

towards ‘their’ political community (or communities) can be a reason to

argue in favor of a differentiated allocation of rights (Carens 2000)

As we will see, differences between conceptions of citizenship centre

around four disagreements: over the precise definition of each element

(legal, political and identity); over their relative importance; over the

causal and/or conceptual relations between them; over appropriate

normative standards.

Two models of citizenship: republican and liberal

Discussions about citizenship usually have, as their point of reference, one

of two models: the republican or the liberal. The republican model's

sources can be found in the writings of authors like Aristotle, Tacitus,

Cicero, Machiavelli, Harrington and Rousseau, and in distinct historical

experiences: from Athenian democracy and Republican Rome to the Italian

city-states and workers' councils.

The key principle of the republican model is civic self-rule, embodied in

classical institutions and practices like the rotation of offices, underpinning

Aristotle's characterization of the citizen as one capable of ruling and being

296 John Rawls (1972), A Theory of Justice. Oxford: Clarendon Press, 1972, pp. xv, 607.

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papakonstantinidis Page 165

Davidson 2000). Implicit in this idea of legal rights was the equality

of these protections, and participation in the democratic process.

Indeed, Kant equated citizen rights with citizen involvement. Thus,

freedom from the state meant a right to the state as well. Citizen

status involves, then, a fundamental set of freedoms, democratic

participation, and the obligation to comply with the directives that

emerge from the democratic process

Gödel’s incompleteness theorems: Consistency, completeness and incompleteness All such formal details are irrelevant to the working mathematician’s use of arguments by induction on the natural numbers, but for the

logician, the way a formal system S is specified can make the

difference between night and day. This is the case, in particular,

concerning the questions whether S is consistent, i.e. no

contradiction is provable from S and whether S is complete,

i.e. every sentence A is decided by S in the sense that

either S proves A or S proves ¬ A

If neither A nor ¬ A is provable in S then A is said to be

undecidable by S , and S is said to be incomplete.

As an example of how matters of consistency and completeness can change dramatically depending on the formalization taken, consider the subsystem of PA obtained by restricting throughout to terms and formulas that do not contain the multiplication symbol ×. That system, sometimes called Presburger Arithmetic, was shown to be complete by Moses Presburger in 1928, and his proof of completeness also gives a finite combinatorial proof of its consistency. Gödel’s discovery in 1931 was that we have a radical

change when we move to the full axiom system PA What Gödel showed was that PA is not complete and that, unlike Presburger Arithmetic, its consistency cannot be established by finite combinatorial means, at least not those that can be formalized

in PA Before going into the mathematical significance of these results, let us take a closer look at how Gödel formulated and established them not only for PA, but also for a very wide class of its extensions

2S To do this he showed that the language of PA is

much more expressively complete than appears on the surface. A

primitive recursive .).( rp function on N

N (in any number of arguments) is a function generated from zero and successor both by explicit definition and definition by recursion

ruled in turn. Citizens are, first and foremost, “those who share in the

holding of office” (Aristotle Politics, 1275a8)297. Civic self-rule is also at the

heart of Rousseau's project in the Contrat Social: it is their co-authoring of

the laws via the general will that makes citizens free and laws

legitimate.[8] Active participation in processes of deliberation and decision-

making ensures that individuals are citizens, not subjects.[9] In essence, the

republican model emphasizes the second dimension of citizenship, that of

political agency.

The liberal model's origins are traceable to the Roman Empire and early-

modern reflections on Roman law (Walzer 1989). The Empire's expansion

resulted in citizenship rights being extended to conquered peoples,

profoundly transforming the concept's meaning. Citizenship meant being

protected by the law rather than participating in its formulation or

execution. It became an “important but occasional identity, a legal status

rather than a fact of everyday life” (Walzer 1989, 215). The focus here is

obviously the first dimension: citizenship is primarily understood as a legal

status rather than as a political office. It now “denotes membership in a

community of shared or common law, which may or may not be identical

with a territorial community” (Pocock 1995, 37). The Roman experience

shows that the legal dimension of citizenship is potentially inclusive and

indefinitely extensible.

The liberal tradition, which developed from the 17th century onwards,

understands citizenship primarily as a legal status: political liberty is

important as a means to protecting individual freedoms from interference

by other individuals or the authorities themselves. But citizens exercise

these freedoms primarily in the world of private associations and

attachments, rather than in the political domain.

At first glance, the two models present us with a clear set of alternatives:

citizenship as a political office or a legal status; central to an individual's

sense of self or as an “occasional identity”. The citizen appears either as

the primary political agent or as an individual whose private activities leave

little time or inclination to engage actively in politics, entrusting the

business of law-making to representatives. If the liberal model of

citizenship dominates contemporary constitutional democracies, the

republican critique of the private citizen's passivity and insignificance is still

alive and well.

Republicans have problems of their own. First and foremost is a concern,

297

Aristotle's political theory.18 His theory is based on the fundamental principle that a... others in court or are judged there

themselves” (Politics 3.1.1275a8–11).

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papakonstantinidis Page 166

along N

A .).( rp relation (which may be unary, i.e. a set) is a relation

whose characteristic function is .).( rp Gödel showed that

every .).( rp function is definable in the language of

PA and its defining equations can be proved there. For

example, the operations of exponentiation,

yx the

factorial, !x , and the sequence of prime numbers, xp , each

of which is .).( rp can all be represented in this way in

PA , facts that are not at all obvious Each instance of a

.).( rp relation is decidable by PA ; for example

if R is a binary .).( rp relation,

then for each Nmn ,. either PA

proves ),.( mnR

or it proves ¬ ),.( mnR

Gödel’s incompleteness theorems To apply these notions to the language and deductive structure of

PA , Gödel assigned natural numbers to the basic symbols.

Then any finite sequence of symbols gets coded by a

number # , say, using prime power representation; # is

nowadays called the Gödel number ..ng of .

A relation R between syntactic objects (terms, formulas, etc.) is

said to be .).( rp if the corresponding relation

between ..ng ’s is .).( rp For example, with a basic

finite vocabulary, the sets of terms and wffs 265 are both

often repeated since Benjamin Constant, that their ideal has become

largely obsolete in the changed circumstances of the “grands États

modernes” (Constant 1819). Aiming to realize the original republican ideal

in the present context would be a disaster, as was the Jacobins' attempt

during the French revolution (Walzer 1989, 211). Today's citizens will not

be Romans: first, the scale and complexity of modern states seem to

preclude the kind of civic engagement required by the republican model. If

an individual's chances of having an impact as an active citizen are close to

nil, then it makes more sense for him to commit himself to non-political

activities, be they economic, social or familial. His identity as citizen is not

central to his sense of self and politics is only one of his many interests

(Constant 1819). Second, the heterogeneity of modern states does not

allow the kind of “moral unity” and mutual trust that has been projected

onto the ancient polis, qualities deemed necessary to the functioning of

republican institutions (Walzer 1989). But if ancient virtue is irrecoverable,

the republican model may still act today as “a benchmark that we appeal

to when assessing how well our institutions and practices are

functioning”(Miller 2000, 84). In essence, this involves a reformulation of

the model, questioning some of its original premises while holding onto

the ideal of the citizen as an active political agent.

Instead of opposing the two models, we could reasonably see them as

complementary. Political liberty, as Constant pointed out, is the necessary

guarantee of individual liberty. Echoing Constant, Michael Walzer

considers that the two conceptions “go hand in hand” since “the security

provided by the authorities cannot just be enjoyed; it must itself be

secured, and sometimes against the authorities themselves. The passive

enjoyment of citizenship requires, at least intermittently, the activist

politics of citizens” (Walzer 1989). There are times when individuals need

only be “private citizens” and others when they must become

“private citizens” (Ackermann 1988). But can we expect passive spectators

of political life to become active citizens should the need arise? This is no

easy question and may explain why Constant ended his famous essay by

insisting that the regular exercise of political liberty is the surest means of

moral improvement, opening citizens' minds and spirits to the public

interest, and to the importance of defending their freedoms. Such

habituation underpins their capacity and willingness to protect their

265 A formula is a syntactic formal object that can be given a semantic meaning by means of semantics. In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word (i.e. a finite sequence of symbols from a given alphabet) that is part of a formal language A formal language can be considered to be identical to the set containing all and only its formulas. A formula is a syntactic formal object that can be given a semantic meaning by means of semantics.

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papakonstantinidis Page 167

.).( rp . Finally a formal system S for such a language is

said to be .).( rp if its set of axioms and its rules of inference

are both .).( rp The formal system PA and its

subsystems defined above are all .).( rp

The language of Presburger (P.A) arithmetic contains constants 0

and 1 and a binary function +, interpreted as addition. In this

language, the axioms of Presburger arithmetic are the universal

closures of the following:

¬(0 = x + 1)

x + 1 = y + 1 → x = y

x + 0 = x

x + (y + 1) = (x + y) + 1

Let P(x) be a first-order formula in the language of Presburger

arithmetic with a free variable x (and possibly other free variables).

Then the following formula is an axiom:

)()))1()(()0(( yyPxPxPxP

(5) is an axiom schema of induction, representing infinitely many

axioms. Since the axioms in the schema in (5) cannot be replaced by

any finite number of axioms, Presburger arithmetic (PA) is not

finitely axiomatizable in first-order logic. Presburger arithmetic(PA)

cannot formalize concepts such as divisibility or prime number.

Generally, any number concept leading to multiplication cannot be

defined in Presburger arithmetic, since that leads to incompleteness

and undecidability. However, it can formulate individual instances

of divisibility; for example, it proves "for all x, there exists

nxyyxyyy )1()(: This states that

every number is either even or odd.

Informal and formal axiom systems One big reason for the expressed disconnect is that Gödel’s theorems are about formal axiom systems of a kind that play no role in daily mathematical work. Informal axiom systems for various kinds of structures are of course ubiquitous in practice, viz. axioms for groups, rings, fields, vector spaces, topological spaces, Hilbert spaces, etc., etc.; these axioms and their basic consequences are so

liberties and the institutions that support them (Constant 1810)298

“COMMUNITY” is like the giant “Leviathan” (Thomas Hobbs, 1651)

A robust civil society is widely recognized as being one of the hallmarks of

strong states. The state-society framework that once dominated political

science and viewed state institutions and power as dichotomous from

civilian organizations and social structures has generally given way to a

more inclusive conceptualization of state as incorporating both

components. Measurements of stateness that focused exclusively on the

coercive and extractive powers of the central government’s institutions

are now considered incomplete: a cohesive and activated civil society that

participates in the political process, societal practices and beliefs that

legitimate state institutions, a unifying sense of national identity that

inspires public responsibility and promotes civic-mindedness, and the

citizenry’s loyalty to the state are also crucial determinants of overall state

strength and performance299.

Capraro V (2013) A Model of Human Cooperation in Social Dilemmas. PLoS ONE 8(8): e72427. doi:10.1371/journal.pone.0072427 Editor: Attila Szolnoki, Hungarian Academy of Sciences, Hungary

Social dilemmas are situations in which collective interests are at odds with private interestsIn other words, they describe situations in which the fully selfish and rational behavior leads to an outcome smaller than the one the individuals would obtain if they acted collectively. Social dilemmas create then a tension between private interests and public interests, between selfishness and cooperation. Classically, several different social dilemmas have been distinguished, including the Prisoner’s dilemma, Chicken, Assurance, Public Goods, the Tragedy of the Commons , and, more recently, the Traveler’s dilemma . Each of these games has been studied by researchers from different disciplines, as economists, biologists, psychologists, sociologists, and political scientists, because of the intrinsic philophical interest in understanding human nature and since many concrete and important situations, as pollution, depletion of natural resources, and intergroup conflict, can be modelled as social dilemmas.

The classical approaches explain tendency to cooperation dividing people in proself and prosocial types , or appealing to forms of external control or to long-term strategies in iterated social dilemmas But, over the years many experiments have been accumulated to show cooperation even in one-shot social dilemmas without external control These and other earlier experiments have also shown that the rate of cooperation in the same game depends on the particular payoffs, suggesting that most likely humans are engaged in some sort of indirect reciprocity [25], [26] and the same person may behave more or less cooperatively depending on the payoffs. Consequently, the problem of making a predictive division in

298 Benjamin Constant,(1810) Fragments d'un ouvrage abandonné sur la possibilité d'une constitution républicaine dans un

grand pays (1803–1810) 299 Mason Ann C. (2002) Department of Political Science Universidad de los Andes Bogotá, Colombia “Citizenship Scarcity and Weak States: The Colombian Experience” This paper was prepared for presentation at the 5th Failed States Conference in Santa Barbara, CA, September 9-11, 2002.

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familiar it is rarely necessary to appeal to them explicitly, but they serve to define one’s subject matter. They are to be contrasted with foundational axiom systems for the “mother” structures--the natural numbers (Peano) and the real numbers (Dedekind)--on the one hand, and for the general concepts of set and function (Zermelo-Fraenkel) used throughout mathematics, on the other. Mathematicians may make explicit appeal to the principle of induction for the natural numbers or the least upper bound principle for the real numbers or the axiom of choice for sets, but reference to foundational axiom systems in practice hardly goes beyond that. One informal statement of the basic Peano axioms for the natural numbers is that they concern a structure (N, 0, s) where 0 is in N, the successor function s is a unary one-one map from N into N which does not have 0 in its range, and the Induction Principle is satisfied in the following form:

(IP) for any property P(x), if P(0) holds and if for all x in N, P(x) implies P(s(x)) then for all x in N, P(x) holds.

“There are many math problems that have achieved the cachet of tremendous significance, e.g. Fermat, 4 color, Kepler’s packing, Gödel, etc. Of Fermat, I have read: ‘the most famous math problem of all time.’ Of Gödel, I have read: ‘the most mathematically significant achievement of the 20th century.’ … Yet, these problems have engaged the attention of relatively few research mathematicians—even in pure math.” What accounts for this disconnect between fame and relevance? Before going into the question for Gödel’s theorems, it should be distinguished in one respect from the other examples mentioned, which in any case form quite a mixed bag. Namely, each of the Fermat, 4 color, and Kepler’s packing problems posed a stand-out challenge following extended efforts to settle them; meeting the challenge in each case required new ideas or approaches and intense work, obviously of different degrees. By contrast, Gödel’s theorems were simply unexpected, and their proofs, though requiring novel techniques, were not difficult on the scale of things. Setting that aside, my view of Gödel’s incompleteness theorems is that their relevance to mathematical logic (and its offspring in the theory of computation) is paramount; further, their philosophical relevance is significant, but in just what way is far from settled; and finally, their mathematical relevance outside of logic is very much unsubstantiated but is the object of ongoing, tantalizing efforts266. Solomon Feferman (2006)267 The impact of the incompleteness

theorems on mathematics NOTICES OF THE AMS. VOL 53, Nr4

proself and prosocial types becomes extremely difficult, if not even impossible.

From these experiments, we can argue two conclusions: first, the observation of cooperation in one-shot social dilemmas without external controls suggests that the origin of cooperation relies in the human nature; second, the fact that the rate of cooperation depends on the payoffs suggests that it could be computed, at least approximatively, using only the payoffs. The word approximatively stands for the fact that numerous experimental studies have shown that cooperation is based on a number of factors, as family history, age, culture, gender, even university course religious beliefs and decision time Therefore, we cannot expect a theory able to say, given only the payoffs, the individual-level rate of cooperation in a social dilemma. We can expect instead a model predicting quite accurately population average behaviour using the mean value of parameters that could be theoretically updated at an individual-level.

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267

Solomon Feferman (2006)267 The impact of the incompleteness theorems on mathematics NOTICES OF THE AMS. VOL 53,

Nr4

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TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

BIBLIOGRAPHY ACCORDING TO THE EXISTING THEORY

The SOCIAL VALERIO CAPRARO: Social dilemmas are situations in which collective interests are at odds with private interests: pollution, depletion of natural resources, and intergroup conflicts, are at their core social dilemmas. Because of their multidisciplinarity and their importance, social dilemmas have been studied by economists, biologists, psychologists, sociologists, and political scientists. These studies typically explain tendency to cooperation by dividing people in proself and prosocial types, or appealing to forms of external control or, in iterated social dilemmas, to long-term strategies. But recent experiments have shown that cooperation is possible even in one-shot social dilemmas without forms of external control and the rate of cooperation typically depends on the payoffs. This makes impossible a predictive division between proself and prosocial people and proves that people have attitude to cooperation by nature. The key innovation of this article is in fact to postulate that humans have attitude to cooperation by nature and consequently they do not act a priori as single agents, as assumed by standard economic models, but they forecast how a social dilemma would evolve if they formed coalitions and then they act according to their most optimistic forecast. Formalizing this idea we propose the first predictive model of human cooperation able to organize a number of different experimental findings that are not explained by the standard model. We show also that the model makes satisfactorily accurate quantitative predictions of population average behavior in one-shot social dilemmas.

300 Baez John(1994)” Network Theory” the Azimuth Project

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2

Network theory is the study of complex interacting systems that can be represented as graphs equipped with extra structure. A graph is a bunch of vertices connected by edges Suppose, a population of agents of two kinds: ‘aggressive’ (A) and ‘cooperative’ (C). ( Baez, John C. 1994)300 Their dynamics might be described by this reaction

/////////////////////////////////////

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NETWORKING

network:

,,......... CONSTANTSsomefor

CCCCC

CA

AAAa

Eulerian Path

Definition: An Euler path is a continuous path that passes through every arc once and only once.

Theorem: If a network has more than two odd vertices, it does not have an Euler path.

Theorem: If a network has two or zero odd vertices, it has at least one Euler path. In particular, if a network has exactly two odd vertices, then its Euler paths can only start on one of the odd vertices, and end on the other.

The famous Seven Bridges of Königsberg problem”

The problem of crossing each bridge exactly once reduces to one of traversing the network representing these bridges.

Euler made the remarkable discovery that whether a network is traversable depends on the number of odd vertices. In the Königsberg network, there are an odd number of arcs at point A, so A is called an odd vertex. If the number of arcs meeting at a point is even, the point is called an even vertex. Euler found that the only traversable networks are those that have either no odd vertices or exactly two odd vertices. Since the Königsberg network has four odd vertices, it is not traversable. Therefore, it is not possible to take a walk over the bridges of Königsberg and cross each bridge only once

“win-win-win network” has no odd vertices

So it is traversable

A new view of economic, political social human relations’ networks

win-win-win papak model transfers the “win-win conflict perception in a

cooperative perception

the “nodes” of the win-win-win human relation network

We should imagine human units to react each-other inside any network,

strictly defined (see definitions)

Yet we should consider how we could "pass" by aggressive counter in the

network in cooperation behavioral reactions

The model “win-win-win papakonstantinidis equilibrium” is aimed

precisely at creating behavior that tends to continuous cooperation This

is a perpetual process that has its limit of ultimate cooperation

the conjecture prevails in this study that " the real conversion of

aggression in collaboration behavior is possible in real terms, through the

process of sensitization

Especially nowadays, such a message is strictly necessary

The “win-win-win network” has no odd vertices

So it is traversable

Now, Combining the “network theory” with the “concept of forces

(number ten(10) of the work, we have

Specifically, forces are defined through Newton’s laws of motion 0. A

`particle’ is a small mass at some position in space.

1. When the sum of the forces acting on a particle is zero, its velocity is

constant;

2. The sum of forces acting on a particle of constant mass is equal to the

product of the mass of the particle and its acceleration;

3. The forces exerted by two particles on each other are equal in

magnitude and opposite in direction. The second law provides the

definition of a force – if a mass m has acceleration a, the force F acting

on it is

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301

Benati Stefano, Rizzi Romeo, Tovey Craig A.(2015,April) The complexity of power indexes with graph restricted

coalitions”- Mathematical Social Sciences 76 · April 2015

MATH (M-A-T-H) GRAPH

M=3 T=3 A=5 H=5

Degree of a vertex: a non-negative number which indicates the number of lines (arcs or edges) that enter the vertex. This is easily seen if you draw a circle around the vertex and count the number of edges which enter the circle.

Degree of a graph: the total number of degrees of the vertices

Euler circuit: a graph in which you can trace all of the edges exactly once without picking up your pencil. You also must start and end at the same point.

Euler path: a graph in which you can trace all of the edges exactly one without pick in up your pencil. This is the same as a graph being traversable

Graph: a picture made up of vertices and edges which shows the relationship between the two

Graph

In the most common sense of the term a graph is an ordered pair

G = (V, E) comprising a set V of vertices or nodes or points together

with a set E of edges or arcs or lines, which are 2-element subsets

of V (i.e. an edge is related with two vertices, and the relation is

represented as an unordered pair of the vertices with respect to the

particular edge). To avoid ambiguity, this type of graph may be

described precisely as undirected and simple301.

The proposed network model following the win-win-win situation:

),,,,,,,( enlpnsotpecbcadvnfPnet ,

where,

Newton's 2nd law of motion states that if an object of mass m which is

measured in kilograms is acted on by a force of magnitude F measured in

Newtons, the magnitude of the acceleration a (measured in meters per

second squared) can be found according to the physics formula F equals

m times a or Force is Mass times Acceleration.

In this framework we must analyze the structure of the “win-win-win”

ensures

1. It is traversable

2. There is a force that “flows” among the three nodes, that is

the 3 negotiators in social negotiation (A-B and the

Community as a whole-the “C” factor

3. This force is the "bargaining power" which supports each-

one's individual interest, vs the other two, by rational

argumentation

Proposed network model following the win-win-win situation:

),,,,,,,( enlpnsotpecbcadvnfPnet ,

where,

nodes(n), arcs (a), degree (odd-even) of vertices (dv), betweenness centrality (bc), eccentric(ec), tactical positioning (tp), strong orientation (so), the Extent to which

4. ///////////////////////

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papakonstantinidis Page 172

nodes(n), arcs (a), degree (odd-even) of vertices (dv), betweenness centrality (bc), eccentric(ec), tactical positioning (tp), strong orientation (so), the Extent to which

To set the “win-win-win papakonstantinidis equilibrium in the

framework of networks

Network theory contributes to the suggested “win-win-win”, by

introducing 2 very important points:

1. Complex interactive systems

2. Forms of agents (2) kinds

A. Aggressive

B. Cooperative

Exploring the reactionary social systems (social groups), especially of

complex social systems provides the tools to look for trends that

determine the "aggressive" ticked and cooperation behavior

These two are predominant in the formation of the win-win-win

papakonstantinidis wording

From this point the action of traveling in or through an unfamiliar

area in order to learn about has the meaning of finding the “paths”

(Euler) from aggressive to cooperation behavior

LP NODES:

EVEN (2) +

ODD (2) DEGREE OF VERTICES

Vertex: a union of points Also called “a node” (the plural of vertex is

vertices

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▲

ARC DEGREE OF A

VERTEX

DEGREE OF A

GRAPH EDGE EULER CIRCUIT

EULER

PATH

Traversable Networks:

A network is traversable if you can trace each arc exactly once by

beginning at some point and not lifting your pencil from the paper.

1, A network with exactly two odd vertices is traversable.

2, Either odd vertex may be the beginning point and the other odd vertex is the ending point

3.Even and Odd Verticies

Once you have the degree of the vertex you can decide if the vertex or node is even or odd. If the degree of a vertex is even the vertex is called an even vertex. On the other hand, if the degree of the vertex is odd, the vertex is called an odd vertex.

4. A network with no odd vertices is traversable. Any vertex may be the beginning point, and the same vertex will also be the ending point.

5. A network with more than two odd vertices is not traversable.

6. Traversable: a network in which all the arcs may be traced exactly once without lifting your pencil

▲

7. The “win-win-win network” has no odd vertices

So it is traversable

COMMUNICATION GRAPH:

In a communication graph, player i is a node of the graph

),( EVG There is a

link

ecommunicatcanjandiplayersifEji ..............,..),(

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GRAPH NETWORK NODE TRAVERS

ABLE VERTEX

END OF

PAGE

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CONTRIBUTION OF EXISTING THEORY IN THE

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PARTICIPATION OF 3D “WIN-WIN-WIN” IN THE CURRENT

BIBLIOGRAPHY ACCORDING TO THE EXISTING THEORY

3

PARETO

1848-1923

▲

PARETO

OPTIMALITY

PARETO

EFFICIENCY

(1906)

)..*....(......

..*

}.....2,1{..,...0

....

)....(max..:....max

..

21

i

iii

ii

ii

n

xquantitiesppriceproductstheofsum

xquantitiespricesxp

nxx

Mxp

xxxUFunctionUtility

EFFICIENCYPARETO

In all countries and times, the distribution of income and wealth is highly skewed, with a few holding most of the wealth. He argued that all observed societies follow a regular logarithmic pattern(Vilfredo Pareto)

xmAN log..log..log

where, N is the number of people with wealth higher than x, and A and m are constants. Over the years, Pareto's Law has proved remarkably close to observed data.

It is the basis of the arguments on which the proposal win-win-win is

based The win-win-win does not just point out the value of the triple

benefit in any negotiations between the two, (A-B) assuming that there

is a common interest, or else the Community (C) as a third party but

goes further : seeks to maximize this triple ”win”, in a way

nonnegotiable the maximum point (the triple ”win”) is the equilibrium

point of the "objective function Z" This is where is the effective point

you get no movement, no redistribution that might benefit the one or

two of the three parts (A-B-C) without worsening the situation of the

other or other party (ies)

A clear extension of the “win-win”2pl bargaining perception:

win-win-win papak model transfers the “win-win conflict perception in

a new domain of mental reflection:

It is a discipline in a new field of thinking which starts from the "what

we think about the others, not only the (competitive) bargainer, but

also for total population (of the Community, of State, of Continents, of

the World)

It is the responsibility of each person for the realization of an overall

plan, in which individualism subordinated to the collective scheme: If

every human unit knows exactly its individual interest then should

work to maximize not just its own (interest ) but at the same time

maximizing the collective interest of the Community (factor K) See now

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te statistics 2016 Sixty-two (62) People hold 50% of global wealth He

and only the number introduced to the imbalance of the world system

that causes various reactions (wars, blockades, poverty misery) While

it may seem paradoxical this situation produces a psychological

imbalance, uncertainty, hatred, passions, upset

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4

UTILITY

FUNCTION

In economics, the utility function measures welfare or satisfaction

of a consumer as a function of consumption of real goods, such as

food, clothing and composite goods rather than nominal goods

measured in nominal terms. Utility function is widely used in the

rational choice theory to analyze human behavior.

(INVESTOPEDIA)

Utility function U(x, y) shows the utility level derived from consuming x and y, where x and y are the quantity of two goods. A utility function can be illustrated in a three-dimensional diagram when there are only two goods.

If there are more than two goods, it is customary to write the utility function,

U(x ,y, z) or U(x1,x2, ..., xn),

where xi is the quantity of good i.

Utility curve shows the relationship between one good and the utility level holding the quantities of all other goods consumed

n-d space as domain

This work raises a very subtle distinction here, that in the same time it is

an objection for world economic system: This work does not accept the

deliberate distinction in consumption of "a" or "b" product

Instead considers that people consume either "knowledge", either / or

"experience"

He considers the dilemma "a" or "b" product is intentionally false (false

dilemma) and misleading

Instead, the proper -in this task- distinction relates to

The knowledge consumers (SENSITIZATION included)

and

The experiences consumers

In the last, the false dilemma posed by the market to maximize its own

benefit (the “a” or “b” product) is included

As a result,

This work does not interfere there but spoke to the point that created

the so-called social (for others "class") problem How is created?

Generated when the attempt by "A" to achieve of his individual

satisfaction hinders the efforts of "B" to satisfy his own individual

interest: The basic idea at this point is that

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Consumption

EXAMPLE

To postulate the utility function, economists typically make

assumptions about the human preferences for different goods. For

example, in certain situations, tea and coffee can be considered

perfect substitutes of each other and the appropriate utility

function must reflect such preferences with a utility form of u(c, t) =

c + t, where "u" denotes the utility function and "c" and "t" denote

coffee and tea. A consumer who consumes 1 pound of coffee and

no tea derives a utility of 1util.

In the suggested win-win-win papakonstantinidis model it is the

strategy profiles that are taken into consideration, followed by the

fit satisfaction

Why can we not say that two people who chose to buy the same

quantity of a good at the same price have the same marginal

utility?

Answer: We cannot interpersonally compare utility between

people, so even if the tradeoffs they face between one good and

another, measured by their relative prices, are the same, we do not

know their marginal utilities.

Undoubtedly the utility function concerns the ordinal (not cardinal)

utility of a single person (the definition of this utility does not make

acceptable interpersonal comparison of utility) just tells us whether

a person prefers the good x over the good y (the consumer’s utility)

Economic science (new-classical school of thought) studies

individual consumption of households, because the study

recommends the sales planning basis

On this point there is main objection (see at the last column)

this work raises a very subtle distinction here, that in the same time

it is an objection for world economic system: This work does not

accept the deliberate distinction in consumption of "a" or "b"

product

Instead considers that people consume either "knowledge" or

"experience"

The marginal rate of substitution does not examine a combination

of goods that a consumer would prefer more or less than another

combination, but examines which combinations of goods the

consumer would prefer just as much. It also does not examine

marginal utility – how much better or worse off a consumer would

be with one combination of goods rather than another – because

all combinations of goods along the I.C are valued the same by the

consumer.

In this way the utility function resulting from a comparison (ordinal

utility two different behaviors i.e.

(a) aggressive behavior [especially coming from those experiences

consumers] It includes all these encompasses all those attitudes and

postures that gradually transform human behavior totally selfish,

assertive, without even care for the personality, continuity and problems

of the negotiator who is faced with

The two negotiators arrive in negotiating with mentality reminiscent of

"boxing match" seconds before the match starts

The strange thing is that over time, this behavior not only adopted

around (today) the planet, but also praised rewarded glorified

Socially successful was he who managed to "foisted" himself in social

trading, regardless of whether this would reduce (as always) the really

worthy not succeeded-as fluent culture - to have a measurement range

of real, true value to society Our Instead, this system is capitalism (as

today) made him unworthy that to hide his disability made him exactly

what this society revealed in "qualification":

insolence, demonstration greed Unlike the more worthy spent on the

sidelines precisely because they did something to rival the first -see the

"silky People"

and

(b) cooperative behavior coming mainly from knowledge consumers

now exceeds the individual personality and relates to all of us through

the time

Capitalism was established and based on the "aggressive behavior" But

precisely this aggressive behavior has created a distorted and destructive

for mankind perspective

In spite of rational action people realize in nowadays that something has

to change:

Rousseau had written on "Social Contract" that People understand that

perpetual satisfaction of private profit sooner or later leads to conflict

Therefore, people are intelligent enough to understand the value of the

collateral to each other interaction

They should give up a piece of their personal freedom to a superior

creature, i.e the "State" (the Leviathan Hobbes) in exchange for their

political freedom, freedom of expression and the transaction security

Each of them is rather “knowledge consumer” or rather “experiences’

consumer”

From this point of view, it is easier to interpersonally compare utility

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302 John Forbes Nash ((1951 (1950))paper titled NON-COOPERATIVE GAMES, JOHN FORBS NASH (NOBEL PRIZE 1994) – EDITED IN

Annals of Mathematics Vol 54 No 2, September 1951 304

Capraro Valerio (2013) A Solution Concept For Games With Altruism And Cooperation Econometrica 45 (7) (1977), 1623-

1630

IN the NON-COOPERATIVE GAME,302 philosophy:

Let ),( fS be a game with n players, where iS is the strategy

set for player nSSSSandi *....**...,. 21 is the set of

strategy profiles AND ))()........(( 1 xfxff n is the

payoff function for Sx

Let ix be a strategy profile of player ixandi .... be a strategy

profile of all players except for player i : When each

player },......1{ ni chooses strategy ix resulting in strategy

profile )......( 1 nxxx then player i obtains payoff )(xf i

Note that the payoff depends on the strategy profile chosen, i.e.,

on the strategy chosen by player i as well as the strategies chosen

by all the other players.

A strategy profile Sx * is a Nash equilibrium (NE) if no

unilateral deviation in strategy by any single player is profitable for

that player, that is

),().(:, ***

iiiiiiii xxfxxfSxi

Focused on Marginal Utility

)()( 12 SUSUU

pcgpc g

U

g

U.0.

lim

pcg g

U

g

U.0

lim

according to the diminishing M.U corresponds to the condition:

02

2

g

U

between people, on the base of the dipole

“knowledge – experiences”

▲

Valerio Capraro(2013)304:

Proposal for “gain functions” instead of “utility functions”.

▲

Under the ambiguous title "knowledge" is implied a huge range of

stimuli, especially social education despite the bare knowledge which

provides an encyclopedia It is synonym of the word “pester”

The word "education" is a derivative of the GREEK ancient verb "pester"

which means I teach, educate Synonyms: the word culture refers to the

mental and spiritual cultivation of a child, which is achieved mainly

through education (at various levels of). The word culture incorporates

the statement of both spiritual culture and spiritual culture (as opposed

to the technical / material). Besides providing knowledge training also

aims at human educated and in physique, namely in shaping the

personality and the development of good character. These concepts are

also attributed to the term treatment.

The teaching on freedom and democracy without guaranteeing the exercise of freedom and real democracy, there is education; education is the verbosity and often education in absurdity, immorality and selfishness. Treatment, education, teaching specific and systematic processes influencing and shaping. In particular the application is an orientation process that directs people to establish and evaluate their experiences with a generally defined manner. Education leads people to acquire knowledge, values, skills, dispositions, etc. Finally, teaching is a transmission process, creation of conditions for the acquisition by humans of specific knowledge, to internalize certain values, development of specific skills in addiction specific ways of action / reaction etc. Teaching: a tool for achieving education. Education : a tool to achieve the treatment Education: a tool for achieving education

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

0 5 10 15 20

u

f(u

)

uuf )(

ukuf2

1)(

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papakonstantinidis Page 178

MARGINAL RATE OF SUBSTITUTION (MRS)

y

xxy

MU

MU

dx

dyMRS

y

xxy

P

PMRS )(

Equilibrium point

In the utility/prices equilibrium, an infinitely small change in the indifference curve(IC) (negative as to the origin) brought about a change in the slope of prices (negative for the origin) The tangent point of the two curves is the point of equilibrium (the consumer uses when optimally preferences / budget for buying these goods

y

x

x p

p

dx

dy)1()1(lim

0

(*)

*(-1) opposite to the principle axes

Suppose the consumers (A-B) should be chosen (how each)

between two "consumer" products:

1. Knowledge: x

2. Experiences: y

Thus, the utility function for each is

Papakonstantinidis 2003

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papakonstantinidis Page 179

),..(..:.

),..(...:.

22

11

yxUB

yxUA

Each of them is rather “knowledge consumer” or rather

“experiences’ consumer”

The utility function is necessary and imperative

The “A” consumer would change an infinitesimal amount of Y with

a unit X in order to maintain "the two goods maintain the utility

level (Indifferent Curve) Mathematically, it is the implicit derivative

y

xxy

indifxy

MU

MUMRS

dx

dymMRS

y

xxy

MU

MU

dx

dyMRS

Defined as the units of the good Y which the consumer has to

leave, so that increasing the consumption of X by one unit,

maintain the utility level Also noted:

y

UMU

x

UMU

y

x

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papakonstantinidis Page 180

Finally, the relation between the IC and the rate of prices

(MRS)=MRE: consumer equilibrium

Marginal Rate of Substitution (MRS) must be equal to the ratio of prices, also called the Market Rate of Exchange (MRE) to attain consumer equilibrium. First let's understand what's the difference between the two

MRS is the rate at which the consumer is willing

to sacrifice units of one good in order to obtain a

unit of another.

MRE is the rate at which consumer has

to sacrifice units of one good in order to obtain a

unit of another, in accordance with market prices.

Now, let's analyze the two unstable cases

1. MRS > MRE

This means consumer is willing to sacrifice greater quantities of one

good (say X) to obtain a unit more of the other(say Y). Thus, he

values good Y more than good X and is likely to consume more

good Y.

Eventually as the consumption of good Y increases and that of good

X falls, he becomes reluctant to shell out large quantities of good X

for an additional unit of good Y because now his utility from good Y

falls due to operation law of diminishing marginal utility(DMU).

This implies his MRS falls and consequently becomes equal to MRE.

2. MRE > MRS

This means the consumer is willing to sacrifice lesser units of good X

than the market demands, to obtain an additional unit of good Y. In

short, he values good X more than good Y. In such a case, he is

willing to pay a price lower than the market price for good Y.

Thus, the transactions cannot take place and he will end up

consuming more units of good X. With an increase in consumption

of good X, the utility derived from it falls due to law of DMU. Now,

he starts valuing good Y and is now ready to substitute greater

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303 Quora, 2015 March15

quantities of good X to obtain a unit more of good Y.

As a result, MRS increases and becomes equal to MRE.

Thus, in both the cases, the final outcome is

MRS = MRE

This is the point of consumer equilibrium303.

y

x

x p

p

dx

dy)1()1(lim

0

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN” IN THE CURRENT

BIBLIOGRAPHY ACCORDING TO THE EXISTING THEORY

5. Terminolog

y “he” and

“She”

In game theory found very often "he", "she" particularly when we want to separate the two players who interact each other instance, is the concept of pre-introduction note do Osborne Martin J. and Rubinstein Ariel (1990) in their work Bargaining and Markets” are very useful and give us to understand exactly how these terms are used

A Note on the Use of "He" and "She"

The English language forces us to refer to individuals as "he" or

"she". We disagree on how to handle this problem.

Ariel Rubinstein argues that we should use a "neutral" pronoun, and

agrees to the use of "he", with the understanding that this refers to

both men and women. Given our socio-political environment,

continuous reminders of the she/he issue simply divert the reader's

attention from the main issues. Language is extremely important in

shaping our thinking, but in academic material it is not useful to

wave it as a flag.

Influences on win-win-win terminology

The discrimination between “he” and “she”, made by Osborne Martin J.

and Rubinstein Ariel (1990) in game theory helped us to make a clear

vis-à-vis of men and women taking part in a bargain, or otherwise, a

person or group occupying a corresponding position to that of another

person or group in a different area or domain; a counterpart.

In the proposed “win-win-win papakonstantinidis model” we have to

define THREE (3) different separate “players”

o The A

o The B

and

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305 Osborne Martin J. and Rubinstein Ariel (1990) “Bargaining and Markets” ACADEMIC PRESS, INC. Harcourt Brace

Jovanovich, Publishers

Martin Osborne argues that no language is "neutral". Every

choice the author makes affects the reader. "He" is exclusive, and

reinforces sexist attitudes, no matter how well intentioned the user.

Language has a powerful impact on readers' perceptions and

understanding. An author should adopt the style that is likely to

have the most desirable impact on her readers' views ("the point . . .

is to change the world"). At present, the use of "she" for all

individuals, or at least for generic individuals, would seem best to

accomplish this goal. We had to reach a compromise. When referring to specific

individuals, we sometimes use "he" and sometimes "she". For

example, in two-player games we treat Player 1 as female and

Player 2 as male; in markets games we treat all sellers as female and

all buyers as male. We use "he" for generic individuals305

The “C” (Community)

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN” IN THE CURRENT BIBLIOGRAPHY

ACCORDING TO THE EXISTING THEORY

6

GAME THEORY

Focused on

coordination

game -bargain

NON-COOPERATIVE GAME (NCG)

In his famous (Received October 11, 1950) paper titled NON-

COOPERATIVE GAME, JOHN FORBS NASH (NOBEL PRIZE 1994) –

EDITED IN Annals of Mathematics Vol 54 No 2, September 1951 has as starting point the book “Theory of Games and

Economic Behavior” of Von Neumann and Morgenstern who

have developed a theory of two-person zero-sum games

This book also contains a theory of η-person games of a type

which we would call cooperative. This theory is based on an

analysis of the interrelationships of the various coalitions

which can be formed by the players of the game. By introducing in his “NCG theory Nash indicates that in contradistinction, is based on the absence of coalitions in that it is assumed that each participant acts independently, without collaboration or communication with any of the

The theory of games is a mathematical discipline designed to treat rigorously

the question of optimal behavior of participants in games of strategy and to

determine the resulting equilibria. In such games each participant is striving for

his greatest advantage in situations where the outcome depends not only on

his actions alone, nor solely on those of nature, but also on those of other

participants whose interests are sometimes opposed, sometimes parallel, to his

own. Thus, in games of strategy there is conflict of interest as well as possible

cooperation among the participants. There may be uncertainty for each

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309 Shubik Martin (1968) “Theoretical Aspects” International Encyclopedia of the Social Sciences, 1968

KEY OBJECTIVE

The Nash

equilibrium

others.

The notion of an equilibrium point is the basic ingredient in his NCG theory. This notion yields a generalization of the concept of the solution of a two-person zero-sum game. It turns out that the set of equilibrium points of a two-person zero-sum game is simply the set of all pairs of opposing "good strategies.'' In the immediately following sections he defined equilibrium points and proved that a finite non-cooperative game always has at least one equilibrium point. He also introduced the notions of solvability and strong solvability of a non-cooperative game and proved a theorem on the geometrical structure of the set of equilibrium points of a solvable game. As an example of the application of his theory he included a solution of a simplified three person poker game.

Formal Definitions and Terminology

Nash firstly defined the basic concepts of this paper and set up standard terminology and notation The non-cooperative idea was a brilliant one, implicit, rather than explicit Finite Game: For him an η-person game was a set of η players, or positions, each with an associated finite set of pure strategies; and corresponding to each player },......1{ ni

a payoff function ip which maps the set of all

tuplesn of pure strategies into the real

numbers. When we use the term tuplen we shall

always mean a set of η items, with each item associated with a different player.

Mixed Strategy, is

A mixed strategy of player i is a collection of non-negative

numbers which have unit sum and are in one to one correspondence with his pure strategies. From this point, supposed that

iplayerofstrategies

purethearesthewhere

c

and

cwithcs

ia

a ia

iaiaa iai

.......

.......'....

...1

...0.....

. We regard the is ’s as points in a simplex whose vertices

are the ia ’s . This simplex may be regarded as a convex

subset of a real vector space, giving us a natural process of linear combination for the mixed strategies.

participant because the actions of others may not be known with certainty.

Such situations, often of extreme complexity, are found not only in games but

also in business, politics, war, and other social activities. Therefore, the theory

serves to interpret both games themselves and social phenomena with which

certain games are strictly identical. The theory is normative in that it aims at

giving advice to each player about his optimal behavior; it is descriptive when

viewed as a model for analyzing empirically given occurrences. In analyzing

games the theory does not assume rational behavior; rather, it attempts to

determine what “rational” can mean when an individual is confronted with the

problem of optimal behavior in games and equivalent situations.

The results of the interlocking individual actions are expressed by numbers,

such as money or a numerically defined utility for each player transferable

among all. Games of strategy include games of chance as a sub-case; in games

of chance the problem for the player is merely to determine and evaluate the

probability of each possible outcome. In games of strategy the outcome for a

player cannot be determined by mere probability calculations. Specifically, no

player can make mere statistical assumptions about the behavior of the other

players in order to decide on his own optimal strategy. But nature, when

interfering in a game through chance events, is assumed to be indifferent with

regard to the player or players affected by chance events. Since the study of

games of chance has given rise to the theory of probability, without which

modern natural science could not exist, the expectation is that the

understanding of the far more complicated games of strategy may gradually

produce similar consequences for the social sciences (Shubik Martin (1968)

“Theoretical Aspects” International Encyclopedia of the Social Sciences, 1968)309

Game theory concepts

Games are described by specifying possible behavior within the rules of the

game. The rules are in each case unambiguous; for example, certain moves are

allowed for specific pieces in chess but are forbidden for others. The rules are

also inviolate. When a social situation is viewed as a game, the rules are given

by the physical and legal environment within which an individual’s actions may

take place. (For example, in a market individuals are permitted to bargain, to

threaten with boycotts, etc., but they are not permitted to use physical force to

acquire an article or to attempt to change its price.) The concrete occasion of a

game is called a play, which is described by specifying, out of all possible,

allowable moves, the sequence of choices actually made by the players or

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He used the suffixes kji ,, for players and ya ,0,

to indicate various pure strategies of a player. The symbols

iii randts ...., . etc. will indicate mixed strategies; ia

will indicate the thi player's

tha pure strategy, etc.

Payoff function ip

The payoff function, ip used in the definition of a finite

game above, has a unique extension to the tuplen

of mixed strategies which is linear in the mixed strategy of

each player linearn

This extension we shall also denote by ip

writing )...,( 21 ni sssp

We shall write is to denote an tuplen of mixed

strategies and if )..,( 21 nssss then )( spi

then shall mean

),..,( 21 ni sssp Such an tuplen

is will also

be regarded as a point in a vector space, the product space of the vector spaces containing the mixed strategies And the

set of all such tuplen forms, of course, a convex

polytope, the product of the sumplices representing the mixed strategies. For convenience we introduce the

substitution notation ),( itsto stand for

)..,(,.....,..,..,..,....,( 211121 nniii sssswheresstsss

The effect of successive substitutions ));,;(( ii rtswe

indicate by );;( ii rtsetc.

Equilibrium Point:

An tuplen s is an equilibrium point if and only if

for every i

);(max)( iii rspsp Thus an equilibrium

point is an tuplen s such that each player's

mixed strategy maximizes his payoff if the strategies of the others are held fixed. Thus each player's strategy is optimal against those of the others. We shall occasionally abbreviate equilibrium point by eq. pt.

We say that a mixed strategy is uses a pure strategy ia if

iaa iai cs and 0iac

From the linearity of ),..,( 21 ni sssp in

is );(max;(max sprsp iii

participants. After the final move, the umpire determines the payments to each

player. The players may act singly, or, if the rules of the game permit it and if it

is advantageous, they may form coalitions. When a coalition forms, the

distribution of the payments to the coalition among its members has to be

established. All payments are stated in terms of money or a numerically defined

utility that is transferable from one player to another. The payment function is

generally assumed to be known to the players, although modifications of this

assumption have been introduced, as have other modifications—for example,

about the character of the utilities and even about the transferability of

payments.

The “extensive” form of a game, given in terms of successive moves and

countermoves, can be represented mathematically by a game tree, which

describes the unfolding of the moves, the state of information of the players at

the moment of each choice, and the alternatives for choices available to each

player at each occasion. This description can, in a strict mathematical sense, be

given equiv alent^ in a “normalized” form: each player, uninformed about the

choices made by any other player, chooses a single number that identifies a

“strategy” from his given finite or infinite set of strategies. When all personal

choices and a possible random choice are made (simultaneously), the umpire

determines the payments. Each strategy is a complete plan of playing, allowing

for all contingencies as represented by the choices and moves of all other

players and of nature. The payoff for each player is then represented by his

mathematical expectation of the outcome for himself. The final description of

the game therefore involves only the players’ strategies and no further chance

elements.

The theory explicitly assumes that each player, besides being completely

informed about the alternative payoffs due to all moves made or strategies

chosen, can perform all necessary computations needed to determine his

optimal behavior. (This assumption of complete information is also com

monplace in current economic theory, although seldom stated explicitly.)

The payments made by all players may add up to zero, as in games played for

entertainment. In this case the gains of some are exactly balanced by the losses

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We define ),()( iaiia spsp

Then we obtain the following trivial necessary and

sufficient condition for s

to be an equilibrium

point: )(max)( spsp iai

(3)

If

)()(

..)..,..,( 21

scsp

then

csandssss

iaa iai

iaa iain

consequently for (3) to hold we must have 0iac

whenever )(max)( spsp iaia which is to

say that s

does not use ia unless it is an optimal pure strategy

for player i. So we write

)(max)(..,............ spspthensinusedisIf iaiaia

as another necessary and sufficient condition for an

equilibrium point.

(4)

▲ CONCLUDING

Let ),( fS be a game with n players, where iS is the

strategy set for

player nSSSSandi *....**...,. 21 is the set of

strategy profiles AND ))()........(( 1 xfxff n is

the payoff function for Sx

Let ix be a strategy profile of player ixandi .... be a

strategy profile of all players except for player i : When each

player },......1{ ni chooses strategy ix resulting in

strategy profile )......( 1 nxxx then player i obtains

payoff )(xf i

of others. Such games are called zero-sum games. In other instances the sum of

all payments may be a constant (different from zero) or may be a variable; in

these cases all players may gain or lose. Applications of game theory to

economic of political problems require the study of these games, since in a

purchase, for example, both sides gain. An economy is normally productive so

that the gains outweigh any losses, whereas in a war both sides may lose.

If a player chooses a particular strategy as iden tified by its number, he selects

a pure strategy; if he allows a chance mechanism, specified by himself, to make

this selection for him, he chooses a mixed or statistical strategy. The number of

pure strategies for a player normally is finite, partly because the rules of games

bring the play to an end after a finite number of moves, partly because the

player is confronted with only a finite number of alternatives. However, it is

possible to treat cases with infinitely many strategies as well as to consider

even the borderline case of games with infinitely many players. These serve

essentially to study pathological examples or to explore certain mathematical

characteristics.

Game theory uses essentially combinatorial and set-theoretical concepts and

tools, since no specific calculus has as yet evolved—as happened when

differential and integral calculus were invented simultaneously with the

establishment of classical mechanics. Differential calculus is designed to

determine maxima and minima, but in games, as well as in politics, these are

not defined, because the out come of a player’s actions does not depend on his

actions alone (plus nature). This applies to all players simultaneously. A

maximum (or minimum) of a function can be achieved only when all variables

on which the maximum (minimum) depends are under the complete control of

the would be maximizer. This is never the case in games of strategy. Therefore,

in the equivalent business, political, or military operations there obtains no

maximum (minimum) problem, whether with or with out side conditions, as

assumed in the classical literature of these fields; rather one is confronted there

with an entirely different conceptual structure, which the theory of games

analyzes.

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Note that the payoff depends on the strategy profile chosen,

i.e., on the strategy chosen by player i as well as the

strategies chosen by all the other players.

A strategy profile Sx * is a Nash equilibrium (NE) if no

unilateral deviation in strategy by any single player is

profitable for that player, that is

),().(:, ***

iiiiiiii xxfxxfSxi

When the inequality above holds strictly (with > instead of ≥)

for all players and all feasible alternative strategies, then the

equilibrium is classified as a strict Nash equilibrium. If

instead, for some player, there is exact equality

between*

ix and some other strategy in the set S , then the

equilibrium is classified as a weak Nash equilibrium.

(In a sense, this is a result of the application of Pareto

efficiency in all considerations of microeconomics)

▲

Game Theory-Strategy: In game theory player’s strategy is

any of the options he or she can choose in a setting where

the outcome depends not only on his own actions but on the

action of others.[1] A player's strategy will determine the

action the player will take at any stage of the game.

The strategy concept is sometimes (wrongly) confused with

that of a move. A move is an action taken by a player at some

point during the play of a game (e.g., in chess, moving

white's Bishop a2 to b3). A strategy on the other hand is a

complete algorithm for playing the game, telling a player

what to do for every possible situation throughout the game.

A strategy profile (sometimes called a strategy combination)

is a set of strategies for all players which fully specifies all

actions in a game. A strategy profile must include one and

only one strategy for every player.

A player's strategy set defines what strategies are available

for them to play.

A player has a finite strategy set if they have a number of

discrete strategies available to them. For instance, in a single

game of rock-paper-scissors each player has the finite

strategy set {rock, paper, scissors}.

A strategy set is infinite otherwise. For instance, an action

A normal-form game

Player 1 \ Player 2 Player 2

chooses left

Player 2

chooses

right

Player 1 chooses top 4, 3 −1, −1

Player 1 chooses bottom 0, 0 3, 4

The matrix to the right is a normal-form representation of a game in which

players move simultaneously (or at least do not observe the other player's

move before making their own) and receive the payoffs as specified for the

combinations of actions played For example, if player 1 plays top and player 2

plays left, player 1 receives 4 and player 2 receives 3. In each cell, the first

number represents the payoff to the row player (in this case player 1), and the

second number represents the payoff to the column player (in this case player

2).

The main tool of this work is game theory: It is usually described bargaining situations as (extensive) games. Predictions about the resolution of conflict are derived from game-theoretic solutions (variants of subgame perfect equilibrium). The analysis is intended to be precise. Starting from the game theory we discuss five (5) points: The first uses the philosophy of “game” as a “tool” to extend the bargaining procedure in order to conclude the COMMUNITY © The second applies the theory of bargaining to the study of “community forces” as to absorb the bargaining trends The third is to construct theory of bargaining in which risk &time are modeled explicitly. The fourth to build solid theories on which to set the suggested “win-win-win model The fifth is to prove the existence of a “win-win-win” situation

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310

R. Baye, Michael (2008) “Managerial Economics and Business Strategy” McGraw-Hill/Irwin

with mandated bid increments may have an infinite number

of discrete strategies in the strategy set {$10, $20, $30, ...}.

Alternatively, the cake-cutting game has a bounded

continuum of strategies in the strategy set {Cut anywhere

between zero percent and 100 percent of the cake}.

In a dynamic game the strategy set consists of the possible

rules a player could give to a robot or agent on how to play

the game. For instance, in the ultimatum game the strategy

set for the second player would consist of every possible rule

for which offers to accept and which to reject.

In a Bayesian game the strategy set is similar to that in a

dynamic game. It consists of rules for what action to take for

any possible private information.

Choosing a strategy set

In applied game theory, the definition of the strategy sets is

an important part of the art of making a game

simultaneously solvable and meaningful. The game theorist

can use knowledge of the overall problem to limit the

strategy spaces, and ease the solution.

For instance, strictly speaking in the Ultimatum game a

player can have strategies such as: Reject offers of ($1, $3,

$5, ..., $19), accept offers of ($0, $2, $4, ..., $20). Including all

such strategies makes for a very large strategy space and a

somewhat difficult problem. A game theorist might instead

believe they can limit the strategy set to: {Reject any offer

≤ x, accept any offer > x; for x in ($0, $1, $2, ..., $20)}.

Pure and Mixed Strategies: A pure strategy provides a

complete definition of how a player will play a game. In

particular, it determines the move a player will make for any

situation he or she could face. A player's strategy set is the

set of pure strategies available to that player.

A mixed strategy is an assignment of a probability to each

pure strategy. This allows for a player to randomly select a

pure strategy. Since probabilities are continuous, there are

infinitely many mixed strategies available to a player.

The proposed new “win-win-win papakonstantinidis equilibrium is based on

“bargaining theory” may be consider an NE extension or even as an N.E

application in 3d space

In the win-win-win philosophy, the payoff depends on the strategy profile

chosen, i.e., on the strategy chosen by player as well as the strategies chosen by all the other players and the Community, both as the third party of bargain AND as an overall “player”, with the responsibility of “fair bargaining” In the game, the players have to make decisions sequentially in a pre-specified order. The order reflects the procedure of bargaining Simultaneous-Move, One-Shot Games: Normal Form Game310 •A Normal Form Game consists of: �Set of players i∈{1, 2, …n} where nis a finite number. �Each players strategy set or feasible actions consist of a finite number of strategies. •Player 1’s strategies are S1={a, b, c, …}. •Player 2’s strategies are S2={A, B, C, …}. �Payoffs. •Player 1’s payoff: π1(a,B) = 11. •Player 2’s payoff: π2(b,C) = 12. R. Baye, Michael (2008) “Managerial Economics and Business Strategy” McGraw-Hill/Irwin /////////////////////////16 The main issue we focuses on it is the “bargaining problem”: There is a close relation between game and bargain It is resulted that

GAMEBARGAIN

A Nash bargaining solution is a Pareto efficient solution to a Nash bargaining game. […..The two-person bargaining problem is a problem of understanding how

two agents should cooperate when non-cooperation leads to Pareto

inefficient results. It is in essence an equilibrium selection problem; many

games have multiple equilibria with varying payoffs for each player, forcing the

players to negotiate on which equilibrium to target. Solutions to bargaining

come in two flavors: an axiomatic approach where desired properties of a

solution are satisfied and a strategic approach where the bargaining procedure

is modeled in detail as a sequential game- see a bargaining discussion, below….]

It is assumed that there are only three (3) “players” participating in a

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311. Tovey Craig A (2010): The probability of majority rule instability in the 2D Euclidean model with an even numbers of voters

Oct 2010 · Social Choice and Welfare (Keywords Spatial voting-Equilibrium-Stability-Euclidean preferences-Majority rule)

Of course, one can regard a pure strategy as a degenerate

case of a mixed strategy, in which that particular pure

strategy is selected with probability 1 and every other

strategy with probability 0.

A totally mixed strategy is a mixed strategy in which the

player assigns a strictly positive probability to every pure

strategy. (Totally mixed strategies are important for

equilibrium refinement such as trembling hand perfect

equilibrium

Mixed Strategy: Illustration: Consider the payoff matrix

pictured to the right (known as coordinator game). Here

one player chooses the row and the other chooses a column.

The row player receives the first payoff, the column player

the second. If row opts to play A with probability 1 (i.e.

play A for sure), then he is said to be playing a pure strategy.

If column opts to flip a coin and play A if the coin lands heads

and B if the coin lands tails, then he is said to be playing a

mixed strategy, and not a pure strategy.

Significance: In his famous paper, John Forbs Nash proved

that there is an equilibrium for every finite game One can

divide Nash equilibria into two types. Pure strategy Nash

equilibria are Nash equilibria where all players are playing

pure strategies. Mixed strategy Nash equilibria are equilibria

where at least one player is playing a mixed strategy. While

Nash proved that every finite game has a Nash equilibrium,

not all have pure strategy Nash equilibria. For an example of

a game that does not have a Nash equilibrium in pure

strategies, see Matching pennies However, many games do

have pure strategy Nash equilibria (e.g. the coordination

game the Prisoner’s Dilemma, the Stag hunt Further, games

can have both pure strategy and mixed strategy equilibria.

A B

A 1,1 0.0

game/bargain: According to Nash, a “bargaining solution” is a Pareto efficient solution, on Nash bargaining game. That is the bargaining solution among three parties (A-B and the Community as the third and overall player of the bargain) There is an infinity number of sets (not exactly “solutions” Each match induces a bargaining game between the two parties. The agents are motivated to reach agreement by two factors: their own impatience and the exogenous risk that their partnership will terminate. Their utilities in the latter case depend on the equilibrium prevailing in the market; the agents take these utilities as given. We assume that the agents' behavior in the bargaining game does not depend on events in other matches. The equilibrium that we characterize does not coincide with the competitive equilibrium of the market when the demand and supply functions are those of the steady state stock of agents in the market As we enter the bargain, we see that the three participating parts (i.e A-B and the Community as a third, but overall negotiator, ensuring at the same time and benefit the rest of society except for the two negotiators), make offers towards the other two bargainers targeting to an agreement that favors mostly the same, in accordance with the principle of Rationalism So, one side proposes the present time “t” the an own proposal. If it is accepted by the other two parties, the negotiation reaches in agreement If even one of the other two have an objection then the "game" continues until the conclusion of the negotiation agreement or disagreement

the win-win equilibrium

BINOMIAL DISTR

o Coalitions of weighted voting games can be restricted to be connected components of a graph As a consequence, coalition formation, and therefore a player’s power, depends on the topology of the graph.

o The classic instability theorems of Euclidean voting theory

definitively treat all cases except that of an even number of voters in

two dimensions. For that case, all that has been known is that the

set of stable configurations is neither measure 0 nor measure 1. We

prove that instability occurs with probability converging rapidly to 1

as the population increases.311

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306

John Forbs Nash(1950) TWO-PERSON COOPERATIVE GAMES August 31, 1950 -the RAND Corporation (P-172)

B 0,0 1,1

Pure Coordination Game

Payoffs matrix

Behavior strategy: While a mixed strategy assigns a

probability distribution over pure strategies, a behavior

strategy assigns at each information set a probability

distribution over the set of possible actions While the two

concepts are very closely related in the context of normal

form games, they have very different implications for

extensive form games. Roughly, a mixed strategy randomly

chooses a deterministic path through the game tree, while a

behavior strategy can be seen as a stochastic path.

The relationship between mixed and behavior strategies is

the subject of Kuhn’s Theorem The result establishes that in

any finite extensive-form game with perfect recall, for any

player and any mixed strategy, there exists a behavior

strategy that, against all profiles of strategies (of other

players), induces the same distribution over terminal nodes

as the mixed strategy does. The converse is also true.

COOPERATIVE GAME In his famous (P-172) paper titled TWO-PERSON COOPERATIVE GAMES August 31, 1950 John Forbs Nash (the RAND Corporation)306 defined e the concept of a general two-person cooperative game and developed a concept of a solution for such games. There are two different ways in which the solution may be derived. One is "by the use of a set of axioms describing general properties a solution should possess and from which it can he deduced that there is hut one possibility in each case. The other proceeds why setting up a model of the negotiation process which the players go through in deciding upon a course of action. This is done in such a way as to obtain a non-cooperative game. - By using the term cooperative we mean to imply that the players have complete freedom of communication and complete information on the structure of the game. Furthermore, there should be the possibility of making enforced agreements, "binding either one or both players to a certain agreement or policy. It is assumed that either player may secure a commitment (enforced policy contract) upon himself if he so desires. But each player is supposed not to have any commitments upon himself before entering into the negotiation involved in this game, or at least none relevant to the situation. And we assume that while one player is obtaining a commitment upon himself the other may do likewise. Finally, we assume that the situation may be regarded as an isolated incident in the life of each player, and not one where a player's behavior could set up

Allele :

any of several forms of a gene, usually arisingthrough mutation, that are respon

sible forhereditary variation.

▲

According to Valerio Carparo (2013) who is an excellent The conflict between

cooperation and competition is one of the most important conflicts in human

decision making. Competition is individually optimal, but may lead to war and

destruction; cooperation leads to peaceful, healthy, and ultimately more

successful societies, but it requires individuals to pay a cost for the benefit of

others.

I combine math models and behavioral experiments to understand how people

solve this and related conflicts, with the goal of helping institutions to create

more collaborative societies.

Since its foundation by Morgenstern and von Neumann the major challenge of

modern game theory has been to predict which actions a human player would

adopt in a strategic situation. A first prediction was proposed in an earlier paper

by J. von Neumann for two-person zero-sum games and then generalized to

every finite game by J. Nash in Since then Nash equilibrium has certainly been

the most notable and used solution concept in game theory. Nevertheless, over

the last sixty years, it has been realized that it makes poor predictions of human

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an advantageous or disadvantageous precedent. The possible usefulness of a commitment is fairly clear. If one player can announce to the other that he is bound to accept only the most favorable sort of proposal for an agreement and the other is uncommitted, then the committed player should have an advantage, provided the other is rational and the commitment still allows some mutually profitable arrangement. The mathematical description of the game is as follows:

each player has a convex compact metric space is of

mixed strategies is ; there is similar space J of Joint

strategies; each pair

).( 21 ss corresponds to a certain joint strategy, and

this correspondence induces a mapping JxSS 21

which is linear on each space 1S

For each joint strategy there are two payoffs,

)(..)..( 21 pandp which are linear continuous

functions on J Since the joint strategies are to be employed

when agreement has been reached the only significant properties which one of them possesses are its utilities to the players, that is the

numbers )(..)..( 21 pandp corresponding to it.

Consequently we need only to know the set of utility pairs,

).,( 21 uu

which correspond to some such joint strategy. This set will be

simply a set

in the plane whose coordinates are the utility functions of the players, and Λ will be compact and convex. The mappings

21

21

....

....

xSS

mappingainduce

JandJxSS

which is linear on each space 1S or bilinear.

It may be written

)),(),..,((),( 21221121 sspsspss

In the actual negotiation model we restrict each player to a special class of commitments which appears to contain enough variety to enable a player to bring all the strong points of his position into the negotiation so that a greater range of possibilities would be useless to a player. The arrangement of the negotiation in a two stage form with two simultaneous moves by the two players in each stage appears at first to be a very artificial device. It is really simply a convenience, since a one stage form could be used, but would be essentially equivalent to putting the two stage game in normal form, and hence messier to handle Now for the formal model: Stage 0. Players are informed of the situation, may talk it over, if they like. Stage 1. Each player goes to his attorney and arranges to be

forced to play a certain mixed strategy it if the two do not

eventually reach agreement; it is called player i's "threat".

play and, indeed, a large number of experiments have been conducted on

games for which it dramatically fails to predict human behavior.

There are many reasons behind this failure. On the one hand, when there are

multiple equilibria, it is not clear which one we should expect is going to be

played. A whole stream of literature, finalized to the selection of one

equilibrium, arose from this point, including the definitions of evolutionarily

stable strategy perfect equilibrium trembling hand perfect equilibrium, proper

equilibrium sequential equilibrium, limit logit equilibrium, and, very recently,

settled equilibrium

On the other hand, the criticism of Nash equilibrium is motivated by more seri-ous problems: there are examples of games with a unique Nash equilibrium which is not played by human players. Typical examples of such a fastidious situation are the Prisoner's Dilemma, the Traveler's Dilemm and, more generally, every social dilemma [Ko88]. This point has motivated another stream of literature devoted to the explanation of such deviations from Nash equilibria. Part of this literature tries to explain such deviations assuming that players make mistakes in the computation of the expected value of a strategy and therefore, assuming that errors are identically distributed, a player may also play non-optimal strategies with a probability described by a Weibull distribution. if two agents played the Prisoner’s dilemma according to the coco value, then they would both cooperate for sure. This prediction contradicts the experimental data collected in recent researches Valerio Capraro tried to attribute the failure of all these attempts to two basic problems. The first problem is the use of utility functions in the very definition of a game. Indeed, the experimental evidence have shown that expected utility theory fails to predict the behavior of decision makers This problem could be theoretically overcome replacing utility functions with gain unctions and applying Kahneman-Tversky’s cumulative prospect theory CAPRARO VALERIO (2013) took into account that cooperation is not casual and depends on the payoffs of the game. These findings suggest that humans have attitude to cooperation by nature and the same person may act more or less cooperatively depending on the particular payoffs. In other words, people do not act a priori as single agents, but they forecast how the game would be played if they formed coalitions and then they play according to their best forecast. Capraro defined a a new solution concept for one-shot normal form games. CAPRARO VALERIO (2013) proved that the cooperative equilibrium exists for all finite games and it explains a number of different experimental findings, such as (1) the rate of cooperation in the Prisoner’s dilemma depends on the cost-benefit ratio; (2) the rate of cooperation in the Traveler’s dilemma depends on the bonus/penalty; (3) the rate of cooperation in the Public Goods game depends on the pro-capite marginal return and on the numbers of players; (4) the rate of cooperation in the Bertrand competition depends on the number of players; (5) players tend to be fair in the bargaining problem; (6) players tend to be fair in the Ultimatum game; (7) players tend to be altruist in the Dictator game; (8) offers in the Ultimatum game are larger than offers in the Dictator game. Since its foundation by Morgenstern and von Neumann , the major challenge of modern game theory has been to predict which actions a human player would adopt in a strategic situation. A first prediction was proposed in an earlier paper by J. von Neumann for two-person zero-sum games and then generalized to every finite game by J. Nash in Since then Nash equilibrium has certainly been the most notable and used solution concept in game theory. Nevertheless, over the last sixty years, it has been realized that it makes poor predictions of human play and, indeed, a large number of experiments have been conducted on games for which it drammatically fails to predict human behavior. There are many reasons behind this failure. On the one hand, when there are multiple equilibria, it is not clear which one we should expect is going to be played. A whole stream of literature, finalized to the selection of one equilibrium, arose from this point, including the definitions of evolutionarily stable strategy perfect equilibrium , trembling hand perfect equilibrium proper equilibrium, sequential equilibrium limit logit equilibrium

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312 See at appendix to this table

Stage 1,5 The players return from their attorneys and display the commitments they have made. Stage 2. They return to their attorneys and each commits

himself to a "demand" id which is a point on his utility

scale, the idea being that player i will accept no deal which has utility less than d^ to him. The payoffs in this model are defined as follows: If there is a

point

2211

21

....

........)..,(

duanddu

thatsuchinuu

then the payoff to each player is his demand, id

If not, then the payoffs are

),(..)..,( 212211 ttpandttp

The interpretation is that if their demands are compatible they should get what they demanded, but otherwise they must execute their threats. This method of defining payoffs makes each player want his demand to be as large as possible without loss of consistency.

▲

We discuss on three main issues:

The NCG

Preferences

Instant reflection mixed strategies taken inside the frame of

feasible region, with the community including this frame

The "Theory of Non-Cooperative Game (NCG)of John Nash

(1951) is the basis of all considerations discussed in this

paper

Especially the "Nash Equilibrium" was a key inspiration of

the "win-win-win papakonstantinidis model"

This effort focused on "Nash Equilibrium" with key elements comparing "strategic profile" choices, decisions and payoffs (shares) and the probabilities (under conditions of uncertainty) of such strategies to be realized the payoff depends on the strategy profile chosen, i.e., on the strategy

chosen by player as well as the strategies chosen by all the other players.

A strategy profile Sx * is a Nash equilibrium (NE) if no

unilateral deviation in strategy by any single player is

profitable for that player, that is

),().(:, ***

iiiiiiii xxfxxfSxi

Usually bargaining situations are described mainly as

(extensive) games. Predictions about the resolution of

conflict are derived from game-theoretic solutions (variants

of subgame perfect equilibrium). The analysis is intended to

and, very recently, settled equilibrium On the other hand, the criticism of Nash equilibrium is motivated by more serious problems: there are examples of games with a unique Nash equilibrium which is not played by human players. Typical examples of such a fastidious situation are the Prisoner's Dilemma the Traveler's Dilemma (see at appendix), and, more generally, every social dilemma. This point has motivated another stream of literature devoted to the explanation of such deviations from Nash equilibria. Part of this literature tries to explain such deviations assuming that players make mistakes in the computation of the expected value of a strategy and therefore, assuming that errors are identically distributed, a player may also play non-optimal strategies with a probability described by a Weibull distribution. This intuition led to the foundation of the so-called quantal response equilibrium theory by McKelvey and Palfrey. A variant of this theory, called quantal level-k theory and proposed by Stahl and P. Wilson in , was recently shown to perform better in the prediction of human behavior In the same paper, Wright and Leyton-Brown have also shown that quantal level-k theory predicts human behavior significantly better than all other behavioral models that have been proposed in the last decade, as the level-k theory and the cognitive hierarchy model. However, an obvious criticism of quantal level-k theory is that it is not scale invariant, contradicting one of the axioms of expected utility theory of Morgenstern and von Neumann. A perhaps more fundamental criticism stems from the fact that quantal level-k theory only makes use of some parameters describing either the incidence of errors that a player can make computing the expected utility of a strategy or the fact that humans can perform only a bounded number of iterations of strategic reasoning. These features first imply that quantal level-k theory is not predictive, in the sense that one has to conduct experiments to estimate the parameters; second, they imply that quantal level-k theory intrinsically affirms that deviation from Nash equilibria can descend only from two causes, computational mistakes and bounded rationality, that are hard to justify for games with very easy payoffs, like the Prisoner's Dilemma, or for games where the deviation from Nash equilibrium is particularly strong, like the Traveler's Dilemma312 with small bonus-penalty.

Indeed, the general feeling is that the motivation must rely somewhere deeper

and that Nash equilibrium should be replaced by a conceptually different

solution concept that takes into account other features of human behavior and

coincides with Nash equilibrium only in particular cases. A number of

researchers presented their work on this subject and “gave solutions”

Nevertheless, even though these solution concepts can explain deviations from

Nash equilibria in some particular games, all of them make unreasonable

predictions for many games of interest. For instance, the maximum perfect

cooperative equilibrium is too rigid and predicts cooperation for sure in the

Prisoner's and Traveler's Dilemmas, contradicting the experimental data

collected in a number of researchers . The iterated regret minimization proce-

dure introduced in papers can explain deviations towards cooperation in some

variants of the Traveler's Dilemma, the Bertrand competition, the Centipede

Game, and other games of interest, but it does not predict deviation towards

cooperation in the Prisoner's Dilemma and in the public good game it cannot

explain altruistic behaviors in the ultimatum game and in the dictator game and

makes unreasonable predictions for the Traveler's dilemma with punishment

and a certain zero-sum game The solution concept defined using algorithmic

rationability can explain deviation towards cooperation in the iterated Pris-

oner's and Traveler's dilemmas, but it does not predict deviation towards

cooperation in one-shot versions of the Prisoner's dilemma or in one-shot

versions of the Traveler's dilemma with very small bonus-penalty, contradicting

the experimental data reported in different ideas CAPRALO tried to attribute

the failure of all these attempts to two basic problems.

The first problem is the use of utility functions in the very definition of a game.

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307

Nash John Forbs 1953 Two-person cooperative games. Econometrica 21: 128 - 140. 313We mention that anonimity is not really a necessary assumption: the effect of any sort of contact among the players would be a different evaluation of the so-called prior probability τ. The point is that at the moment it is not clear how this prior probability should be re-evaluated.

be precise. We do not hold the position that every claim in

economic theory must be stated formally. Sometimes formal

models are redundant—the arguments can be better made

verbally. However, the forms in this work , we believe,

demonstrate the usefulness of formal models. They provide

clear analyses of complex situations and lead us to a better

understanding of some economic phenomena.

An interpretation of the theories in this book requires an

interpretation of game theory. At several points we make

comments on the interpretation of some of the notions we

use, but we do not pretend to present a complete and

coherent interpretation.

For finding the “win-win-win” solution it is taken into

account both “cooperative” and “non-cooperative game

solution”

MIXED STRATEGY is

iplayerofstrategies

purethearesthewhere

c

and

cwithcs

ia

a ia

iaiaa iai

.......

.......'....

...1

...0.....

In Nash’s words, one makes the players’ steps of negotiation

. . . moves in the non-cooperative model. Of course, one

cannot represent all possible bargaining devices as moves in

the non-cooperative game. The negotiation process must be

formalized and restricted, but in such a way bat each

participant is still able to utilize all the essential strengths of

his position

Nash’s “Variable Threat” Model In Nash’s axiomatic model the point d, which is interpreted as the outcome in the event that the players fail to reach agreement, is fixed. Nash (1953)307 extended his theory to encompass situations in which the players can influence this outcome. The primitive of this later model is a two-person strategic game, which we denote G, in which each player has finitely many pure strategies.

Let siplayerbePi ..'...... set of pure strategies, let

)....(total be his set of mixed strategies (i.e.

probability distributions over pure strategies),, and let

RxH i 21: be his payoff function.

Indeed, the experimental evidence have shown that expected utility theory fails

to predict the behavior of decision makers This problem could be theoretically

overcome replacing utility functions with gain functions and applying

Kahneman-Tversky's cumulative prospect theory

But one can easily convince himself that in most cases such a replacement

could explain only quantitative deviations.

The second problem is indeed that experiments conducted on the Prisoner's

dilemma, the Traveler's dilemma, Dictator game, and other games, show

qualitative deviations from classical solution concepts. These qualitative

deviations suggest that humans are altruistic and have attitude to cooperation.

These observations motivate the definition of a new solution concept, able to

take into account altruism and cooperation and using gain functions instead of

utility functions. This paper represents a first endeavor in this direction. Indeed,

here we consider only one-shot normal form games where the players are

completely anonymous, that is, they do not know each other and they are not

allowed to exchange information313. The aim of this paper is to define a new

solution concept for this class of games. This solution concept will be called

cooperative equilibrium. Indeed, we will see that altruism plays only a marginal

role and the main idea behind this new equilibrium notion is the formalization

of the following principle of cooperation:

(C) Players try to forecast how the game would be played if they formed

coalitions and then they play according to their best forecast.

The study of cooperation in games is not a new idea. Economists,

biologists, psychologists, sociologists, and political scientists, have been

studying cooperation in social dilemmas for forty years. These classical

approaches explain tendency to cooperation dividing people in pro-self and

pro-social types or appealing to forms of external control or to long-term

strategies in iterated games[Ax84]. But, over the years many experiments have

been accumulated to show cooperation even in one-shot social dilemmas

without external control These and other earlier experiments have also shown

that the rate of cooperation in the same game depends on the particular

payoffs, suggesting that most likely humans cannot be merely divided in pro-

self and pro-social types, but they are engaged in some sort of indirect

reciprocity and the same person may behave more or less cooperatively

depending on the payoffs. In other words, humans have attitude to cooperation

by nature.

To the best of our knowledge, this is the first attempt to lift this well known

tendency to cooperate up to a general principle which is nothing more than a

deeper and smarter realization of selfishness.

The idea to formalize the principle of cooperation and define the cooperative

equilibrium can be briefly summarized as follows:

• We assume that players do not act a priori as single players, but they

try to forecast how the game would be played if they formed

coalitions.

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308 Osborne Martin J. and Rubinstein Ariel (1990) “Bargaining and Markets” ACADEMIC PRESS, INC. Harcourt Brace

Jovanovich, Publishers

The players begin by simultaneously selecting mixed

strategies in G These strategies are interpreted as the

actions the players are bound to take if they fail to reach agreement; we refer to them as threats. The players must carry out their threats in case of disagreement even when the pair of threats is not a Nash equilibrium of G. Once the threats have been chosen, the agreement that is reached is given by the Nash solution of the bargaining problem in which the set of possible agreements is the set of probability

distributions over 21xPP and the disagreement point is the

pair of payoffs in G in the event the threats are carried out.

Given the threat of Player. )( j Player si' payoff in

the Nash solution is affected by his own threat; each player chooses his threat to maximize his payoff, given the threat of the other player308

A disputed meaning

During the 1980s, the concept of mixed strategies came

under heavy fire for being "intuitively problematic"

.Randomization, central in mixed strategies, lacks behavioral

support. Seldom do people make their choices following a

lottery. This behavioral problem is compounded by the

cognitive difficulty that people are unable to generate

random outcomes without the aid of a random or pseudo-

random generator

In 1991 game theorist Ariel Rubinstein described alternative

ways of understanding the concept. The first, due to Harsanyi

(1973), is called purification and supposes that the mixed

strategies interpretation merely reflects our lack of

knowledge of the players' information and decision-making

process. Apparently random choices are then seen as

consequences of non-specified, payoff-irrelevant exogenous

factors. However, it is unsatisfying to have results that hang

on unspecified factors.

A second interpretation imagines the game players standing

for a large population of agents. Each of the agents chooses a

pure strategy, and the payoff depends on the fraction of

agents choosing each strategy. The mixed strategy hence

represents the distribution of pure strategies chosen by each

• Each forecast is represented by a number v (p), called value of the

coalition structure p for player i , which is a measure of the expected

gain of player i when she plays according to the coalition structure p.

• The numbers )(pVi induce a sort of common beliefs: we

consider the induced game Ind(G,p) which differs from the original

game G only for the set of allowed profiles of mixed strategies: the

profiles of mixed strategies allowed in Ind(G,p) are the profiles

(σι,. . . , σΝ) such that «ί(σι,. . . , σΝ) > Vj(p), for any player i.

• The exact cooperative equilibrium is one where player i plays an

equilibrium of the game Ind(G,p) induced by a coalition structure

which maximizes the value function Vi

• The notion of equilibrium for the induced game Ind(G,p) is not

defined using classical Nash equilibrium, but using a prospect

theoretical analogue.

In order to apply prospect theory we must replace utility functions by gain

functions, that are, functions whose values represent the monetary outcomes

or, more generally, the quantity of some good which is won or lost by a player.

This replacement comes at the price that we must take into account explicitly

new data that were implicitly included in the utility functions. Indeed, while

utility functions were supposed to contain all relevant information about

players' preferences, gain functions do contain only the quantity of some good

which is won or lost by the players. These new data include the fairness

functions f i and the altruism functions a i j . An interesting feature of the

cooperative equilibrium is that, in many games of interest, it does not depend

on these functions. This implies that the cooperative equilibrium is a predictive

solution concept for many games of interest. A bit more precisely, in this paper

we prove the following statements.

FACT 1.1. The cooperative equilibrium for the Prisoner's dilemma is predictive

(i.e., it does not depend on fairness functions and altruism functions) and has

the following property: the predicted rate of cooperation increases as the cost-

benefit ratio increases.

FACT 1.2. The cooperative equilibrium for the Traveler's dilemma is

predictive and has the following property: the predicted rate of cooperation

decreases as the bonus/penalty increases. A typical example is the following.

(see at Appendix to this table)

FACT 1.3. The cooperative equilibrium for the Bertrand competition is

predictive and it has the following property: the predicted rate of cooperation

decreases as the numbers of players increase.

FACT 1.4. The cooperative equilibrium for the public good game is predictive and

it has the following properties: (1) the predicted rate of cooperation increases

as the marginal return increases, and (2) the predicted rate of cooperation

decreases as the number of players increases and then increases again as the

number of players gets sufficiently large.

FACT 1.5. The cooperative equilibrium predicts the (50,50) solution in the

Bargaining problem under natural assumptions on the fairness functions.

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APPENDIX TO TAPLE : The traveler's dilemma In game theory, the (sometimes abbreviated TD) is a type of non-zero

sum game in which two players attempt to maximize their own payoff, without any concern for the other player's payoff

Formulation: The game was formulated in 1994 by Kaushik Basu and goes as follows: An airline loses two suitcases belonging

to two different travelers. Both suitcases happen to be identical and contain identical antiques. An airline manager tasked to

settle the claims of both travelers explains that the airline is liable for a maximum of $100 per suitcase—he is unable to find out

directly the price of the antiques.To determine an honest appraised value of the antiques, the manager separates both travelers

so they can't confer, and asks them to write down the amount of their value at no less than $2 and no larger than $100. He also

tells them that if both write down the same number, he will treat that number as the true dollar value of both suitcases and

reimburse both travelers that amount. However, if one writes down a smaller number than the other, this smaller number will

be taken as the true dollar value, and both travelers will receive that amount along with a bonus/malus: $2 extra will be paid to

the traveler who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher

amount. The challenge is: what strategy should both travelers follow to decide the value they should write down?

Analysis One might expect a traveler's optimum choice to be $100; that is, the traveler values the antiques at the airline

manager's maximum allowed price. Remarkably, and, to many, counter-intuitively, the Nash Equilibrium (N.E) solution is in

fact just $2; that is, the traveler values the antiques at the airline manager's minimum allowed price. For an understanding of

why $2 is the N.E consider the following proof:

Alice, having lost her antiques, is asked their value. Alice's first thought is to quote $100, the maximum permissible

value.

population. However, this does not provide any justification

for the case when players are individual agents. Later,

Aumann and Brandenburger (1995), re-interpreted Nash

equilibrium as an equilibrium in beliefs, rather than actions.

For instance, in rock-paper-scissors an equilibrium in beliefs

would have each player believing the other was equally likely

to play each strategy. This interpretation weakens the

predictive power of Nash equilibrium, however, since it is

possible in such an equilibrium for each player

to actually play a pure strategy of Rock.

Ever since, game theorists' attitude towards mixed

strategies-based results have been ambivalent Mixed

strategies are still widely used for their capacity to provide

Nash equilibria in games where no equilibrium in pure

strategies exists, but the model does not specify why and

how players randomize their decisions

Roughly speaking, the natural assumption is that the two players have the

same perception of money. We believe that this assumption is natural, since it

is predictable that a bargain between a very rich person and a very poor person

can have a different solution.

FACT 1.6. The cooperative equilibrium explains the experimental data

collected for the dictator game, via altruism.

This happens just because we define the altruism in terms of human

behavior in the dictator game. To treat the dictator game as the quintessence

of altruism is certainly not a new idea

FACT 1.7. The cooperative equilibrium explain the experimental data collected

for the ultimatum game, via a combination of cooperation and altruism.

In particular, the observation that offers in the ultimatum game are larger then

the offers in the dictator game is explained in terms of cooperation, which is

generated by the fact that the responder has the power to reject proposer's

offer.

Another case where the cooperative equilibrium is only descriptive is when

the mistakes that players can make in the computations have a very strong

influence on the result.

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papakonstantinidis Page 195

On reflection, though, she realizes that her fellow traveler, Bob, might also quote $100. And so Alice changes her

mind, and decides to quote $99, which, if Bob quotes $100, will pay $101.

But Bob, being in an identical position to Alice, might also think of quoting $99. And so Alice changes her mind, and

decides to quote $98, which, if Bob quotes $99, will pay $100. This is greater than the $99 Alice would receive if both she

and Bob quoted $99.

This cycle of thought continues, until Alice finally decides to quote just $2—the minimum permissible price.

Another proof goes as follows:

If Alice only wants to maximize her own payoff, choosing $99 trumps choosing $100. If Bob chooses any dollar value

2–98 inclusive, $99 and $100 give equal payoffs; if Bob chooses $99 or $100, choosing $99 nets Alice an extra dollar.

A similar line of reasoning shows that choosing $98 is always better for Alice than choosing $99. The only situation

where choosing $99 would give a higher payoff than choosing $98 is if Bob chooses $100—but if Bob is only seeking to

maximize his own profit, he will always choose $99 instead of $100.

This line of reasoning can be applied to all of Alice's whole-dollar options until she finally reaches $2, the lowest

price.

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN” IN THE CURRENT BIBLIOGRAPHY

ACCORDING TO THE EXISTING THEORY

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE EXISTING THEORY

In mathematical optimization a feasible region, feasible set,

search space, or solution space is the set of all possible

points (sets of values of the choice variables) of an

optimization problem that satisfy the problem's constraints

potentially including inequalities equalities and integer

constraints. This is the initial set of candidate solutions to the

problem, before the set of candidates has been narrowed

down.

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314 Benati Stefano, Rizzi Romeo, Tovey Craig A.(2015,April) The complexity of power indexes with graph restricted

coalitions”- Mathematical Social Sciences 76 · April 2015

7 Feasible region

A problem with five linear constraints (in blue, including the

non-negativity constraints). In the absence of integer constraints the feasible set is the entire region bounded by blue, but with integer constraints it is the set of red dots.

A closed feasible region of a linear programming problem

with three variables is a convex polyhedron

A convex feasible set is one in which a line segment

connecting any two feasible points goes through only other

feasible points, and not through any points outside the

feasible set. Convex feasible sets arise in many types of

problems, including linear programming problems, and they

are of particular interest because, if the problem has

a convex objective function that is to be maximized, it will

generally be easier to solve in the presence of a convex

feasible set and any local optimum will also be a global

optimum

Let 1,0 denote the real interval from 1....0 to let n be the

number of players, and let jm

be the number of pure strategies available to player j Then player

sj' set of mixed strategies is the simplex

1}{}^1_{..0: jmisumxx The set of all possible points is the Cartesian

product of these simplices for ntoj ...,..1 This set is not a ball or sphere.

(Craig A. Tovey - Georgia Institute of Technology)314

Finding a close form for the sum $nisum }1_{\

1 1)1(

m

jj

The win-win-win equilibrium

▲

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papakonstantinidis Page 197

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE EXISTING THEORY

8

THE

BARGAINING

PROBLEM

Usually, the “bargaining problem” is referred to the case of

two players: }2,1{N The players either reach an

agreement in the set A or fail to reach agreement, in

which case the disagreement event D occurs. Each

Player Ni has a preference ordering i over the set

}{DA

(a complete transitive reflexive binary relation).

(The interpretation is that ba i if

and only if Player i either prefers

btoa ..... or is indifferent between them)

The objects

The two-person bargaining problem is a problem of understanding how two

agents should cooperate when non-cooperation leads to Pareto

inefficient results. It is in essence an equilibrium selection problem; many

games have multiple equilibria with varying payoffs for each player, forcing the

players to negotiate on which equilibrium to target. Solutions to bargaining

come in two flavors: an axiomatic approach where desired properties of a

solution are satisfied and a strategic approach where the bargaining procedure

is modeled in detail as a sequential game.

The Bargaining problem: “Bargaining”

The term “bargaining” (according to Nash) is used to refer to a situation in which (i ) individuals (“players”) have the possibility of concluding a mutually beneficial agreement, (ii) there is a conflict of interests about which agreement to conclude, and (iii ) no agreement may be imposed on any individual without his approval . A bargaining theory is an exploration of the relation between the outcome of bargaining and the characteristics of the situation. We are not concerned with questions like “what is a just agreement?”, “what is a reasonable

outcome for an arbitrator to decide?” or “what agreement is optimal for the society at large?” Nor do we discuss the practical issue of how to

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317 Osborne Martin J. and Rubinstein Ariel (1990) “Bargaining and Markets” ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers

NieachforandDAN i ............,..,.

define a bargaining situation. The set

A of possible agreements may take many

forms. An agreement can simply be a

price, or it can be a detailed contract

that specifies the actions to be taken by

the parties in each of many

contingencies. One respect in which the

framework is restrictive is that it

specifies a unique outcome if the players

fail to reach agreement. The players’

attitudes toward risk play a central role

in Nash’s theory. According to the

theoretical view, “each player’s

preferences be defined on the set of

lotteries over possible agreements, not

just on the set of agreements

themselves”. There is no risk explicit in

a bargaining situation as it has been

defined However, uncertainty about other

players’ behavior, which may cause

negotiation to break down, is a natural

element in bargaining. Thus it is

reasonable for attitudes toward risk to

bargain effectively. All the theories that they317 discuss assume that the individuals are rational, and the theories abstract from any differences in bargaining skill between individuals. We consider the possibility that the individuals are not perfectly informed, but we maintain throughout the assumption that each individual has well-defined preferences over all relevant outcomes, and, when he has to choose between several alternatives, chooses the alternative that yields a most preferred outcome

▲

A two-person bargaining situation involves two individuals who have the

opportunity, either to be competitors to each-other (win-lose)[von Neumann-

Morgenstern, 1928/1947zero sum two players game” Theory] or to make

coalitions, or even to create pure individual strategies, based on bargainers’

instant reflection behavior (win-win)[ Nash, 1950

It is assumed that each player’s preference ordering on the set of lotteries over possible agreements satisfies the assumptions of von Neumann and

Morgenstern. Consequently, for each Player i there is a function

RDaui }{: called a utility function, such that one lottery

is preferred to another if and only if the expected utility of the first exceeds that of the second. Such a utility function is unique only up to a positive affine

transformation. Precisely, if iu is a utility function that represents i and

iv is a utility function, then iv represents i i if and only

if .. ii auv for some real numbers

0......... awithanda Given the set of possible agreements,

the disagreement event, and utility functions for the players’ preferences, we can construct the set of all utility pairs that can be the outcome of bargaining.

This is the union of the set S of all

pairs ....))..(),.(( 21 Aaforauau and the point

))(),(( 21 DuDud Nash takes the pair dS, as the

primitive of the problem. (Note that the same set of utility pairs could result from many different combinations of agreement sets and preferences.) The objects of our subsequent inquiry are bargaining solutions. A bargaining solution associates with every bargaining situation in some class an agreement or the disagreement event. Thus, a bargaining solution does not specify an outcome for a single bargaining situation; rather, it is a function. Nash’s central

definition(formally): A bargaining problem is a pair dS, where

2RS is compact (i.e. closed and bounded) and convex, ,Sd

and there

exists 2,1..,...... ifordsthatsuchSs ii The set of

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papakonstantinidis Page 199

318 J. F. Nash (1950) “TWO-PERSON COOPERATIVE GAMES” -RAND Corporation RAND Journal of Economics 17: 176–188.

- P-172 31 AUGUST 1950

be part of a theory of bargaining.

/////////////////////////////////////////

The two-person bargaining problem is a problem of

understanding how two agents should cooperate when non-

cooperation leads to Pareto Efficient results. It is in essence

an equilibrium selection problem; many games have multiple

equilibria with varying payoffs for each player, forcing the

players to negotiate on which equilibrium to target. Solutions

to bargaining come in two flavors: an axiomatic approach

where desired properties of a solution are satisfied and a

strategic approach where the bargaining procedure is

modeled in detail as a sequential game. The bargaining

game or Nash bargaining game is a simple two-player game

used to model bargaining interactions. In the Nash

bargaining game, two players demand a portion of some

good (usually some amount of money). If the total amount

requested by the players is less than that available, both

players get their request. If their total request is greater than

that available, neither player gets their request. A Nash

bargaining solution is a Pareto Efficient solution to a Nash

bargaining game

A feasibility set F a closed convex subset of 2R the

elements of which are interpreted as agreements Set F is

convex because an agreement could take the form of a

correlated combination of other agreements

A disagreement, or threat, point:

2......1.........

..........,...),..,( 2121

playerandplayertopayoffsrespective

thearedanddwhereddd

The problem is nontrivial if agreements in F are better for

both parties than the disagreement

Feasibility Set: When binding contracts are allowed, any joint

action is playable, and the feasibility set consists of all

attainable payoffs better than the disagreement point. When

binding contracts are unavailable, the players can defect

(moral hazard), and the feasibility set is composed of

correlated equilibria, since these outcomes require no

all bargaining problems is denoted B A bargaining solution is a function

2: RBf that assigns to each bargaining problem

BdS , a unique element of S Of course, this definition

restricts a bargaining problem in a number of ways318. Preferences (assumptions). GENERAL: each player’s preference

Ordering i over }){*( DTX is complete, transitive, and reflexive.

A1. (Disagreement is the worst outcome):

For every DtxhaveweTXtx i ),..(....*),(

The remaining conditions concern the behavior of i on TX * First, we

require that among agreements reached in the same period, Player i prefers

larger values of ix and prefers to obtain any given share of the pie sooner

rather than later. A2 (Pie is desirable) For..any

iii yxifonlyandiftytx

haveweXyandXxTt

........)..,(),(

....,.......,..

A3 (Time is valuable)

For any stifsxtx

haceweXxandTsTt

i ..),..,(),(

........,

with strict

preference if 0ix Next we assume that Player si' preference ordering

is continuous. A4 (Continuity)

Let:

11 ),..(...)},{( nnnn syandtx be sequences of members of

TX * for which

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papakonstantinidis Page 200

315 Osborne, Martin (1994). A Course in Game Theory MIT Press

exogenous enforcement

Disagreement Point: The disagreement point d is the value

the players can expect to receive if negotiations break down

This point directly affects the bargaining solution, however,

so it stands to reason that each player should attempt to

choose his disagreement point in order to maximize his

bargaining position. Strategies are represented in the Nash

bargaining game by a pair (x, y), x and y are selected

from the interval [d, z], where d is the disagreement point

and z is the total amount of good. If x + y is equal to or

less than z, the first player receives x and the second y.

Otherwise both get d; often 0d There are many Nash

Equilibria in the Nash bargaining game. Any x and y such

that x + y = z is a Nash equilibrium. If either player

increases their demand, both players receive nothing. If

either reduces their demand they will receive less than if

they had demanded x or y. There is also a Nash

equilibrium where both players demand the entire good.

Here both players receive nothing, but neither player can

increase their return by unilaterally changing their strategy.

The Nash Bargaining solution315:

A current agreement, say ).( yx is on the table.

One of the players, say

…player 2 can raise an objection.

An objection is an alternative agreement, ),( yx

Probably, the alternative agreement is better for player

2 )..( yy and worse for player 1 )( xx .

Raising such an objection has some probability of

ending the negotiation. This probability p can be selected by

player 2 (e.g, by the amount of pressure he puts on

player 1 to agree).

The objection is effective only if

sureforyagreement

originaltheoverpchancea

withyagreementealternativthe

prefersplayereiyyp

.........

.......,.......

.............

..2..........2*

iofordering

NOTE

nallfor

syyx

whenever

sytxThen

yy

andxx

i

nin

i

nn

nn

.....

:

..........

).(),..(

)..,(),..(

,lim

....,lim

///////////////////////////////////////

J.F. Nash focused on payoff shares/utilities combination:

Bargain may result either in agreement or disagreement. Utility expresses the

constraint or the “fear factor” of disagreement for the negotiator who desires

negotiations to be led in agreement more than the other one. Who needs

more, negotiation leading to an agreement expects more utility, but –probably

there is a loss in terms of “shares”, due to lack of risk. On the contrary, who is

indifferent about “agreement” or expects less utility /per unit, has- to win in

“shares” under the dogma “the more risk, the more profit”

It is necessary to analyze the Nash “non-cooperative- instant reflection game”

/or a “win-win perception” as follow:

Non-co-operative game, is a game between TWO (2) players/ individuals who

have opposite interests

Each player makes his own choices, based on instant reflections’ rational

movements and his physical cleverness

The game/ bargain is defined by the result (pay-off) and not by players

expectations- It presupposes best choices by both players towards meeting

individual interests [“winning strategies”]

Players/ or negotiators do not regret, a posteriori, from their own decision

taken, based on personal choices, during the bargain. Each of the players knows

a priori that the other negotiator (or player) is as clever as he is.

During the game/ bargain, a “mutual respect” between the TWO (2) bargainers

to each other’s best choices’ is necessary

It is recognized that “The more decisive to break down the negotiation (= less

utility), the more satisfied (=better shares) – the more risk, the more profit

Social behavior is not recognized as an acceptable one in the bargain, thus

deriving unfair results: That means, “who needs the agreement as the result of

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papakonstantinidis Page 201

319 Papakonstantinidis L.A (2010) Applying The Win-Win-Win Papakonstantinidis Model In School Management Crisis The Greek Case Sociology On The Move I.S.A: Xvii W. G Gothenburg (2010)

Player 1 can then raise a counter-objection by claiming

that for him, xxp 1* This means that player 1

prefers to insist on the original agreement even if this might

blow up the negotiation; player 1 prefers the original

agreement x with a chance p over the alternative

agreement x for sure.

An agreement ),( yx is a Nash-bargaining-solution if, for

every objection raised by one of the players, there is a

counter-objection by the other player. It is an agreement

which is robust to objections

BARGAINING: INTERPRETATION

SUPPOSE:

The Structure of Bargaining: Two players bargain over

a “pie” of size 1

A usual (ie buying a house etc) agreement is a pair :

pieofsharesiPlayera

isxwhichinxx i

.......'........

.......,),,( 21

The set of possible agreements is:

}2,1..,0....1:),{( 21

2

21 iforxandxxRxxX i

The players’ preferences over X are diametrically opposed. Each player is concerned only about the share of the pie that he receives, and prefers to

receive more rather than less. That is, Player i

prefers

ii yxifonlyandifXytoXx ..............

Note that X is the set of agreements, not the set of utility pairs; In the case of bargaining over the division

of a dollar, we interpret ix as the amount that

Player i receives. In the case of negotiating the sale

price of an indivisible good, is the price the buyer pays

to the seller. In the model of wage negotiation, 1x

is the profit of the firm. The bargaining procedure is as

a bargain, has to loose in shares, by accepting any result”.

Information may be the “link” between knowledge creation and the bargaining

process. In particular, “Information” is a power factor in pure individuals

winning strategies.

The more information, the better winning strategy, the more profit. Each of

the players / negotiators, starting negotiations with the other, expects to gain

the maximum profit.

Interaction, based on instant reflection individual winning strategies, is the base

of the Nash Non Cooperative Games Theory A two (2) 2–person anticipation is

based on utilities.

According to Nash Theory, a unique solution exists that maximises the product

of the participants’ utilities. There is, therefore an interaction between

“utilities” and “strategies” In particular, “utility” expresses individual choices

based on individual necessities “Strategies” express choices + will in personal

level, taking into account the interaction factor (the other’s choices) Utility is

the subjective and strategy is the objective factor of the same anticipation.

Negotiation may lead either to “agreement” or disagreement Utility expresses

the “fear factor” constraint of disagreement for those who desire the

agreement, more than the other negotiators.

In conclusion, at any moment –according to the “N. C. G Theory”- there is only

one “equilibrium point” at which any individual–at any moment- makes the

best choices for himself, in relation with the other persons’ best choices319.

Bargaining Problem is mainly based on “Utility Theory”- a mathematical theory

of the Neo-classical School of Thought, able to satisfactory explain individual

expectations/ anticipations, of a possible outcome. Usually it is expressed in the

form of a mathematical function, f(u) = u 1/2

The discrete entity’s “diversification rate” from globalization/ or bargaining

rules, may be the crucial parameter which would define “Local Development”

as a social cohesion result at local level

GAMEBARGAIN

A Nash bargaining solution is a Pareto efficient solution to a Nash bargaining game. Bargaining is a basic activity associated with trade. Even when a market is large and the traders in it take as given the environment in which they operate, there is room for bargaining when a pair of specific agents is matched.

We analyze:

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papakonstantinidis Page 202

follows. The players can take actions only at times in

the (infinite) set ,...}2,1,0{T In each

period Tt one of the players, say i proposes

an agreement (a member of X ) , and the other

player )( j either accepts the offer (chooses Y )

or rejects it (chooses N ) If the offer is accepted,

then the bargaining ends, and the agreement is implemented. If the offer is rejected, then the play

passes to period ;1t in this period Player

)( j proposes an agreement, which Player i

may accept or reject. The game continues in this manner; whenever an offer is rejected, play passes to the next period, in which it is the rejecting player’s turn to propose an agreement. There is no limit on the number of periods. Once an offer has been rejected, it is void; the player who made the offer is free to propose any agreement in the future, and there is no restriction on what he may accept or reject. At all times, each player knows all his previous moves and all those of the other player.

Preferences (assumptions). GENERAL: each player’s preference

Ordering i over }){*( DTX is complete,

transitive, and reflexive. A1. (Disagreement is the worst outcome):

For every DtxhaveweTXtx i ),..(....*),(

The remaining conditions concern the behavior of i on

TX * First, we require that among agreements reached

in the same period, Player i prefers larger values of

ix and prefers to obtain any given share of the pie sooner

rather than later. A2 (Pie is desirable) For..any

iii yxifonlyandiftytx

haveweXyandXxTt

........)..,(),(

....,.......,..

A3 (Time is valuable)

Bargaining problem (Nash,1950))

Egalitarian bargaining Ehu Kalai

Arbitration game (Walter Bossert Guofu Tan (1995))

General cooperative games

Disagreement in Bargain (Crawfo

Gain functions instead of utility functions.(CAPRARO)

Bargaining and markets Osborne Martin J. and Rubinstein Ariel (1990)

“Bargaining and Markets” ACADEMIC PRESS, INC. Harcourt Brace Jovanovich,

Publishers..

…in order to find acceptable solution for the win-win-win

We start from the question, on which the Osborne Martin J. and Rubinstein

Ariel (1990) [as well as Nash] have avoided to response :

“what agreement is optimal for

the society at large?”

[ win-win-win Papakonstantinidis model (2002, August, SW) may, thus,

transform individual winning –instant reflection –strategies (the win-win Nash

Theory) in a NEW –three poles-equilibrium point, including the COMMUNITY

(Classroom, other people Environmental Protection, Value Systems, Ethic etc),

which is the “absolute cooperation” limit point in the bargain between TWO.

According to referees, win-win-win papakonstantinidis model is a revolution in

Social Science Theory: By introducing the third pole (Community- in this case,

Educational Organizations, parents, etc) in any bargain between two players in

a game (through the sensitization process), this model is of great contribution

to behavioral Sciences. It forms the foundation for “Social Trust” creation,

leading to Social Cohesion (at Local Level, or School Crisis Managing).

At the same time, the win-win-win papakonstantinidis model could be applied

in a number of other fields, especially, in the marketing field:

If a marketing aspect exists in this model, then we are not quiet far from a new

era of the win- win- win papakonstantinidis model in the marketing literature.

Conceptualization can trigger a new research thrust in the fields of promotion

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papakonstantinidis Page 203

320

Osborne Martin J. and Rubinstein Ariel (1990) (the same)

321 Osborne Martin J. and Rubinstein Ariel (1990) “Bargaining and Markets” ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers

For any

stifsxtx

haceweXxandTsTt

i ..),..,(),(

........,

with

strict preference if 0ix Next we assume that

Player si' preference ordering is continuous.

A4 (Continuity)

Let:

11 ),..(...)},{( nnnn syandtx be sequences

of members of

TX * for which

iofordering

NOTE

nallfor

syyx

whenever

sytxThen

yy

andxx

i

nin

i

nn

nn

.....

:

..........

).(),..(

)..,(),..(

,lim

....,lim

///////////////////////////////////////

NOTE:

The relationship between axiomatic bargaining solutions and equilibria of strategic models has first been studied by Nash (1953) in his pioneering paper. He considers a strategic model of bargaining that supports his axiomatic solution, namely, the Nash (1950) bargaining solution. His game consists of a single stage in which the two players simultaneously announce "demands" in terms of utilities. If these demands are compatible given the set of feasible utility vectors, then each player receives the amount he or she demanded; otherwise the disagreement event occurs. This game has many Nash equilibria. In order to refine the set of equilibria, Nash further considers a perturbed demand game and shows that if the disagreement outcome is excluded, the

management and pricing in the Marketing Science, where new definitions,

assumptions and hypotheses can examine better the marketing situations of

the bargaining processes among the seller – the buyer – the third pole (the

community).

It seems that there are some limitations in the conceptualization related to the

parameters that determine whether the seller is willing to bargain. Such

parameters are religion (for example: Jews had a limit on the allowable profit

margin) and regional customization [for example: in North America and Europe

bargaining is restricted to expensive or one-of-a-kind items (automobiles,

jewellery, art, real estate, trade sales of businesses) and informal sales settings

such as flea markets and garage sales. In other regions of the world, bargaining

may be the norm even for small commercial transactions].

In terms of empowering the win-win papakonstantinidis model

conceptualization (strongly related to the integrative/interest based

bargaining), it must be proven how the underlined conceptual model

integrated].

That’s the point of agreement, expressing “fear of breaking down the

agreement for “player” “A” and , at the same time, the risk for the “player” “B”

of breaking down the agreement. In a 2-person anticipation, each of the two (2)

bargainers may ask themselves one question, as a result of “good strategies”

[instant reflection thinking] in the bargain:

What should be the best for me, taking into account that the other person

(bargainer in a negotiation) should try for the best for himself –thus recognizing

that the other person may be as clever as I am?

According to the afore-mentioned analysis, paper contribution in the scientific

thought (2008) should be summarized in introducing “the third “WIN” for the

COMMUNITY (the third-part pole).

According to my suggestion320, COMMUNITY –the “C” factor- must participate

in any bargain by its “bargainers’ characteristics” (shares/utilities), thus adding

the THIRD “WIN” in any two bargainers’ win-win expectation between TWO

(the METRON analysis or the THREE POLES analysis), like in other fields e. g

philosophy, economy, creating an interactional flow.

By introducing the THIRD POLE in the bargain, the crucial bargainers’

QUESTION must be changed in:

All the theories that they321 discuss assume that the individuals are rational, and the theories abstract from any differences in bargaining skill between individuals. We consider the possibility that the individuals are not perfectly informed, but we maintain throughout the assumption that each individual has

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papakonstantinidis Page 204

316Selten , R. (1975) A reexamination of the perfectness concept for equilibrium points in extensive games. International Journal

of Game Theory 4:25-55.

Cohen, D. K & Ball, D. L.. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes and L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey Bass.

only equilibrium that is robust with respect to certain perturbations in the structure of the game yields the Nash bargaining solution. The refinement used by Nash bears some similarity to Selten's (1975) "trembling hand"316 perfection. Nash's demand game has been extended and modified in other contributions. For example, Binmore (1987) has proposed a bargaining game of alternating offers and shown that the Nash bargaining solution is the limit of the unique subgame- perfect equilibrium of his game as the probability of the negotiation process breaking down approaches zero. Carlsson (1991) has studied a variation of the perturbed demand game by assuming that the players make errors in choosing their actions in the bargaining process. He shows that the equilibrium outcome converges to the Nash solution when errors go to zero. Osborne and Rubinstein (1990, Ch. 4) have provided more detailed discussions on these extensions. The purpose of all these studies is to examine the strategic foundations of cooperative bargaining solutions. In most cases, justifications of the Nash solution are obtained. Another interesting cooperative bargaining solution is the egalitarian solution developed by Kalai (1977) and Myerson (1977). Without using Nash's axiom of independence of scale of utility they have provided alternative axioms under which interpersonal comparisons of utility must be possible. These axioms lead to the proportional solution and, in a symmetric bargaining situation, the egalitarian solution. One of the main axioms in this approach is a monotonicity axiom with respect to expansions of the feasible set. An alternative is a condition that involves a step-by-step negotiation process. This axiom imposes an invariance condition under decomposition of the bargaining process into several stages. As Kalai and Myerson pointed out, step-by-step negotiation has at least two advantages. First, it makes it easier to implement a solution since the negotiation can be broken up into several stages. Second, the players do not have incentives to change the order of the negotiations. This process is likely to be observed in actual negotiations.

well-defined preferences over all relevant outcomes, and, when he has to choose between several alternatives, chooses the alternative that yields a most preferred outcome

What should be the best for me, taking into account that the other person

(bargainer in a negotiation) should try for the best for himself –thus recognizing

that the other person may be as clever as I am and, at the same time, taking

into account that COMMUNITY, as the third or invisible part also participates by

the “bargainers’ characteristics” (shares/utilities)?

We adopt the five preferences assumptions (the general included) of Osborne

Martin J. and Rubinstein Ariel (1990) in their work “Bargaining and Markets” as

well as the whole concept especially in “Structure of Bargaining”:

1. Preferences (assumptions).

1. GENERAL: each player’s preference

Ordering i over }){*( DTX is complete, transitive, and reflexive.

2. (Disagreement is the worst outcome): For every DtxhaveweTXtx i ),..(....*),(

The remaining conditions concern the behavior of i on TX * First, we

require that among agreements reached in the same period, Player i prefers

larger values of ix and prefers to obtain any given share of the pie sooner

rather than later.

3. (Pie is desirable) For..any

iii yxifonlyandiftytx

haveweXyandXxTt

........)..,(),(

....,.......,..

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papakonstantinidis Page 205

322 Ehud Kalai (1977) Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons Econometrica

Vol. 45, No. 7 (Oct., 1977), pp. 1623-1630

4. (Time is valuable)

For any stifsxtx

haceweXxandTsTt

i ..),..,(),(

........,

with strict

preference if 0ix Next we assume that Player si' preference ordering

is continuous.

5. (Continuity)

Let:

11 ),..(...)},{( nnnn syandtx be sequences of members of

TX * for which

A bargaining situation is described by a set of alternative which are feasible to

n individuals when they do cooperate, and an alternative which comes about

when they do not cooperate. The paper addresses the question of which

cooperative outcome will be chosen. A Nash-type approach is used to prove

that, under plausible axioms describing the underlying bargaining process, the

individuals must be doing interpersonal comparison of utility322.

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papakonstantinidis Page 206

323 Capraro Valerio (2013) A Solution Concept For Games With Altruism And Cooperation Econometrica 45 (7) (1977), 1623-1630 326 Kalai Ehud (1985) "Monotonic Solutions to General Cooperative Games," Econometrica, 1985 (with D. Samet

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE EXISTING THEORY

9 BARGAINING

WITH

ALTRUISM

In my work I tried to find

1. A new equilibrium point in 3D

2. A prove of feasibility of a 3D absolute cooperation

among the 3-parties, i.e A-B and “the Community”

(the rest of population, “c”) with strategy profiles:

ccii xxx ,,

….then, player i obtains payoff )(xf i

In a first approach we focus on “family game” (household

“bargain)”, as a first application of “cooperation game” :

Within the household unit and in the mathematical study of

game theory scholars have defined two distinct types of

bargaining cooperative and non-cooperative In cooperative

bargaining models (also called collaborative decision

making), the outcomes of negotiations are more equally

beneficial to all members of the household, and have

therefore been considered a more “natural” means of

analyzing the family unit in comparison to non-cooperative

models. In non-cooperative bargaining models (also called

unitary decision making), personal interests motivate

individuals within the household rather than the desire to

work in a collaborative manner and maximize the benefit of

all household members As for the “economic bargain” and

generally “bargain”, within the capitalist system, the

cooperation between individuals is not casual and depends

on the payoffs of the game. These findings suggest that

humans have attitude to cooperation by nature and the

same person may act more or less cooperatively depending

on the particular payoffs. In other words, people do not act a

priori as single agents, but they forecast how the game

would be played if they formed coalitions and then they play

according to their best forecast. Valerio Carpalo323

formalized this idea and defined a new solution concept for

one-shot normal form games. He proved that this

cooperative equilibrium exists for all finite games and it

explains a number of different experimental findings, such as

Social : Recent literature – points

Kenneth Wilkinson (1970) : Focus on the endogenous local

Social capital-social equilibrium:

Friedman / Weaver – UCLA (1978) “Territory and Function”: “The base of an

autonomous local development may be a discrete value system, an ideology,

local people’s reaction to the dominant local principles (including local

communication code, customs, culture), creating thus the “social cohesion

environment” at local level.

Coleman (1988) “Social Capital describes the deep cooperation processes of

individuals, which minimize possible dilemma, coming from individuals’,

networks and common actions.

Putnam (2000) describes social capital as the basis of social schemes creation

(i. e networks)

In conclusion, an increasing number of recent literature in the local

development field, currently recognizes the existence of links among local

development process, social capital & social trust

“ The Political Entity” (Freedman-Weaver, UCLA, 1978, the “Selected Closed-

Spatial Discrete Entity” of the Intra-Scientific Vienna Centre (Stohr & Todtling

1980), The “S.H.I.E.L.D Model, Papakonstantinidis, 1997, Rome)

The “Tre Italy” Model, Bagnasco, 1987, The “parallel system” and “The

sensitized Community” (Papakonstantinidis, 1998 & 2002), The “political

Democracy (LSE, Fotopoulos, 1998), the “Grass Roots” Model in Latin America

(Luis Llambi, 2003) are few of theoretical L-D approaches pre-existed to the

suggested win-win-win

Equilibrium Theory in (infinitive) feasible space: the set of feasible allocations

belongs to an order interval..is always compact with in the compatible

topology326

▲

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papakonstantinidis Page 207

26.Bossert W.& Guofu (1995) “An arbitration game and the egalitarian bargaining solution” 327Journal of Economic Literature Classification (Numbers: C72, C78)

328 Kalai Ehud (1975) "Other Solutions to Nash's Bargaining Problems," Econometrica, 1975 (with M. Smorodinsky 329 Kalai Ehud (2004) “Large Robust Games,” Econometrica, 2004 330

Kalai Ehud (1988) "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, 1988 (with W.

Stanford) 331

Kalai Ehud (1993) "Rational Learning Leads to Nash Equilibrium," Econometrica, 1993 ( with E. Lehrer)

(1) the rate of cooperation in the Prisoner's dilemma

depends on the cost-benefit ratio; (2) the rate of cooperation

in the Traveler's dilemma depends on the bonus/penalty; (3)

the rate of cooperation in the Public Goods game depends on

the pro-capite marginal return and on the numbers of

players; (4) the rate of cooperation in the Bertrand

competition depends on the number of players; (5) players

tend to be fair in the bargaining problem; (6) players tend to

be fair in the Ultimatum game; (7) players tend to be altruist

in the Dictator game; (8) offers in the Ultimatum game are

larger than offers in the Dictator game. Valerio Capraro

suggested the substitution of the “utility theory” by the

“gains theory” due to failure to predict human behavior in

several strategic situations: “the use of utility functions and

the use of solution concepts that do not take into account

human attitude to cooperation”. While the former problem

could be theoretically overcome replacing utility functions by

gain functions and applying cumulative prospect theory, the

second problem needs a different analysis of the structure of

a game. He founded this new analysis on a seemingly

reasonable principle of cooperation. Players try to forecast

how the game would be played if they formed coalitions and

then they play according to their best forecast. To make this

idea formal, it has required some effort. Capraro observed

that passing from utility functions to gain functions implies

that he took into account new phenomena, such as

altruism and perception of gains…. He has formalized these

phenomena defining the so-called games in explicit form.

The main idea on his perception was to formalize the

principle of cooperation and define the cooperative

equilibrium for games in explicit form without using altruism

parameters and cumulative prospect theory. The reason of

this choice is that altruism and cumulative prospect theory

play an active role only on a limited class of games. It has

been shown that the cooperative equilibrium without

altruism and cumulative prospect theory already performs

well in a number of relevant games. Besides, cumulative

prospect theory starts playing an active role in bargain in

History in short on the social bargaining form :

Altruism bargain

In cooperative game theory327, the Kalai-Smorodinsky solution reopened the

study of bargaining by showing that the long unchallenged Nash solution is not

unique. He later axiomatized the Egalitarian solution328 to bargaining problems

and, with D. Samet329, formulated its extension to general (NTU) cooperative

games, unifying it with the Shapley (TU) Value. In non cooperative game theory,

the Kalai-Lehrer330 model of rational learning showed that rational players with

truth-compatible beliefs eventually learn to play Nash equilibria of repeated

games. In particular, in Bayesian equilibria of repeated games all relevant

private information eventually becomes common knowledge. Kalai's work on

large games331 showed that the equilibria of Bayesian games with many players

are structurally robust, thus large games escape major pitfalls in game-theoretic

modeling. Kalai is also known for seminal collaborative research on flow

games and totally balanced games; strategic complexity and its implications in

economics and political systems; arbitration, also, the strategic delegation and

commitments; extensions of Arrow’s Impossibility Theorem (one of the

incobabilities which the “win-win-win concept is based on

SOLUTION CONCEPT FOR GAMES WITH ALTRUISM AND COOPERATION

The exact computation of the cooperative equilibrium is hard for several

reasons. First because it goes through the computation of the equilibria in

beliefs of several18 (sub) games. These equilibria are computationally hard to

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papakonstantinidis Page 208

332 Quantal response equilibrium (QRE) is a solution concept in game theory. it provides an equilibrium notion with bounded

rationality QRE is not an equilibrium refinement, and it can give significantly different results from Nash Equilibrium QRE is only

defined for games with discrete strategies, although there are continuous-strategy analogues. In a quantal response

equilibrium, players are assumed to make errors in choosing which pure strategy to play. The probability of any particular

strategy being chosen is positively related to the payoff from that strategy. In other words, very costly errors are unlikely. The

equilibrium arises from the realization of beliefs. A player's payoffs are computed based on beliefs about other players'

probability distribution over strategies. In equilibrium, a player's beliefs are correct. 333 Kalai, Ehud (1977). "Proportional solutions to bargaining situations: Inter-temporal utility comparisons" Econometrica 45 (7): 1623–1630 334 Rawls John (1971) A theory of Justice Cambridge, Massachusetts: Belknap Press of Harvard University Press, 1971.

order to be applied to every game in explicit form and using

cumulative prospect theory.

CARPARO used this arithmetical; example” Consider the

selfish coalition structure })2{},1({ps The value for

the second player is again 30)(2 psv , whereas this

time one gets 15)(1 psv Indeed, this is one of the

cases where the natural symmetry of the game implies that

we can restrict the set )},2({ psMf taking its bary-

center. In other words, when player 2 plays according

to ps she is indifferent among her choices and so she

plays uniformly. Player 1’s best reply to player 2’s uniform

measure is the uniform measure, that gives payoff 15.

Since this is a Nash equilibrium, there are no possible

deviations and so 15)(2 psv So in this case, the

unique cooperative equilibrium is )0,0( In other words,

player 2 favors player 1 playing 0 and player 1 knows that

player 2 is going to favor her and so she plays 0 as well. This

seems a very natural solution but: Do humans really

play )0,0( ? In his work “A SOLUTION CONCEPT FOR

GAMES WITH ALTRUISM AND COOPERATION” he tried to

simulate this game with colleagues and friends and

something interesting apparently came out. One friend,

asked to play the game in the role of player 2, said: “It

depends. If player 1 is very rich, I would play 30 for sure!”.

The most common question we were asked after explaining

find Second, because it uses cumulative prospect theory that is

computationally harder than expected utility theory On one hand, the method

that we have proposed is perfectly algorithmic and therefore it might be helpful

to write a computer program to compute the cooperative equilibria and make

easier the phase of test them on easy real-life situations. On the other hand, it

would be important to investigate some computationally easier variant. Of

course, Quantal -Response-Equilibrium QRE332 can be seen as a

computationally easier variant, but this theory has the serious issue that it

would not be predictive, in the sense that one has to conduct experiments to

estimate the error parameter. One could try to avoid this problem using the

level-k theory (i.e., only bounded rationality). (6) Iterated deletion of strategies

using altruism functions in Section 8 was certainly quite sketchy and it is likely

that future researches will suggest a different procedure. In particular, the

definition of unplayable strategies of the second type for player i requires that

only one particular player j receives a large loss. It is possible that this condition

is not sufficient to convince player i to renounce to her better strategy, in case

when the players in P \ {i, j} receives a large gain. (7) We have defined altruism

functions operationally, meaning that one could theoretically compute them by

conducting an experiment on the generalized dictator game. It would be

important to find an operational way to define the fairness functions.

Egalitarian bargaining solution The egalitarian bargaining solution, introduced

by Ehud Kalai, is a third solution which drops the condition of scale invariance

while including both the axiom of Independence of irrelevant alternatives and

the axiom of monotonicity. It is the solution which attempts to grant equal gain

to both parties. In other words, it is the point which maximizes the minimum

payoff among players. Kalai333 notes that this solution is closely related to the

ideas of John Rawls334

Some philosophers and economists have recently used the Nash bargaining

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papakonstantinidis Page 209

335 Alexander, Jason McKenzie (2000). "Evolutionary Explanations of Distributive Justice" Philosophy of Science 67 (3): 490–

516. AND Alexander, Jason; Skyrms, Brian (1999). "Bargaining with Neighbors: Is Justice Contagious". Journal of

Philosophy 96 (11): 588–598. AND Binmore, Kenneth (1998). Game Theory and the Social Contract Volume 2: Just Playing.

Cambridge: MIT Press. AND Binmore, Kenneth (2005). Natural Justice. New York: Oxford University Press. 336 Walter Bossert and Guofu Tan (1995) An arbitration game and the egalitarian bargaining solution* Soc Choice Welfare

(1995) 12:29-41

the game was: “Do I know the other player?”. After asking to

imagine an anonymous situation, the most common answer

(nine out of ten) was: “Why should I hurt a person that I do

not know? I would play 0.”. One person said: “I don’t care! I

would pick a number randomly”. Of course, these cannot be

considered as experimental data, but we believe that they

represent however a light evidence that badness parameters

do exist. It is not yet clear to the author how to manage them

from a general point of view and we will postpone the

theorization to a new 3D equilibrium (win-win-win)

hopefully helped by more experimental data.

A SOLUTION CONCEPT FOR GAMES WITH ALTRUISM AND

COOPERATION

“Bargaining” is a pervasive phenomenon in modern econo-

mies, ranging from labor negotiations to trade agreements to

strategic arms limitation talks. One need only consider these

examples in the light of past experience to realize that the

potential welfare gains from improving the efficiency of

bargaining outcomes are enormous, perhaps even greater

than those that would result from a better understanding of

the effects of macroeconomic policy. Yet the problem of

designing environments to yield improved bargaining

outcomes has been all but ignored by economists.

A major part of this design problem is ensuring that

impasses are avoided as often as possible. Because such

disagreements, whether they take the form of strikes, trade

restrictions, or arms races, tend to be very costly, reducing

their likelihood is of great welfare importance. But, before

this aspect of the problem can even be approached, a theory

that relates the likelihood of disagreement to the bargaining

environment is needed. Such a theory would serve an

important purpose in guiding attempts to determine this

relationship empirically or experimentally, even if it did not

yield strong theoretical conclusions.

game to explain the emergence of human attitudes toward distributive justice

distributive justice335 These authors primarily use evolutionary game theory to

explain how individuals come to believe that proposing a 50–50 split is the

only just solution to the Nash bargaining game

CAPRARO VALERIO (2013) A SOLUTION CONCEPT FOR GAMES WITH

ALTRUISM AND COOPERATION CORNELL UNIVERSITY Computer Science >

Computer Science and Game Theory

An arbitration game

336:

Definition:

the hearing and determining of a dispute or thes

ettling of differences between parties by a pers

onor persons chosen or agreed to by them

(Dictionary. com)

Arbitration:

a form of alternative dispute resolution (is a

technique for the resolution of disputes outside

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papakonstantinidis Page 210

324 Crawford Visent P.(1982) A Theory of Disagreement in Bargaining Econometrica, Volume 50, Issue 3 (May, 1982), 607-638. 25 Sullivan Arthur Steven M. Sheffrin (2003).Economics: Principles in Action” Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. p. 324. 325 Schelling, Thomas C. (1980). The Strategy of Conflict Harvard University Press p. 309 337

338

Almost all microeconomic and game-theoretic models of

bargaining beg the question of what determines the

probability of disagreement by a s s u m in g that an efficient

settlement is always reached. This is probably due to the

simple and elegant theoretical results often available under

the efficiency assumption and to the common belief that

inefficient outcomes are inconsistent with rational behavior

by well-informed bargainers. But plainly, any theory of

bargaining that assumes away the possibility of disagreement

must fail to capture an aspect of bargaining that is of central

importance in the design problem mentioned above.

Prof Crawford Visent P.(1982)324 proposed a simple

theory that explains the probability of disagreement in

bargaining, and, it is hoped, will therefore prove more useful

in studies of the design problem than existing theories. The

theory develops Schelling's325 view of the bargaining process

as a struggle between bargainers to commit themselves to—

that is, to convince their opponents that they will not retreat

from —advantageous bargaining positions. The potential

benefits of commitment are clear, since once one's opponent

is convinced his best strategy is to yield if he can. Mainly, he

proposes a simple theory to explain bargaining impasses,

which is based on Schelling's view of the bargaining process

as a struggle between bargainers to commit themselves to

favorable bargaining positions. Because bargaining impasses

are generally Pare to-inefficient, anything involving a positive

probability of impasse is Pa re to-inefficient as well. It is

demonstrated that in spite of this avoidable inefficiency,

when successful commitment is uncertain and irreversible it

can still be rational for individuals to attempt commitment

and thereby risk an impasse; in a leading special case, the

model reduces to a Prisoner's Dilemma game, in which only

strategic-dominance arguments are needed to establish this

conclusion. Further, making commitment more difficult, or

changing the costs of disagreement in a way that makes

available a wider range of settlements that are better for

both bargainers than disagreement, need not always lower

the probability of impasse, in spite of the conventional

wisdom to the contrary It is shown that if the outcome of the commitment process is both uncertain and irreversible, it can be rational for bargainers to take actions that imply a positive probability of disagreement, an outcome ex ante inferior for both to outcomes feasible through negotiation. The theory, which determines the probability or frequency of impasse endogenously, permits an evaluation of the assumption, common in the industrial relations and law and economics literature, that enlarging the set of feasible settlements that are at least as good for both bargainers as disagreement—commonly called the c o n t r a c t z o n e in this literature—makes a negotiated settlement more likely. It turns out that this need not be true: in quite "well-behaved" bargaining

the courts ADR),

The parties to a dispute refer it

to arbitration by one or more persons (the

"arbitrators", "arbiters" or "arbitral

tribunal"), and agree to be bound by the

arbitration decision (the "award")337. A third

party reviews the evidence in the case and

imposes a decision that is legally binding on

both sides and enforceable in the courts

mmmmmmmm338

(194)CAPRARO VALERIO (2013) A SOLUTION CONCEPT FOR GAMES WITH ALTRUISM AND COOPERATION CORNELL UNIVERSITY Computer Science > Computer Science and Game Theory Update Sept. 9th, 2013. Parts of this paper

(concerning social dilemmas) have been published in [Ca13] and [CVPJ]. This Working Paper is an attempt to extend the theory developed in those published

paper to all normal form games.

A t w o - p e r s o n b a r g a in in g p r o b le m is a pair

2..),..,( RSwheredS is the feasible set of utility

vectors and

2Rd is the disagreement point.

The problem ),( dS is c o m p r e h e n s iv e ( s t r i c t ly c o m p r e h e n s iv e )

if and only if, for all

yzthatsuchSzand

SydyxandSxRyx

.........(

.........., 2

dxwithSxiii

nsiveiscomprehedSii

convexandcompactisSi

thatsuch

dSproblemsBARGAININGofsettheisR

..,...)..(

,),,)..((

........)...(

,,

).....(............

The set of strictly comprehensive bargaining problems is denoted byR ,

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papakonstantinidis Page 211

situations, enlarging the contract zone by changing the disagreement outcome may actually increase the probability of an impasse.3 It is also shown that attempts (like the common requirement in labor law to bargain "in good faith") to make commitment more difficult, with the goal of reducing the probability of impasse, may have perverse effects

that is,R the subset of

R that is obtained if comprehensiveness is

strengthened to strict comprehensiveness in condition ( i i ) above.

The id e a l p o in t of a bargaining problem

.2,1...,max).(

....)..,(.),(

idxSxxdSa

bydefinedisdSaRdS

ii

A b a r g a in in g s o lu t io n is a function

RdSallfor

SdSFthatsuchRRF

),(..

..),(,.....: 2

The egalitarian solution

xythatsuchSynot

anddxdxthatsuchSx

POINTuniquethebedSERdSallfor

letingbydefinedisKalaiE

..............

............

........),(,),....

..,..)..1977,..(

2211

▲

A generalization of the egalitarian solution is the class of proportional (or weighted egalitarian) solution:

),(,,),..

)1977,)...(.......(

dSERdSFor

KalaiRawithE

a

a

is defined as the unique point Sx such that

xythatsuchSynot

anddxadx

...........

..)..( 2211

Clearly, 1a leads to the egalitarian solution.

According to the above 2-persons game, it should be possible to looking for

another ideal point .2,1...,max).(

....)..,(.),(

idxSxxdSa

bydefinedisdSaRdS

ii

as the above, resulting from the egalitarian solution of bargaining problem

Concluding:

the egalitarian bargaining solution has some strategic justification,

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papakonstantinidis Page 212

but rather, that it is consistent with the non-cooperative outcome of a simple arbitration procedure. This result is not trivial.

there exist multiple equilibria of the arbitration game which may not yield the egalitarian solution.

If the criterion for the penalty rule is not formulated in terms of the gains over the redefined disagreement points, the egalitarian solution may not be an equilibrium outcome of the arbitration game.

Of course, there may exist other simple arbitration procedures which lead to the egalitarian solution.

////////////////////12/2

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”**

POSSIBLE CONTRIBUTION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY *

10.

The suggested

win-win-win

papakonstantin

Formal math type of the suggested model

).,..,().,.,.(:,, *****

cciiicciiicii xxxfxxxfSSxi

▲

[ win-win-win papakonstantinidis model (2002, August, SW) may, thus,

transform individual winning –instant reflection –strategies (the win-win Nash

Theory) in a NEW –three poles-equilibrium point, including the COMMUNITY

(Classroom, other people Environmental Protection, Value Systems, Ethic etc),

which is the “absolute cooperation” limit point in the bargain between TWO.

max commBA UUU

A win-win-win bargaining theory is an exploration of the relation between the outcome of bargaining and the characteristics of the situation, including the

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papakonstantinidis Page 213

idis equilibrium

0**

),().........,(.).........,(

max**max\

CBA

CCBBAA

CBACBA

UUUdx

PsfUPsfUPsfU

UUUUUU

optimumPareto

xf

xf

..

0)(

max)(

“win-win-win papakonstantinidis” utility maximization:

0])100([max...)100( nn yxxyyxxyfirst derivate:

0)100()100( nxyyxxyxy

0)100...( yxif

nyxxy

yxnxyyxyx )1(100(0)100)((

0...

xy

yxconsider

payoffsected

COMMUNITYCtheyxbut

..exp

...(..%..)100..(

mequilibriu

suggestedtheinpayoffsCommunityxthen .........%..........1

)( *

▲

n= the number of independent trials or the number of

possible equilibria (trinomial distribution)

Repeat an experiment n independent times with each

experiment ending in one of three mutually exclusive and

exhaustive ways (“win”, “win-win”, and “win-win-win”(with

the community as the 3rd part).the type of trinomial

distribution is

………………………………………………………………………………………

TRINOMIAL DISTRIBUTION

Community profit

Influences:

Bargaining problem (Nash,1950))

Egalitarian bargaining Ehu Kalai

Arbitration game (Walter Bossert Guofu Tan (1995))

General cooperative games

Disagreement in Bargain (Crawfo

Gain functions instead of utility functions.(CAPRARO)

GAMEBARGAIN

A Nash bargaining solution is a Pareto efficient solution to a Nash bargaining game.

According to referees, win-win-win papakonstantinidis model is a revolution in

Social Science Theory: By introducing the third pole (Community- in this case,

Educational Organizations, parents, etc) in any bargain between two players in

a game (through the sensitization process), this model is of great contribution

to behavioral Sciences. It forms the foundation for “Social Trust” creation,

leading to Social Cohesion (at Local Level, or School Crisis Managing).

At the same time, the win-win-win papakonstantinidis model could be applied

in a number of other fields, especially, in the marketing field:

If a marketing aspect exists in this model, then we are not quiet far from a new

era of the win- win- win papakonstantinidis model in the marketing literature.

Conceptualization can trigger a new research thrust in the fields of promotion

management and pricing in the Marketing Science, where new definitions,

assumptions and hypotheses can examine better the marketing situations of

the bargaining processes among the seller – the buyer – the third pole (the

community).

It seems that there are some limitations in the conceptualization related to the

parameters that determine whether the seller is willing to bargain. Such

parameters are religion (for example: Jews had a limit on the allowable profit

margin) and regional customization [for example: in North America and Europe

bargaining is restricted to expensive or one-of-a-kind items (automobiles,

jewellery, art, real estate, trade sales of businesses) and informal sales settings

such as flea markets and garage sales. In other regions of the world, bargaining

may be the norm even for small commercial transactions].

In terms of empowering the win-win papakonstantinidis model

conceptualization (strongly related to the integrative/interest based

bargaining), it must be proven how the underlined conceptual model

integrated].

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papakonstantinidis Page 214

341Penn State Eberly College of Sciences STAT 414/415 Home » Lesson 17: Distributions of Two Discrete Random Variables

nyx

ny

nx

ppppyxnyx

nyYxXPyxf yxnyx

,..1,..0

....1,..0

)1()!(!!

!),(),( 2121

or

n

i

x

in

i i

nni

x

NxXxXP

11

11

!

!),......(

………………………………………………………..

λ = the buffering factor of the Community Share, thus of the

social welfare, 30

for positionideal.....3

▲ FINAL “WIN-WIN-WIN” PRESENTATION:

Where

G** is increasing behavior reaction

1. N is the set of players.

2. Ω* is the set of the states of the “Intermediate

Community”, depended on local people bargaining intra-

community behavior

3. Ai is the set of actions for player i

4. Ti is the types of player i, decided by the function. So for

each state of the nature, the game will have different types

of players. The outcome of the players is what determines its

type. Players with the same outcome belong to the same

type.

5. ti defines the available actions for player i of some type in

Ti.

6. RAui *: is the payoff function for player I

7. φ The sensitization factor

(Papakonstantinidis IJRCM, 2011)

▲

BINOMIAL DISTRIBUTION

341

knppk

nkXP k

)1()(

)!(!

!

knk

n

k

n

The binomial distribution describes the behavior of a count variable X if the following conditions apply:

1: The number of observations n is fixed. 2: Each observation is independent. 3: Each observation represents one of two outcomes ("success" or "failure"). 4: The probability of "success" p is the same for each outcome.

▲

TRINOMIAL DISTRIBUTION

A binomial random variable models the number of successes in n trials, where

the trials are independent and the only options on each trial are success and

failure. A generalization of this called a multinomial distribution can be

obtained by allowing more than two possibilities on each trial. When there are

three possibilities on each trial, call them "perfect", "acceptable", and "failing",

the result is a trinomial random variable.

Letting X be the number of perfects and Y the number of acceptables in n

trials, the image is a rendering of the joint probability mass function of X and

Y

The cuboid whose lower-left corner is at ),( yx has height equal to the

NiCptTuANG iiiiii ,,,,,*,,**

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papakonstantinidis Page 215

339 Valerio Capraro, Maria Polukarov, Matteo Venanzi, Nicholas R. Jennings (2015) Cooperative Equilibrium beyond Social

Dilemmas: Pareto Solvable Games Computer Science > Computer Science and Game Theory Submitted on 25 Sep 2015) 340 The same 342 Boucher Chris, 2015 Mathematical Association of America (MAA)- the celebrating issue : A century of advancing mathematics edition: Wolfram Demonstrations Project 343 Penn State Eberly College of Sciences STAT 414/415 Home » Lesson 17: Distributions of Two Discrete Random Variables

"cooperative equilibrium"

Win-win-win papakonstantinidis model is mainly based on

Cooperative equilibrium as it has been given by Prof Valerio

Capraro and alle339

A recently introduced concept of "cooperative equilibrium",

based on the assumption that players have a natural attitude

to cooperation, has been proven a powerful tool in

predicting human behaviour in social dilemmas. In this paper,

we extend this idea to more general game models, termed

"Pareto solvable" games, which in particular include the Nash

Bargaining Problem and the Ultimatum Game. Valerio

Capraro and alle showed that games in this class possess a

unique pure cooperative equilibrium. Furthermore, for the

Ultimatum Game, this notion appears to be strongly

correlated with a suitably defined variant of the Dictator

Game. They supported this observation with the results of a

behavioral experiment conducted using Amazon Mechanical

Turk, which demonstrates that our approach allows for

making statistically precise predictions of average behaviour

in such settings340.

probability 342of trialsninsacceptableyandperfectsx .......,.....,

Note that if 1p is the probability of a trial being perfect and 2p the

probability of a trial being acceptable, then the probability of failure on the trial

is 211 pp

The binomial distribution describes the behavior of a discrete random

variable X, where X is the number of successes in n tries, when each try results

in one of only two possible outcomes.

What happens if there aren't two, but rather three, possible outcomes?

That's what we'll explore here on this page, ending up not with the binomial

distribution, but rather the trinomial distribution

nyx

ny

nx

ppppyxnyx

nyYxXPyxf yxnyx

,..1,..0

....1,..0

)1()!(!!

!),(),( 2121 see at column

2

Example343

Suppose n = 20 students are selected at random:

EXAMPLE:

Let A be the event that a randomly selected student went to the football game on

Saturday. Also, let P (A) = 0.20 = p1, say.

Let B be the event that a randomly selected student watched the football game on

TV on Saturday. Let P(B) = 0.50 = p2, say.

Let C be the event that a randomly selected student completely ignored the

football game on Saturday. Let P(C) = 0.30 = 1−p1− p2.

One possible outcome, then, of selecting the 20 students at random is:

BBCABBAACABBBCCBCBCB

Definition. Suppose we repeat an experiment n independent times with each experiment ending in one of three mutually exclusive and exhaustive ways (“win”, “win-win” and “win-win-win”). If we let X denote the number of times the experiment results “win” , let Y denote the number of times the experiment results “win-win” and let Z denote the number of times the experiment results in a “win-win-win” result/situation , then the joint probability mass function of X and Y is: (see at the previous column)

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papakonstantinidis Page 216

Cuboid: a possible domain for win-win-win equilibrium

SPECIAL CASE: Geo Routes Social Contribution

The ‘Win-Win-Win’ model

Geo Routes are under an increasing behavioral reaction (G + dynamic) with every voyager (iеN) part of a group (N) of the international tourism society (Ω), whose participation is subject to the utility probabilities experience (u), the service level provided (τ), the communication strategy (A) and the benefits to the local communities (ρC). The Geo Routes mission statement is related to the level of understanding, the sensitization process and the willingness to collaborate between every voyager and the society (φΤ).

NiCTuANG ,,,,,

The “win-win-win papakonstantinidis model” came following to Nash’ equilibrium point ‘win-win’ bargaining theory; under the Bayesian analysis refinement. Prof. Papakonstantinidis has introduced a 3rd pillar as extension of socio-responsibility ‘win’ dimension, which confirms that no economic development is achieved, while society is been disregarded. The “win-win-win papakonstantinidis model” has been accepted by International Journals as well as by the International Sociological Association -I.S,.A.

*Prof. L. Papakonstantinidis model (2009) ©

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papakonstantinidis Page 217

TWO-PERSON COOPERATIVE GAMES

J. F. Nash (1950) “TWO-PERSON COOPERATIVE GAMES” -RAND Corporation RAND Journal of Economics 17: 176–188. - P-172 31 AUGUST 1950

TABLE: Knowledge Creation and Transfer- Types of Behavior

Papakonstantinidis, 2003

Type of Knowledge-1 Type of Knowledge-2 Synthesis Resulted Behavior

tacit tacit Sympathetic Socialization

tacit codified Conceptual Externalization

codified tacit Procedural Internalization

codified codified Systemic Networking

sympathetic systemic Conceptual Sensitization

systemic systemic Procedural Strategic

Figure 1 shows the set in the point N, the

point Ρ where dxd2g is a maximum, and the

hyperbola AB which touches Λ at the point Q, where

UiU2 is a maximum over π (remember uio and U20 are

now zero)

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papakonstantinidis Page 218

TABLE: Five steps towards Local development

Source: Arnstein (1969)

“win-win-win papakonstantinidis model:

A ifmequilibriuuniqueahasCBAbetweengamefS ...,,......,.,..)..,(

).,..,().,.,.(:,, *****

cciiicciiicii xxxfxxxfSSxi

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE EXISTING

THEORY

partnership

Involvement

Participation

sensitization

Information

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papakonstantinidis Page 219

11

The concept

of force

The idea of a force is introduced to quantify the tendency of objects to

move towards their preferred configuration. If objects accelerate very

quickly towards their preferred configuration, then we say that there’s

a big force acting on them. If they don’t move (or move at constant

velocity), then there is no force. We can’t see a force; we can only

deduce its existence by observing its effect. Specifically, forces are

defined through Newton’s laws of motion 0. A `particle’ is a small

mass at some position in space.

1. When the sum of the forces acting on a particle is zero, its velocity is

constant;

2. The sum of forces acting on a particle of constant mass is equal to

the product of the mass of the particle and its acceleration;

3. The forces exerted by two particles on each other are equal in

magnitude and opposite in direction. The second law provides the

definition of a force – if a mass m has acceleration a, the force F acting

on it is F=ma,

see bellow (R. Nave)

One of the foundation concepts of physics, a force may be thought of as any influence which tends to change the motion of an object. Our present understanding is that there are four fundamental forces in the universe, the Gravity Force the nuclear weak force, the electromagnetic force, and the nuclear strong force in ascending order of strength. In mechanics, forces are seen as the causes of linear motion, whereas the causes of rotational motion are called torques. The action of forces in causing motion is described by Newton Laws under ordinary conditions, although there are notable exceptions. Forces are inherently vector quantities, requiring vector addition to combine them. The SI unit for force is the Newton, which is defined by Newton = kg m/s2 as may be seen from Newton’s second law

Newton's Second Law

Newton's Second Law or Newton's second law of motion is probably the most famous of all of Newton's three laws of motion. Newton's second law of motion introduces one of the most famous mathematical or physics formula concerning mass, force and motion. So, what is this Newton's Second Law of Motion?

Formula for Newton's Second Law of Motion

We can imagine the bargain between 3 as the above scheme. Each of the three negotiators (A-B and “C”-community) "pulls" the

negotiation to his/r side.

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Newton's 2nd law of motion states that if an object of mass m which

is measured in kilograms is acted on by a force of

magnitude F measured in Newtons, the magnitude of the

acceleration a (measured in meters per second squared) can be found

according to the physics formula F equals m times a or Force is Mass

times Acceleration.

Unit of force

Force is measured in Newton which is the standard unit of mechanical force. The unit Newton is often written as capital N. What does one Newton of force mean? One Newton (N) of force is the force that it takes to make a mass of 1 kilogram accelerate at a rate of 1 meter per second squared. Since Force is mass multiplied by acceleration, the Newton is really kilogram, meter per second squared. But, all you really need to remember is that Force is measured in Newton.

That's it. Newton's 2nd Law of Motion is given by F equals m times a or mass times acceleration measured in Newton344.

344 PHYSIC FORMULAS

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PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE EXISTING

THEORY

CALCULUS –

INTEGRAL

12

The fundamental theorem of calculus is a theorem that links the

concept of the derivative of a function with the concept of the

function's integral

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE EXISTING

THEORY

13 cxFfxdx )(

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DIFFERENTIAL

GEOMETRY

DEFINITE INTEGRAL

)()()()( aFbFxFdxxf

b

a

b

a

PRESENTATION

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CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE EXISTING

THEORY

14 Differential

geometry of curves

and surfaces

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE EXISTING

THEORY

15 Parameterization

Fundamental Forms

of General

Parametric Surface

The general form

)),(),,(),,(( vuzvuyvuxr

A parametric surface is a surface in the Euclidean space

which is defined by a parametric

equation with two parameters Parametric representation is a

very general way to specify a surface, although implicit equations

are even more general.

The curvature and arc length of curves on the surface area,

differential geometric invariants such as the first and second

fundamental forms, Gaussian, mean, and principal curvatures can

all be computed from a given parameterization.

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In differential geometry the first fundamental form is the inner

product i on the tangent space of a surface in three-

dimensional Euclidean Space which is induced canonically form of

the dot product of R3.

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE

EXISTING THEORY

16

CURVATURE Curvature-

convexity

Normal Curvature

Curvature in 3D

Curvature: the shape of something curve

o (mathematics) The extent to which a subspace is curved within

a metric space.

o The extent to which a Riemannian manifold is intrinsically

curved.

Convexity: the state of being convex

o a convex line or surface

o a measure of the curvature in the relationship between the

prices and yields of bonds

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Gaussian

Curvature

of Surfaces

Vectors

Eigenvector or

characteristic

vector

Mathematical

representation of

a force

Principal

Curvatures

Tangent plane

Smooth Surface

Fundamental Forms in determining the metric properties of a surface

Principal curvatures of the surface S at the point p . Lines of curvature on a surface.

Definition of Gaussian curvature and mean curvature. Definition of umbilical points on a surface.

Theorem. If all points of a connected surface S are umbilical points, then S is contained in a sphere or a plane

The vectors

vu

vu

rr

rr

are the two unit normals (“inward and

outward”) to the surface at (u, v).

The tangent plane (or tangent space) of a surface at the point a is the vector space spanned by

)(),..( arar vu

Note that this space is independent of parameterization. One should think of the origin of the vector space as the point a. The first fundamental form-1: A smooth curve lying in the surface is a map

))(),(( tvtut

with derivatives of all orders such that

))(),(()( tvturt

is a parametrized curve in R3.

The second fundamental form-2 of a surface is the expression

nrvvnNruvMnruuL

were

NdvMdudvLdu

"**..*

2 22

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE

EXISTING THEORY

17 DOMAIN

of

win-win-win

To find the domain of the (new) "win-win-win papakonstantinidis" utility

function 1),..,,( zyxzyxu x,y,z preferences

According to the “P conjecture”

KEY OBJECTIVE is to define the domain of the utility function

f (u) which is maximized (for both (A-B) bargainers , and for

the community (C) as a whole (the 2 bargainers included) to

the point of the 3D equilibrium (win-win-win) The

equilibrium is defined in the 3R Euclidean space :

the absolute 3D equilibrium, is achieved in the SPHERE

because everyone of its points is an umbilical point (win-

win-win)

DEFINITION: A point p on a surface S where the two principal

curvatures are equal, 21 kk is called an umbilical point.

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A sphere is the graph of an equation of the form x2 + y2 + z2 = p2 for some

real number p. The radius of the sphere is p (see the figure

below). Ellipsoids are the graphs of equations of the

form ax2 + by2 + cz2 = p2, where a, b, and c are all positive. In particular, a

sphere is a very special ellipsoid for which a, b, and c are all equal (any p is

an umbilic (on the head of the pin) and any point on sphere is spherical

(see umbilics)

this is the umbilical point on a sphere (as the best 3D space)

0).',.'..(.........

..........,.

.....,,,,....

0.'.''

..

,,......)..(),(

vutoequivalentisconditionthis

sotindependenlineararerr

thatimpliessurfaceaofdefinitionthe

vrur

and

ordersallofsderivativehavetvtu

vu

vu

This includes the planar points, where 021 kk

Examples. All points of a sphere are umbilical points. The

point (0, 0, 0) is an umbilical point on the

paraboloid22 yxz ///

New 3-D space suggested equilibrium point

Defining the domain of the win-win-win utility function

Building a new model the win-win-win

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE

EXISTING THEORY

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18 SPHERE

parameterization

A sphere is defined as the set of all points in three-dimensional Euclidean

space3R that are located at a distance (the “radius” from a given point

(the “center”)

)cos(

)sin(*)cos(

)sin(*)sin(

vzz

vuyy

vuxx

c

c

c

we normally describe a sphere like this, with radius r:

Parametrically we can describe the coordinates for a point on the sphere’s

surface like this:

As “r” has the same length in any direction in sphere, as well as φ=β (i.e

then it is obvious that

22222

222

sin

..............

..,...0..,...sin...

...

..sin....cos....cos..sin....

.,....sin....sin...sin....cos..

..cos..sin..cos..sin..sin.),(

vduadva

formlfundamentafirstthegetwesoand

arrGrrFvarrE

thatso

vkavjaviuar

vjuaviuar

gives

vkavjuaviuavur

vvvuuu

v

u

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE

EXISTING THEORY

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19

UMPILICAL

POINTS

DEFINITION: A point p on a surface S where the two principal curvatures

are equal, 21 kk is called an umbilical point. This includes the planar

points, where 021 kk

Examples. All points of a sphere are umbilical points. The point (0, 0, 0) is

an umbilical point on the paraboloid22 yxz

In cycle (reflected in Flat surface is 2 points

The Sphere

1:),,{(

..,....

22232

2

zyxRzyxS

asdefinedS

is compact subset of 3R and cannot be any open

homeomorphism 2RU However, if a point deducted, the

subset that remains is uniformly the level

Suppose we will consider smaller parts of sphere, let a

hemisphere, which is uniform with open subsets of the plane.

So we define the imaging

……………………… …………… D(0,1)

223 1,(),(:)1,.(: vuvuvuRODrz

Where

1:),(:)1,0( 222 vuRvuD

In differential geometry the Gaussian curvature or Gauss

curvature Κ of a surface at a point is the product of the principal

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covertures , κ1 and κ2, at the given point:

21 *kkK

For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere,

and a flat plane and a cylinder have Gaussian curvature 0 everywhere. The

Gaussian curvature can also be negative, as in the case of a hyperboloid or

the inside of atourus

Gaussian curvature is an intrinsic measure of curvature depending only on

distances that are measured on the surface, not on the way it is

isometrically embedded in any space. This is the content of the theorem

egregium

Gaussian curvature is named after Carl Friedrich Gauss who published the

Theorema egregium345 in 1827.

In cycle (reflected in Flat surface is 2 points

The Sphere

1:),,{(

..,....

22232

2

zyxRzyxS

asdefinedS

is compact subset of 3R and cannot be any open

homeomorphism 2RU However, if a point deducted, the

subset that remains is uniformly the level

Suppose we will consider smaller parts of sphere, let a

hemisphere, which is uniform with open subsets of the plane.

So we define the imaging

345

Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a foundational result in differential geometry proved

by Carl Friedrich Gauss that concerns the curvature of surfaces. The theorem says that the Gaussian curvature of a surface does not change if one bends the surface without stretching it. In other words, Gaussian curvature can be determined entirely by measuring angles, distances and their rates on the surface itself, without further reference to the particular way in which the surface is embedded in the ambient 3-dimensional Euclidean space. Thus the Gaussian curvature is an intrinsic invariant of a surface. A consequence of the Theorema Egregium is that the Earth cannot be displayed on a map without distortion. The Mercator projection, shown here, preserves angles but fails to preserve area.

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……………………… …………… D(0,1)

223 1,(),(:)1,.(: vuvuvuRODrz

Where

1:),(:)1,0( 222 vuRvuD

In differential geometry the Gaussian curvature or Gauss

curvature Κ of a surface at a point is the product of the principal

covertures , κ1 and κ2, at the given point:

21 *kkK

For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere,

and a flat plane and a cylinder have Gaussian curvature 0 everywhere. The

Gaussian curvature can also be negative, as in the case of a hyperboloid or

the inside of atourus

Gaussian curvature is an intrinsic measure of curvature depending only on

distances that are measured on the surface, not on the way it is

isometrically embedded in any space. This is the content of the theorem

egregium

Gaussian curvature is named after Carl Friedrich Gauss who published the

Theorema egregium346 in 1827.

346

Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a foundational result in differential geometry proved

by Carl Friedrich Gauss that concerns the curvature of surfaces. The theorem says that the Gaussian curvature of a surface does not change if one bends the surface without stretching it. In other words, Gaussian curvature can be determined entirely by measuring angles, distances and their rates on the surface itself, without further reference to the particular way in which the surface is embedded in the ambient 3-dimensional Euclidean space. Thus the Gaussian curvature is an intrinsic invariant of a

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From left to right: a surface of negative Gaussian curvature (hyperboloid)

a surface of zero Gaussian curvature (cylinder) and a surface of positive

Gaussian curvature (sphere)

Some points on the torus have positive, some have negative, and

some have zero Gaussian curvature.

At any point on a surface we can find a NORMAL VECTOR which is at right

angles to the surface; planes containing the normal are called normal

planes The intersection of a normal plane and the surface will form a curve

called a normal section and the curvature of this curve is the normal

curvature For most points on most surfaces, different sections will have

different curvatures; the maximum and minimum values of these are

called the principal curvature call these κ1, κ2. The Gaussian curvature is

the product of the two principal curvatures Κ = κ1 κ2.

surface. A consequence of the Theorema Egregium is that the Earth cannot be displayed on a map without distortion. The Mercator projection, shown here, preserves angles but fails to preserve area.

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The sign of the Gaussian curvature can be used to characterize the surface

If both principal curvatures are the same sign: κ1κ2 > 0, then the Gaussian

curvature is positive and the surface is said to have an elliptic point. At

such points the surface will be dome like, locally lying on one side of its

tangent plane. All sectional curvatures will have the same sign

If the principal curvatures have different signs: κ1κ2 < 0, then the Gaussian

curvature is negative and the surface is said to have a hyperbolic point. At

such points the surface will be saddle shaped. For two directions the

sectional curvatures will be zero giving the asymptotic directions

If one of the principal curvatures is zero: κ1κ2 = 0, the Gaussian curvature is

zero and the surface is said to have a parabolic point.

Most surfaces will contain regions of positive Gaussian curvature (elliptical

points) and regions of negative Gaussian curvature separated by a curve of

points with zero Gaussian curvature called a parabolic line

The 3-D equilibrium

o In the differential geometry of surfaces in three

dimensions, umbilics or umbilical points are points on a surface

that are locally spherical. At such points the normal curvature

in all directions are equal, hence, both principles

curvatures are equal, and every tangent vector is a principal

direction.

o Umbilic points generally occur as isolated points in the elliptical

region of the surface; that is, where the Gaussian curvature is

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positive. For surfaces with genus 0 e.g. an ellipsoid, there must

be at least four umbilics, a consequence of the Poincare-Hopf

theorem

o The sphere is the only surface with non-zero curvature where

every point is umbilic. A flat umbilic is an umbilic with zero

Gaussian curvature.

From left to right: a surface of negative Gaussian curvature (hyperboloid)

a surface of zero Gaussian curvature (cylinder) and a surface of positive

Gaussian curvature (sphere)

Some points on the torus have positive, some have negative, and

some have zero Gaussian curvature.

At any point on a surface we can find a NORMAL VECTOR which is at right

angles to the surface; planes containing the normal are called normal

planes The intersection of a normal plane and the surface will form a curve

called a normal section and the curvature of this curve is the normal

curvature For most points on most surfaces, different sections will have

different curvatures; the maximum and minimum values of these are

called the principal curvature call these κ1, κ2. The Gaussian curvature is

the product of the two principal curvatures Κ = κ1 κ2.

The sign of the Gaussian curvature can be used to characterize the surface

If both principal curvatures are the same sign: κ1κ2 > 0, then the Gaussian

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papakonstantinidis Page 233

curvature is positive and the surface is said to have an elliptic point. At

such points the surface will be dome like, locally lying on one side of its

tangent plane. All sectional curvatures will have the same sign

If the principal curvatures have different signs: κ1κ2 < 0, then the Gaussian

curvature is negative and the surface is said to have a hyperbolic point. At

such points the surface will be saddle shaped. For two directions the

sectional curvatures will be zero giving the asymptotic directions

If one of the principal curvatures is zero: κ1κ2 = 0, the Gaussian curvature is

zero and the surface is said to have a parabolic point.

Most surfaces will contain regions of positive Gaussian curvature (elliptical

points) and regions of negative Gaussian curvature separated by a curve of

points with zero Gaussian curvature called a parabolic line

o In the differential geometry of surfaces in three

dimensions, umbilics or umbilical points are points on a surface

that are locally spherical. At such points the normal curvature

in all directions are equal, hence, both principles

curvatures are equal, and every tangent vector is a principal

direction.

o Umbilic points generally occur as isolated points in the elliptical

region of the surface; that is, where the Gaussian curvature is

positive. For surfaces with genus 0 e.g. an ellipsoid, there must

be at least four umbilics, a consequence of the Poincare-Hopf

theorem

o The sphere is the only surface with non-zero curvature where

every point is umbilic. A flat umbilic is an umbilic with zero

Gaussian curvature.

PRESENTATION

TOPICS

CONTRIBUTION OF EXISTING THEORY IN THE

“WIN-WIN-WIN”

PARTICIPATION OF 3D “WIN-WIN-WIN”

IN THE CURRENT BIBLIOGRAPHY ACCORDING TO THE

EXISTING THEORY

20 CARATHEODORY

The Carathéodory conjecture

The Carathéodory conjecture

The Conjecture claims that any convex,

closed and sufficiently smooth surface in

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CONJECTURE The Conjecture claims that any convex, closed and

sufficiently smooth surface in three dimensional (3-D)

Euclidean Space needs to admit at least two umbilical

points In the sense of the Conjecture, the spheroid with

only two umbilic points and the sphere all points of

which are umbilic, are examples of surfaces with

minimal and maximal numbers of umbilics. For the

conjecture to be well posed, or the umbilical points to

be well-defined, the surface needs to be at least twice

differentiable

It is obvious that the term refers equilibrium (generally) in a state in which

opposite forces, or stresses, neutralize one another, leading to errors

But as every situation (state) this one has the "domain" of. The variation in

other situations is that balance should be defined and specified in the

"three-dimensional space-3D"

From this point as a starting point, the further analysis consists (in short):

Are the umbilical points of a sphere, the "heads of the pins" for a

win-win-win papakonstantinidis Equilibrium?

Let 1,0 denote the real interval from 1....0 to let n be the

number of players, and let jm

be the number of pure strategies available to player j Then player

sj' set of mixed strategies is the simplex

1}{}^1_{..0: jmisumxx The set

of all possible points is the Cartesian product of these simplices for

ntoj ...,..1 This set is not a ball or sphere.

(Craig A. Tovey - Georgia Institute of Technology)347

Finding a close form for the sum $nisum }1_{\

1 1)1(

m

jj BINOMIAL DISTRIBUTION

three dimensional (3-D) Euclidean Space

needs to admit at least two umbilical points

In the sense of the Conjecture,

the spheroid with only two umbilic points and

the sphere all points of which are umbilic, are

examples of surfaces with minimal and

maximal numbers of umbilics. For the

conjecture to be well posed, or the umbilical

points to be well-defined, the surface needs

to be at least twice differentiable

347 Tovey Craig A (2010): The probability of majority rule instability in the 2D Euclidean model with an even numbers of

voters Oct 2010 · Social Choice and Welfare (Keywords Spatial voting-Equilibrium-Stability-Euclidean preferences-

Majority rule)

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But, according to the “umbilical’s former

definition/////////////////////////////////////////////

SOLVING THE PRINCIPAL-AGENT “WIN-WIN-WIN” PROBLEM, INCLUDING THE “C”:

PART IV: Community in the centre

of Principal-Agent theory

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CHAPT III Introduction

In this chapter we try to define the “Community’s role” towards the “satisfaction level”, and

“what social enterprises are, not only for bargainers, but also for the Community (potential

revenues, coming from selling “State Bargaining Services(SBS) , toward the bargainers We have

also to “see” that “social enterprises: According to Adalbert Evers(1998)348 “…Quite often, new

forms of social and economic action have to be conceptualized and the groups concerned

seek their own vocabulary. This is also the case with regard to the development of

organisational forms of action which have been labeled as 'social purpose businesses', 'civic

enterprises', 'community businesses', 'community wealth enterprises and 'social enterprises'.

The challenge for analytical debates is that the term 'social enterprise' seems to blur exactly

those frontiers which have been deliberately constructed - between action for the public good

and private action, between social action as non-profit and enterprises as private market

organizations. The theoretical and conceptual sketch that we want to put forward suggests

that to understand social enterprises we need to see them as organizations that intertwine a

multiplicity of goals and resources. Such a theoretical orientation is to a large extent shared

with others in the field that point to the role of non-market and non-state resources like

donations and volunteering. It also underlines the fact that third-sector organizations can

integrate various social goals, ranging from serving the poor to the delivery of public goods.

///////////////////////////////////////////////////////////////

CHAPT III – Community’s role toward the satisfaction of citizens

Let’s

a commonly acceptable level of citizens’ satisfaction coming from a mix of policies, (state

services packages) with more, ( little above the Average), ie education or health measures, or policies for

protecting the bargaining weak players coming from a bargain with rational players and also depending

on the cultural specificities of each country-state and Rqi the commonly accepted quality of

living, Rti the price of bargaining services, in the form of taxes, that every citizen of this the State

pay, and which belongs to some bounded domain

pR Besides bargainers expect payoffs,

from any bargain payoffsp ji , with its probability

Now, let ),( qg denote the satisfaction of each of bargainers of type

using state guarantees

i.e with quality q ..

Then the welfare or utility, from community intervention in any 2-persons bargain, by its “Bargaining State

Services (BSS) is of this agent, defined here bya

is:

348

Adalbert Evers (1998) The significance o f social capital in the multiple goal and resource structure of social enterprises” –

Social Enterprises and Social Capital pp 296-307

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)())(,()( tqgUa

Generalization, let )(aU quantifies how much a customer with the majority of the

preferences

(i.e, enjoys the safety and services of the state in negotiations with another or others to the extent

possible quality

mq knowing that he spends the amount t for it. If )(qC represents the cost of

“producing” state bargaining and safety state services, of a quality

mq , then the utility of the principal

(defined here by "" p is

))(()()( qCtU p

Here )(pU can be viewed as the profit that the State (the Community, with its Services) makes in

“selling” the safety and its services, to the Citizens in negotiations with another or with quality

mq

to the CITIZEN with, a “level of accepted state /political bargaining services”

Since the goal of the

owner is to make more profit, then he tries to anticipate the customers’ choices so that each customer

reveals his taste by choosing the food that is targeted for him. Therefore, the principal’s (CITIZEN)

utility )(pU is subject to some constraints, called incentive compatible constraints, meaning that

the CITIZENS are given incentive to reveal their real accepted level of “bargaining State services”

Mathematically, the incentive compatible constraints can be represented as

,),...())(,()()(,( tqhtqh

So, the principal-agent problem, or, CITIZEN- State (Community) problem, especially, as for state services

quality level, can be formulated as follows:

dfqCtAP MAXtq

)())(()()..()(),(

is the objective function

levelbarservicesstatepreferredofchangeinitesimalthedwhere ........'........inf....,...

under the constraints:

),....2,..1,...0),( nitqh iii

njitqgtqh jjiiii ,...2,..1,......),(),(

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So, the principal-agent problem can be formulated as follows:

dfqCtAP MAXtq

)())(()()..()(),(

Let’s jia , be the outcomes of the bargain or in a MATRIX form 22 without include the “C”

influence

str A1 str A2

str B1 a1,1 a1,2

str B2 a2,1 a2,2

A, B strategies… a1,1…a2,2…the outcomes of A and B, players correspondly

In game theory, an outcome is a set of moves or strategies taken by the players, or it is their payoffs

resulting from the actions or strategies taken by all players. The two are complementary in that, given

knowledge of the set of strategies of all players, the final state of the game is known, as are any relevant

payoffs. In a game where chance or a random event is involved, the outcome is not known from only the

set of strategies, but is only realized when the random event(s) are realized.

A set of payoffs can be considered a set of N-tuples, where N is the number of players in the game, and

the cardinality of the set is equal to the total number of possible outcomes when the strategies of the

players are varied. The payoff set can thus be partially ordered, where the partial ordering comes from the

value of each entry in the N-tuple. How players interact to allocate the payoffs among themselves is a

fundamental aspect of economics.

Choosing among outcomes: Many different concepts exist to express how players might interact. An

optimal interaction may be one in which no player's payoff can be made greater, without making any other

player's payoff lesser. Such a payoff is described as Pareto efficient, and the set of such payoffs is called

the Pareto frontier.

Many economists study the ways in which payoffs are in some sort of economic equilibrium. One example

of such an equilibrium is the Nash equilibrium, where each player plays a strategy such that their payoff is

maximized given the strategy of the other players.

Applications: Equilibria are not always Pareto efficient, and a number of game theorists design ways to

enforce Pareto efficient play, or play that satisfies some other sort of social optimality. The theory of this

is called implementation theory. Other economists seek to design games based on a certain set of

outcomes, an effort which goes under the name of mechanism design349.

First, however, here are definitions of some concepts that will be helpful in analyzing game-trees:

Node: a point at which a player chooses an action.

Initial node: the point at which the first action in the game occurs.

Terminal node: any node which, if reached, ends the game. Each terminal node corresponds to

an outcome.

349 STANFORD ENCYCLOPEDIA of PHILOSOPHY

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Subgame: any connected set of nodes and branches descending uniquely from one node.

Payoff: an ordinal utility number assigned to a player at an outcome.

Outcome: an assignment of a set of payoffs, one to each player in the game.

Strategy: a program instructing a player which action to take at every node in the tree where she could

possibly be called on to make a choice.

The point of representing games using trees can best be grasped by visualizing the use of them in

supporting backward-induction reasoning. Just imagine the player (or analyst) beginning at the end of the

tree, where outcomes are displayed, and then working backwards from these, looking for sets of

strategies that describe paths leading to them. Since a player's utility function indicates which outcomes

she prefers to which, we also know which paths she will prefer. Of course, not all paths will be possible

because the other player has a role in selecting paths too, and won't take actions that lead to less

preferred outcomes for him. We will present some examples of this interactive path selection, and detailed

techniques for reasoning through these examples, after we have described a situation we can use a tree to

model

▲

SYNTHESIS: NASH Equilibrium Strategy vs PRINCIPAL-AGENT THEORY

SYNTHESIS

N.E

Nash Equilibrium:

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papakonstantinidis Page 240

Now, Let

thembetweenresponsebestarestrategyallmequilibriuIn

strategyotheranydenotedS

whereSSSSPSSSSP

iplayersallforifENaisSSSS

then

payoffthedenotedPand

iplayerforstrategymequilibriutheS

i

nini

ni

i

..............,.....

.........

,...)...,...,...,...()...,...,..(

........,........)...,....,..,...(

.....(.).....

....,.........

**

2

*

1

***

2

*

1

***

2

*

1

*

Let the outcome ji ,is the best for both players in a bargain ),( fS where the outcome

ji ,is a function of Strategies and payoffs (Bargaining Solution)

In the Equilibrium points, (and, especially, in Bargaining Solution) the outcome for the two bargainers-

except community profit- the outcome ji ,must be the best

But ji ,is the outcome (or real numbers) of the function

"....".........),( ,, strategyindividualVARIABLEtheisxwherexf jiji

That means, that the first derivative of the outcome’ function of a single variablex

is ZERO

BARGAINERStheoftwothebetweenondistributibestxfMAX jiji ..3..................[0)(,..... ,,

Now, ji ,is the outcome (or real numbers) of the function

"....".........),( ,, strategyindividualVARIABLEtheisxwherexf jiji

So, it could be that )....()......(, functionpayoffxfnumbersrealinoutcomes iiji and this

difference must be minimum:

As all parties in a bargain, “feel” that their outcomes are closer and closer to their expectations, it is more

and more sure, that they will be satisfied from their each-other bargaining process

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papakonstantinidis Page 241

SERVICESSTATEBARGAININGBSS

SERVICESBARGAININGCOMMUNITYCBS

BSSandCBSexcellentcaseuniquetheIf

xfxfa nnij

x

.....

........

.."....."........0..

)](.....)([

1

111lim....

That means that the “organizational structure and level of Bargaining State Services” is estimated as very

good, as 1 gets smaller and smaller, as bargainers constantly update more and more often (in fact

"suggest" over and over) expectations The more times "revise" their expectations in an environment of

security, justice and stability ensure a well-organized state, the better outcome That’s true:

If there is a fixed regime (financial, fiscal and legal provisions under) so as to ensure the highest possible

degree, the sense of justice then, each part of the deal will be in front of a very specific and limited scope

to develop its own action in the negotiation is not statism, liberalism is indeed within the operating

framework of a well-organized, well-governed, self-governing entity

It is excellent”, only in the unique case of 01

But, the State asks from bargainers to pay taxes i. e the fee for the services provided to bargainers for the

security and stability of their negotiations

State bargaining behavior is defined from both the “arbitrator role” and the “Agent role”

Specifically,

The "behavior" of the State determined on:

1. political programs presenting by political parties seeking the vote of the people at the election

day (every 4, 5 years)

2. the” political consequence " , for example, the deviation grade between political program and

government action

3. Its social and safety role

ni

thenxIf

xfxfa nnijx

,....2...,1.,.

0...,......

)](.....)([

1

111lim

Given, that

[Type text]

papakonstantinidis Page 242

alsoimprovedbewilltensionBARGAININGthethenimproved

betogoingisStrategyCommunitythethatNEXPECTATIOtheisthereifoppositetheIn

highlincrementabewillxfadeviationthe

thenpositionCSWWeaknessStrategicCommunityainremainCommunityAs

xfxfa

thethen

playerxtheofstrategyononlydependedpayoffectedtheisxf

and

valuedobserveornrealizatiotheeioutcomesthea

iji

njix

th

ii

ji

................,

..............,..........,......

.......)],(..[..

,..,...")...(......."..........

0)(....)(

,..

.......,.....,,,...exp.....),...(

,......,........,..,...

,

1,

,

lim

Finally, we have to study the “win-win-win situation- an ideal point of the bargain (the Community

included as the third person, as well as the “Peoples Agent” and the bargaining Arbitrator”

We note the n- tuples community role in any bargain between two

Special case: The “3-players PRISONER’S DILEMMA”

Consider a game of Prisoner’s Dilemma350. Only instead of two criminals, the FBI must interrogate three

criminals. What would the payoff matrix look like for this game? What would be the rules? What would be

the Dominate Strategy for each player?

Suppose the payoff matrix for a three-player game of Prisoner’s Dilemma is 3-D, then it would look like a

cube, made up of 8 smaller cubes. Each cube represents a different outcome. Listed below are the

outcomes, C for to confess and NC for not to confess.

(Player 1, Player 2, Player 3)

(C, C, C)

(C, NC, C)

350 THE Cornell University working paper

Option A1 Option A2 Option A3

Option A1 a11 a21 a31

Option A2 a21 a22 a32

Option A3 a31 a23 a33

[Type text]

papakonstantinidis Page 243

(C, C, NC)

(C, NC, NC)

(NC, C, C)

(NC, NC, C)

(NC, C, NC)

(NC, NC, NC)

Suppose there are some rules. If all three players confess, each player gets 8 months in jail. If all three

players refuse to confess, each player gets 4 months. If only one player confesses, he/she walks, and the

other two gets 12 months each. Finally, if two players confess, they get 6 months each, and the third

player gets 12 months. Listed below are the outcomes with appropriate jail times for each player.

(Player 1, Player 2, Player 3) = (#, #, # )

(C, C, C) = (8, 8, 8 )

(C, NC, C) = (6, 12, 6 )

(C, C, NC) = (6, 6, 12 )

(C, NC, NC) = (0, 12, 12 )

(NC, C, C) = (12, 6, 6 )

(NC, NC, C) = (12, 12, 0 )

(NC, C, NC) = (12, 0, 12 )

(NC, NC, NC) = (4, 4, 4 )

Let’s analysis the outcomes from Player 1’s perspective: if Player 2 and Player 3 confesses, Player 1 should

confess, 12>8; if Player 2 confesses and Player 3 refuses to confess, Player 1 should confess, 12>6; if

Player 2 refuses to confess and Player 3 confesses, Player 1 should confess, 12>6; if Player 2 and Player 3

refuse to confess, Player 1 should confess, 4>0. Thus, to confess is a Dominate Strategy for Player 1, this

process works the same way for Player 2 and Player 3.

The above discussion applies only to a game in which all players perceive a specific length of jail time as

equally bad. For example, in an episode of Numb3rs, “Dirty Bomb,” mathematician Charlie Epps used

Game Theory and Risk Analysis to aid FBI agent Don Epps in interrogating three criminals. Charlie

integrated Risk Analysis into the Prisoner’s Dilemma. He argued that one criminal may have more to lose

[Type text]

papakonstantinidis Page 244

by going to jail than anther. Thus, assigning months alone to the payoff matrix may be misleading.

Charlie performed a Risk Analysis for each criminal and derived a factor for each criminal: (Player 1 = 7.9,

Player 2 = 14.9, Player 3 = 26.4). If all three criminals go to jail for the same length of time, Player 3 has

more to lose than the others. Listed below are the outcomes with appropriate jail times multiplied by risk

factors for each player.

(Player 1, Player 2, Player 3) = (#, #, # )

(C, C, C) = (63.2, 119.2, 211.2 )

(C, NC, C) = (47.4, 178.8, 158.4 )

(C, C, NC) = (47.4, 89.4, 316.8 )

(C, NC, NC) = (0, 178.8, 316.8 )

(NC, C, C) = (94.8, 89.4, 158.4 )

(NC, NC, C) = (94.8, 178.8, 0 )

(NC, C, NC) = (94.8, 0, 316.8 )

(NC, NC, NC) = (31.6, 59.6, 105.6 )

Dominate Strategy:

Player 1: C – Player 2: C → Player 3: C

Player 1: C – Player 2: NC → Player 3: C

Player 1: NC – Player 2: C → Player 3: C

Player 1: NC – Player 2: NC → Player 3: C

Player 3’s Dominate Strategy = C

Player 1: C – Player 3: C → Player 2: C

Player 1: C – Player 3: NC → Player 2: C

Player 1: NC – Player 3: C → Player 2: C

Player 1: NC – Player 3: NC → Player 2: C

Player 2’s Dominate Strategy = C

Player 3: C – Player 2: C → Player 1: C

Player 3: C – Player 2: NC → Player 1: C

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papakonstantinidis Page 245

Player 3: NC – Player 2: C → Player 1: C

Player 3: NC – Player 2: NC → Player 1: C

Player 1’s Dominate Strategy = C

The Dominate Strategy for each player is still to confess! In Numb3rs, the FBI agent put all three

criminals into the same room. Then, the mathematician presented each criminal’s risk factor. Player 1

remained indifferent, Player 2 hesitated, and Player 3 confessed almost immediately after. The actual

outcome of the game is (NC, NC, C). Even though each player’s Dominate Strategy is to confess, it should

be considered that some players may be more motivated to confess than others. And if timing matters,

the criminal with the most to lose may confess before the others.

▲

But

nsssS ...21

the set of strategy profiles and ))(),......(()( 1 xfxfxf n

is payoff function, i.

e a strategy profile, by its probability

▲

;

According to above analyzed NE :

A strategy profile Sx * is a Nash Equilibrium NE if no unilateral deviation in strategy by

any single player is profitable for that player, that is:

),(),(:, ***

: iiiiiiii xxfxxfSxi

[Type text]

papakonstantinidis Page 246

First of all, in the suggested “win-win-win” equilibrium” Community is the third (invisible) party of any

bargain between two; It has a distinguished presence It also claims its “own” share by the probability

Usually, the game is played by having all the players simultaneously pick their individual strategies. It will

be useful to imagine that all players pick their strategies at the same time: player 1 picks some

11 Ss player 2 picks some 22 Ss

We can describe the set of strategies chosen by

the n players as the ordered tuplen

This set of choices results in some strategy profile Ss which we call the outcome of the game.

Each player has a set of preferences over these outcomes Ss . We assume that each player’s

preferences over lotteries over S can be represented by some von Neumann-Morgenstern utility

function RSui :

At the conclusion of the game, then, each player Ii receives a payoff

iiiii ssusu ,

The payoff each player receives depends not only on the strategy she picked but also on the strategies

which all the other players picked. In other words the payoff to any one player depends on the entire

strategy profile played.

///////////////////////////////////////////////////////////////////////////////////////

In the case of Community participation in a bargain we can fully describe a game then by the

)(,,,

sfuSSciici i.e. by a player set niiiiI ..,..... 111 , a space of

strategy profiles iS and a vector u of von Neumann-Morgenstern utility functions defined over S .

Generally,

),,(),,(:,,, 1

*

1

*

1

**

1:11 iciiiciiicii xxxfxxxfSxxxi

[Type text]

papakonstantinidis Page 247

stepbystepimprovingisstrategy

BARGAININGservicesCommunityas

xxxfxxxfSxxxi iciiiciiicii

.............

..'......,...0

),,(),,(:,,,

2

21

*

1

*

1

**

1:11

/////////////////////////////////////////////////////////////////////////////

If the Community services’ bargaining strategy is continuously improving, then, in the ideal case, i. e in

the level of the optimum state bargaining services, i.e

02

In this case, the payoff each player and the Community receives depends not only on the strategy the one

player (let A) picked but also on the strategies which all the other players (B-“C”, where “C’ = the

Community) picked.

We’ve assumed that each player’s preferences over lotteries over S can be represented by some von

Neumann-Morgenstern utility function RSui : In other words the payoff to any one player

depends on the entire strategy profile played, by its corresponding probability (player’s preferences over

lotteries)

n

c

B

A

CBA

yxU

yU

xU

where

UUU

)100(

,

,

As the “Community Bargaining Services” (CBS) tend to the optimum level, as consequence of better

“bargaining services strategy”, bargaining outcomes will approach to their most equal and justice level;

As the “Community’s Bargaining Services” (CBS) tend to the optimum level, both

0,.. 21

[Type text]

papakonstantinidis Page 248

IDEAL CASE:

The above math relations, tell us how the

th

ix player behaves, to win It tells us, the payoff that

each player (including the Community) receives, depends not only on strategy that one player picked, but

also on the strategies which all the other players including the Community) picked

But, now we consider,

SERVICESSTATEBARGAININGBSS

SERVICESBARGAININGCOMMUNITYCBS

BSSandCBSexcellentcaseuniquetheIf

xfxfa nnij

x

.....

........

.."....."........0..

)](.....)([

1

111lim....

stepbystepimprovingisstrategy

BARGAININGservicesCommunityas

xxxfxxxfSxxxi iciiiciiicii

.............

..'......,...0

),,(),,(:,,,

2

21

*

1

*

1

**

1:11

)1.(..............................)](.....)([ 111lim

nnijx

xfxfa

)2....(),,(),,(:,,, 21

*

1

*

1

**

1:11 iciiiciiicii xxxfxxxfSxxxi

caseideal...

021

[Type text]

papakonstantinidis Page 249

If,

choicebestitsmakenothaswhichCSWWeaknessStrategicCommunitytheto

duesplayerothertheofstrategiesbesttheionconsideratintaking

withoutsstrategydecisionownhistakesplayergenerallyxthe

then

xxxfxxxfSxxxi

th

i

iciiiciiicii

............),("......."...

),(....................

)..(........,)......(...

)2....(0),,(),,(:,,, 21

*

1

*

1

**

1:11

This means that a STATE relatively weak and insufficient public services’ strategy on “bargaining sector”

(eg non-law-abiding state, tax rates instability status, etc.) is much easier to produce insufficient

outcomes:

This results in a part of the deal (the best informed because of the failure of the state to offer the same

opportunities in 2 parts) to take advantage of this “bias” for the satisfaction of their individual needs at

the highest level, without calculating the corresponding degradation of the other player’s expectations -

see CSW

Nowadays it is now very common in practice,

We support that, the

th

ixplayer must take his (her) own decision having perfect information –or even

no perfect information [Harsanyi, John C.-November 1967]351- but in “Clearly Stability Environment” –CSE

(as it concerns taxation, wages, safety….)

If something from these temporally, does not exist, the bargaining concept does not also exist:

This means that A player, even the most informed, not negotiating but impose its position on the B less

informed and thus less favored because of the state's inability to ensure stability, justice and equal

opportunities for the two negotiators; “A” takes into consideration, only his own strategy

If B is disadvantaged against the A, although they have both on the same bargaining power, then this is

attributed to the state's failure to ensure conditions of stability, justice and equal opportunities

That inequality in the negotiations reflects the state strategic planning inability to negotiate CSW

351 Harsanyi, John C. (November 1967). "Games with incomplete information played by "Bayesian" players, I-III. part I. The

Basic Model". Management Science, special issue: Theory Series (INFORMS) 14 (3): 159–182.

[Type text]

papakonstantinidis Page 250

)2....(),,(),,(:,,,

)1(........................................)](......)([

21

*

1

*

1

**

1:11

111lim

iciiiciiicii

nnijx

xxxfxxxfSxxxi

xfxfa

Now, there are 4 combinations, expressed the four (4) alternative versions:

1 2

0,0 0,0

0,0 0,0

Cases:

1. caseideal.......................021

)2....(0),,(),,(:,,,

)1(........................................0)](......)([

1

*

1

*

1

**

1:11

11lim

iciiiciiicii

nnijx

xxxfxxxfSxxxi

xfxfa

In the above case,

A. Bargaining expectations are (ideal case) are exactly the payoffs of bargainers as well as

the Community expectations:

3......

aoutcomespayoffsCommunnityandindividual

B. NE, on Pareto Optimality: the

thi player, has to take into consideration not only

his/her best strategies, but also the other bargainers/players strategies as well, as the

Community Bargaining Strategy and its services’ COST (for taxations, stability .law,

services)

),,(:,,, 1

*

1:11 iciiicii xxxfSxxxi

[Type text]

papakonstantinidis Page 251

C. We note, that

thi player, does not take into consideration any other player best

strategies, i.e the community strategy and the strategysplayeri ..'..1 But if, he

will take the beshoulditthenxtimesametheatandx ic .................... *

1

*

CASEIDEAL

herexxxfxxxfSxxxi iciiiciiicii

...

)(0),,(),,(:,,, 2

*

1

**

1

*

1

**

1:11

2.

0

0

2

1

)2.......(0),,(),,(:,,,

)1(..................................................0)](......)([

21

*

1

*

1

**

1:11

11lim

iciiiciiicii

nnijx

xxxfxxxfSxxxi

xfxfa

From the above theoretical definitions, payoff reflects the desirability of an outcome to a player, for

whatever reason. When the outcome is random, payoffs are usually weighted with their probabilities.

We can see at01

, but, ,02

That means, that the

thiplayer’s final outcomes correspond to his/her expected payoffs

The

thiplayer takes into consideration only his /her best strategy, due mainly to CSW

Remember, that,

[NASH EQUILIBRIUM: A Nash Equilibrium, also called strategic equilibrium, is a list of strategies, one for

each player, which has the property that no player can unilaterally change his strategy and get a better

payoff].

[Type text]

papakonstantinidis Page 252

Relation (1) shows that the final result (outcome) for the

thiplayer coincides with his expected

payoffs from the bargain with some probability (player’s preferences over lotteries)

As we know,

PAYOFF-OUTCOME: A payoff is a number, also called utility that reflects the desirability of an outcome to

a player, for whatever reason When the outcome is random, payoffs are usually weighted with their

probabilities. The expected payoff incorporates the player’s attitude towards risk352 PAYOFF: THE

INCETIVE: In any game, payoffs are numbers which represent the motivations of players. Payoffs may

represent profit, quantity, "utility," or other continuous measures (cardinal payoffs), or may simply rank

the desirability of outcomes (ordinal payoffs)353. In all cases, the payoffs must reflect the motivations of

the particular player. The payout a player receives from arriving at a particular outcome. The payout can

be in any quantifiable form, from dollars to UTILITY PAYOFF A payoff is a number, also called utility, that

reflects the desirability of an outcome to a player, for whatever reason. When the outcome is random,

payoffs are usually weighted with their probabilities. The expected payoff incorporates the player’s

attitude towards risk. The individual payoffs for all the n players for a particular strategy profile s

define a payoff vector )(su for that strategy profile

sususu n....()( 1

From the relation (2) resulted that that the Community has more or fewer resources to achieve the stability

policy of the civil transactions

So from (1) and (2) that although the outcomes of the

thiplayer coincide with his expectations, but

this was a loss in other areas of policy, ie more costs than it really deserved this result

3.

0

0

2

1

352 Turocy Theodore L. and Stengel Bernhard von (2001) "Game Theory"ƒ CDAM Research Report LSE-CDAM-2001-09 October 8, 2001 353 Game theory net Dictionary

[Type text]

papakonstantinidis Page 253

)2.......(0),,(),,(:,,,

)1...(........................................0)](......)([

21

*

1

*

1

**

1:11

111lim

iciiiciiicii

nnijx

xxxfxxxfSxxxi

xfxfa

Relation (1) shows that the final result for the

thi player does not coincides with the expected

returns

From equation (2) that the Community has spent equal resources to achieve equal result of terms of the

Community expenditure for the stability of bargaining “policy” So from (1) and (2) that although the odds

of the

thiplayer coincide with his expectations, but this was a loss in other areas of policy, ie more

costs than it really deserved this result

4.

0

0

2

1

)2.......(0),,(),,(:,,,

)1...(........................................0)](......)([

21

*

1

*

1

**

1:11

111lim

iciiiciiicii

nnijx

xxxfxxxfSxxxi

xfxfa

The worst result, coming from the worst combination

Neither bargainers are satisfied nor Community spends enough resources, to improve the policy of the

stability of “bargains”

This situation is usually, in nowadays

▲

“Agent of State Population”

Let now consider the prime Community Role that is the “Agent of State Population”

[Type text]

papakonstantinidis Page 254

let )(aU quantifies how much a customer with the majority of the

preferences (i.e, enjoys the

safety and services of the state in negotiations with another or others to the extent possible quality

mq

knowing that he spends the amount t for it. If )(qC represents the cost of “producing” state

bargaining and safety state services, of a quality

mq , then the utility of the principal (defined here by

"" p is

))(()()( qCtU p

Here )(pU can be viewed as the profit that the State (the Community, with its Services) makes in

“selling” the safety and its services, to the Citizens in negotiations with another or with quality

mq

to the CITIZEN with, a “level of accepted state /political bargaining services”

)())(,()( tqgUa

Let:

)(........................ sfueiprofilestrategicoffunctionaisuPayoff iii

We have to maximize the objective- function, i. e the payoff function, which is the “incentive” or the

motivation for starting the bargain with another person

In this frame, Community- the “C” player, must participate with its “own” expectations, its ”own” payoff

function and its own strategic profile

So we have,

},..2,..1{........0

)....,(..max..:...max 21

nxx

Mxp

xxxUfunctionUtility

ii

ii

n

[Type text]

papakonstantinidis Page 255

PARETO EFFICIENCY

Papakonstantinidis:

AUtilityUetcyprobabilitPunderAstrategymixedP

UUMaxURQP

Aii

CBAiiii

....,).....(..,......(&)

(&)(&)(&)lim

3,2,1)....,,(),,(:,

},...2,1{,.....0

,,...

).....(.max:....max

.,..........

,

*

3

*

21

**

1

*

1

21

ixxxfxxxfSxi

Then

nix

strategiesxiesprobabilitpMxp

xxxUFunctionUtility

eiEfficiencyParetotheionconsideratintaking

Generally

iiiiciiiii

i

iiii

n

In the case that “Community” plays role, of the third player (only) in the “game” :

[Type text]

papakonstantinidis Page 256

functionpayoffxfu

profilestrategyx

xxxfxxxfxxxfxxxfSxi

MODELNTINIDISPAPAKONSTAWINWINWIN

iii

i

ciCiiiCiiiCiiiiii

..)(

..

),,(),,.(),..,(),,(:,

.....

21

*

111

*

1

**

1

*

1

),,(),,.(),..,(),,(:,

/....

21

*

111

*

1

**

1

*

1 ciCiiiCiiiCiiiiii xxxfxxxfxxxfxxxfSxi

MEQUILIBRIUMODELNTINIDISPAPAKONSTAWINWINWIN

functionpayoffxfuandprofilestrategyx iiii ....)(.......

“……..It is a contribution in Social Science Theory: By introducing the third pole (Community) in any

bargain between two players in a game (through the sensitization process) this model contributes in

behavioral Sciences. It forms the platform of a “Social Trust” creation, leading to Social Cohesion (at Local

Level, at least)354………” (ISA)

354 win - win - win Papakonstantinidis model has been characterized as a new Theory in Social Sciences in

many countries. It has been translated in Hungarian language. It has been accepted in India, Philippines,

Bangladesh, South Africa (Durban) as well as in World Organization, as for example by the International

Sociological Association (I.S.A) as it produces a new “bargaining philosophy” As it has been written, as a

comment: “it is interesting to note any feedback to such a model, that is open and flexible to reforms,

having as principle the third “win” that is disseminated to all factors of local social – ISA, RG 26

[Type text]

papakonstantinidis Page 257

//////////////////////////////////////

SOLVING THE PRINCIPAL-AGENT “WIN-WIN-WIN” PROBLEM, INCLUDING THE “C”:

From the other hand, we have to define “satisfaction level, not only for bargainers, but also for the

Community (potential revenues, coming from selling “State Bargaining Services(SBS) , toward the

bargainers Let’s

a commonly acceptable level of citizens’ satisfaction coming from a mix of policies,

(state services packages) with more, ( little above the Average), ie education or health measures, or

policies for protecting the bargaining weak players coming from a bargain with rational players and also

depending on the cultural specificities of each country-state and Rqi the commonly accepted

quality of living, Rti the price of bargaining services, in the form of taxes, that every citizen of

this the State pay, and which belongs to some bounded domain

pR Besides bargainers

expect payoffs, from any bargain payoffsp ji , with its probability

Now, let ),( qg denote the satisfaction of each of bargainers of type

using state guarantees

i.e with quality q ..

Then the welfare or utility, from community intervention in any 2-persons bargain, by its “Bargaining State

Services (BSS) is of this agent, defined here bya

is:

)())(,()( tqgUa

Generalization, let )(aU quantifies how much a customer with the majority of the

preferences

(i.e, enjoys the safety and services of the state in negotiations with another or others to the extent

possible quality

mq knowing that he spends the amount t for it. If )(qC represents the cost of

“producing” state bargaining and safety state services, of a quality

mq , then the utility of the principal

(defined here by "" p is

))(()()( qCtU p

[Type text]

papakonstantinidis Page 258

Here )(pU can be viewed as the profit that the State (the Community, with its Services) makes in

“selling” the safety and its services, to the Citizens in negotiations with another or with quality

mq

to the CITIZEN with, a “level of accepted state /political bargaining services”

Since the goal of the

owner is to make more profit, then he tries to anticipate the customers’ choices so that each customer

reveals his taste by choosing the food that is targeted for him. Therefore, the principal’s (CITIZEN)

utility )(pU is subject to some constraints, called incentive compatible constraints, meaning that

the CITIZENS are given incentive to reveal their real accepted level of “bargaining State services”

Mathematically, the incentive compatible constraints can be represented as

,),...())(,()()(,( tqhtqh

So, the principal-agent problem, or, CITIZEN- State (Community) problem, especially, as for state services

quality level, can be formulated as follows:

dfqCtAP MAXtq

)())(()()..()(),(

is the objective function

levelbarservicesstatepreferredofchangeinitesimalthedwhere ........'........inf....,...

under the constraints:

),....2,..1,...0),( nitqh iii

njitqgtqh jjiiii ,...2,..1,......),(),(

So, the principal-agent problem can be formulated as follows:

dfqCtAP MAXtq

)())(()()..()(),(

Let’s jia ,

be the outcomes of the bargain or in a MATRIX form 22 without include the “C”

influence

str A1 str A2

str B1 a1,1 a1,2

str B2 a2,1 a2,2

A, B strategies… a1,1…a2,2…the outcomes of A and B, players correspondly

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DOMAIN

Of the

Win-Win-Win papakonstantinidis model

Nash equilibrium

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Asymptote formula

///////////////////////////////////////////

The surface normal is a vector function

The unit normal is a smooth vector function of the coordinate of the point on the surface so

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),,( zyx nnnn is a smooth function of ).,( zyx that satisfies the equation of surface. A surface is generally

parametrized through two variables, e.g., ),( vur The smooth typically means twice continuously differentiable

A surface (in 3R ) can be given

3

2

..................))..,(),,(),,((),(,..

......

............)..(),(),(

RINTOAfrommapaisvuzvuyvuxvurso

RAsubsetafrom

parametersarevanduwhereuvzzuvyyuvxx

Whenever you fix any parameter, say, u , you'll obtain a curve on your surface, so, if it is possible (if these functions are

differentiable) you can define tangent vectors uv rr , (they are partial derivatives of rr with respect to respective parameters)

for these curves. In some good cases these two vectors will not be parallel and thus will form the base of a tangent plane (but it

doesn't always exist, consider the top of a cone) to your surface at any given point ),( vu Then you can calculate the normal

vector of unit length at any point ),( vu by computing the cross product of uv randr .. dividing it by its length. In this way

you'll obtain a function ),( vun it must be continuous differentiable355

Tangent in sphere

355

Mathematics, http://math.stackexchange.com/questions/448979/what-is-a-smooth-surface#comment964707_448979

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UMBILIC POINTS- THE CARATHEODORY CONJECTION

Introduction:

Now, we need to define the domain of the suggested “win-win-win papakonstantinidis

equilibrium” As it is obvious, the domain of the “win-win-win” is found in a3R space

2#..R of

the win-win equilibrium”

A major problem that preoccupied Mathematicians from antiquity, was the formulation of the

tangent at a point a curve356.

The problem addressed in the course then known (synthetic) Euclidean Geometry. The

responses were only partial and concerned both curves. A better approach became possible

under the Analytic Geometry. Despite the significant progress made in this direction by R.

Descartes, P. Fermat and C. Huygens, again the general method of solving the problem stop

when going to tackle equations of a number higher than 3. The problem of defining the

tangent to the generality of solved using the Differential Calculus, which along with the Done;

ear Calculus exerted enormous influence on the development of mathematics. The use of

Differential Calculus to the study of geometry led to the creation of a new branch of

Differential Geometry. The development of differential geometry of curves had a fundamental

contribution of I. Newton, GW Leibniz, L. Euler, G. Monge, J. Bernoulli,

356 Ε. Βασιλείου-Μ. Παπατριανταφύλλου (2010) «Σημειώσεις Διαφορικής Γεωμετρίας Καμπυλών και Επιφανειών»- Πανεπιστήμιο Αθηνών (ΕΚΠΑ) Τμήμα Μαθηματικό (trnsl)

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In Analytic Geometry “curve” is a set of X points (the space or level) that meet certain

conditions. For example, it can be the locus of points which satisfy a particular property

(circle, ellipse, etc.), The graph of a function RRf : , the trajectory of a mobile, etc. Our

aim is to implement methods of Differential Calculus to the study of X, and to do this you have

to see the curves as images

This in turn is reflected in Tangent in the 2R space suitable functions (continuous imaging).

Equilibrium in Three Dimensions

FREE-BODY DIAGRAMS

The first step in solving 3D equilibrium problems is to draw a free-body diagram of the body:

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Definition issues:

1. Equilibrium is the condition of force where it is acted but simply cancelled out. These

forces may be even large enough to cause permanent deformation.

2. CENTER OF GRAVITY The center of gravity of a body is the point where its entire

weight maybe assumed concentrated. Practical example of equilibrium and center of

gravity: A tight rope walker in a circus carries a weighted pole or an umbrella.

3. Newton’s First Law of Physics: • A body at rest will stay at rest and a body in motion

will stay in motion unless acted upon by an unbalanced force. Therefore, sum of all

forces must be zero. F=0 Resultant of all forces acting on a particle is zero.

4. 'Economic Equilibrium ' A condition or state in which economic forces are balanced

These economic variables will be unchanged from their equilibrium values in the

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absence of external influences. Economic equilibrium may also be defined as the point

where supply equals demand for a product – the equilibrium price is where the

hypothetical supply and demand curves intersect. The term 'economic equilibrium' can

also be applied to any number of variables, such as the interest rate that allows for

the greatest growth of the banking and non-financial sector

////////////////////////////

Necessary Condition for Equilibrium • The necessary conditions for equilibrium are: (i) the

vector sum of all external forces is zero. (ii) the sum of the moments of all external forces

about any line is zero. The moment equations can be determined about any point. Usually,

choosing the point where the maximum number of unknown forces are present simplifies the

solution

Categories of equilibrium according to Force system Equilibrium Equation from Newton’s Law

• If an object is in equilibrium, then the resultant force acting on an object equals zero. This is

expressed as follows: FR F 0 (vector-equation) Some problems can be analyzed using only

2D, while others require 3D.

Three-Dimensional Reaction at Supports & Connections357

Thus, we give the following definition:

“A parametrized curve in the space, spaceaisRIwhereRIa ......,...,..: 3

“A surface parameterization, or 2-dimensional coordinate system (coordinate system) or two-dimensional

chart (chart or patch), or parametrized surface is a triplet

32 :.......)..,,( RUropenRUwhereWrU

If and only if

357 http://www.slideshare.net/imoinul007/equilibrium-equation-of-equilibrium

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11...:)(..),(

)...(:

32

3

areRRqDrUvuq

ISMHOMEOMORPHUrRUr

32 :,....,..),,( RUropenRUcwhereWrU

Imaging,

11....:)(......),(.........2

....)..(:.....1

:....),..(

32

isRRqDraldifferentitheUvuqeveryFor

ISMHOMEOMORPHaisUrWUr

propertiesthewithUrW

In cycle (reflected in Flat surface is 2 points

The Sphere

1:),,{(

..,....

22232

2

zyxRzyxS

asdefinedS

is compact subset of 3R and cannot be any open homeomorphism

2RU However, if a point

deducted, the subset that remains is uniformly the level

Suppose we will consider smaller parts of sphere, let a hemisphere, which is uniform with open subsets of

the plane. So we define the imaging

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……………………… …………… D(0,1)

223 1,(),(:)1,.(: vuvuvuRODrz

Where

1:),(:)1,0( 222 vuRvuD

In differential geometry the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the

principal covertures , κ1 and κ2, at the given point:

21 *kkK

For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian

curvature 0 everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of atourus

Gaussian curvature is an intrinsic measure of curvature depending only on distances that are measured on the surface, not on

the way it is isometrically embedded in any space. This is the content of the theorem egregium

Gaussian curvature is named after Carl Friedrich Gauss who published the Theorema egregium358 in 1827.

358

Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a foundational result in differential geometry proved

by Carl Friedrich Gauss that concerns the curvature of surfaces. The theorem says that the Gaussian curvature of a surface does not change if one bends the surface without stretching it. In other words, Gaussian curvature can be determined entirely by measuring angles, distances and their rates on the surface itself, without further reference to the particular way in which the surface is embedded in the ambient 3-dimensional Euclidean space. Thus the Gaussian curvature is an intrinsic invariant of a surface. A consequence of the Theorema Egregium is that the Earth cannot be displayed on a map without distortion. The Mercator projection, shown here, preserves angles but fails to preserve area.

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From left to right: a surface of negative Gaussian curvature (hyperboloid) a surface of zero Gaussian curvature (cylinder) and

a surface of positive Gaussian curvature (sphere)

Some points on the torus have positive, some have negative, and some have zero Gaussian curvature.

At any point on a surface we can find a NORMAL VECTOR which is at right angles to the surface; planes containing the normal

are called normal planes The intersection of a normal plane and the surface will form a curve called a normal section and the

curvature of this curve is the normal curvature For most points on most surfaces, different sections will have different

curvatures; the maximum and minimum values of these are called the principal curvature call these κ1, κ2. The Gaussian

curvature is the product of the two principal curvatures Κ = κ1 κ2.

The sign of the Gaussian curvature can be used to characterize the surface

If both principal curvatures are the same sign: κ1κ2 > 0, then the Gaussian curvature is positive and the surface is said to have

an elliptic point. At such points the surface will be dome like, locally lying on one side of its tangent plane. All sectional

curvatures will have the same sign

If the principal curvatures have different signs: κ1κ2 < 0, then the Gaussian curvature is negative and the surface is said to have a

hyperbolic point. At such points the surface will be saddle shaped. For two directions the sectional curvatures will be zero

giving the asymptotic directions

If one of the principal curvatures is zero: κ1κ2 = 0, the Gaussian curvature is zero and the surface is said to have a parabolic

point.

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Most surfaces will contain regions of positive Gaussian curvature (elliptical points) and regions of negative Gaussian curvature

separated by a curve of points with zero Gaussian curvature called a parabolic line

The 3-D equilibrium

o In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface

that are locally spherical. At such points the normal curvature in all directions are equal, hence, both principles

curvatures are equal, and every tangent vector is a principal direction.

o Umbilic points generally occur as isolated points in the elliptical region of the surface; that is, where the Gaussian

curvature is positive. For surfaces with genus 0 e.g. an ellipsoid, there must be at least four umbilics, a

consequence of the Poincare-Hopf theorem

o The sphere is the only surface with non-zero curvature where every point is umbilic. A flat umbilic is an umbilic

with zero Gaussian curvature.

The Carathéodory conjecture

The Conjecture claims that any convex, closed and sufficiently smooth surface in

three dimensional (3-D) Euclidean Space needs to admit at least two umbilical points

In the sense of the Conjecture, the spheroid with only two umbilic points and

the sphere all points of which are umbilic, are examples of surfaces with minimal and

maximal numbers of umbilics. For the conjecture to be well posed, or the umbilical

points to be well-defined, the surface needs to be at least twice differentiable

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The Carathéodory conjecture

The Conjecture claims that any convex, closed and sufficiently smooth surface in three

dimensional (3-D) Euclidean Space needs to admit at least two umbilical points In the sense of

the Conjecture, the spheroid with only two umbilic points and the sphere all points of which

are umbilic, are examples of surfaces with minimal and maximal numbers of umbilics. For the

conjecture to be well posed, or the umbilical points to be well-defined, the surface needs to

be at least twice differentiable

DEFINITIONS

DEFINITION PROBLEMS

1. VECTOR a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another. Angular momentum is a vector quantity, meaning it has both magnitude and direction, and can be described by three components (in three dimensions).

2. piecewise- defined function: In mathematics, a piecewise-defined function (also called a piecewise

function or a hybrid function) is a function which is defined by multiple sub-functions, each sub-function

applying to a certain interval of the main function's domain (a sub-domain). Piecewise is actually a way of

expressing the function, rather than a characteristic of the function itself, but with additional

qualification, it can describe the nature of the function. For example, a piecewise polynomial function is a

function that is a polynomial on each of its sub-domains, but possibly a different one on each.

3. B-spline: , In the mathematical subfield of numerical analysis a B-spline, or basis spline, is

a spline function that has minimal support with respect to a given degree smoothness

and domain partition. Any spline function of given degree can be expressed as a linear combination of B-

splines of that degree. Cardinal B- splines have knots that are equidistant from each other. B- splines can

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be used for curve-fitting and numerical differentiation of experimental data. Which will define the whole

new curve

NURBS Surfaces- DEFINITION:

Non-uniform Rational Basis Spline (NURBS) is a mathematical model commonly used in computer graphics for generating and

representing curves and surfaces. It offers great flexibility and precision for handling both analytic (surfaces defined by

common mathematical formulae) and modeled shapes. NURBS are commonly used in computer-aided design (CAD),

manufacturing (CAM), and engineering (CAE) and are part of numerous industry wide standards

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It concerns problems of free-form object matching for the point vs. NURBS surface and the NURBS surface vs. NURBS surface

cases, and its application to copyright protection. Two new methods are developed to solve a global and partial matching

problem with no a priori information on correspondence or initial transformation and no scaling effects, namely the KH and the

umbilic method. The KH method establishes a correspondence between two objects by utilizing the Gaussian and mean

curvatures.

▲

Umbilical points -definition:

Umbilicus =navel (a) The mark on the surface of the abdomen of mammals where the umbilical cord wasattached during

Gestation. Also called umbilicus (b). A central point; a middle Middle English, from Old English nafela;

In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface that are

locally spherical. At such points the normal curvature in all directions are equal, hence, both principal curvatures are equal,

and every tangent vector is a principal direction. The name "umbilic" comes from the Latin umbilicus that means navel

The umbilic method uses the qualitative properties of umbilical points to find correspondence information between two

objects. These two methods are extended to deal with uniform scaling effects. The umbilic method is enhanced with an

algorithm for scaling factor estimation using the quantitative properties of umbilical points. The KH method is used as a

building block of an optimization scheme based on the golden section search which recovers iteratively an optimum scaling

factor. Since the golden section search only requires an initial interval for the scaling factor, the solution process is simplified

compared to iterative optimization algorithms, which require good initial estimates of the scaling factor and the rigid body

transformation. The matching algorithms are applied to problems of copyright protection. A suspect model is aligned to an

original model through matching methods so that similarity between two geometric models can be assessed to determine if

the suspect model contains part(s) of the original model. Three types of tests, the weak, intermediate and strong tests, are

proposed for similarity assessment between two objects. The weak and intermediate tests are performed at node points

obtained through shape intrinsic wire framing. The strong test relies on isolated umbilical points which can be used as

fingerprints of an object for supporting an ownership claim to the original model. The three tests are organized in two decision

algorithms so that they produce systematic and statistical measures for a similarity decision between two objects in a

hierarchical manner. Based on the systematic statistical evaluation of similarity, a decision can be reached whether the suspect

model is a copy of the original model359..

359 Kwang Hee Ko (2003) Algorithms for Three-Dimensional Free-Form Object Matching” Submitted to the Department of Ocean Engineering on March 13, 2003, in partial fulfillment of the requirements for the degree of Doctor of Philosophy

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A vector field in a sphere

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A point A on the sphere corresponds to a point B on the plane when the three points N, A, and B are collinear. The only point

on the sphere that doesn't correspond to a point in the plane is the projection point N, and it corresponds to the point at

infinity, . Thus, we have a correspondence between the plane with a point of infinity with the sphere.

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The connection is just a way to relate the tangent spaces at different places on a manifold to one another, hence the name

"connection"

Sphere

we normally describe a sphere like this, with radius r:

Parametrically we can describe the coordinates for a point on the spheres surface like this:

Sphere

we normally describe a sphere like this, with radius r:

Parametrically we can describe the coordinates for a point on the spheres surface like this:

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PROOF THAT k is constant everywhere in the sfaire surface and hence any p in spfaire is a canditate point of the “win-win-win

papakonstantinidis function”(and hence, equilibrium):

REF

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Nash John Forbes ((1951 (1950))paper titled NON-COOPERATIVE GAMES, JOHN FORBS NASH (NOBEL PRIZE 1994) – EDITED IN Annals

of Mathematics Vol 54 No 2, September 1951

Capraro Valerio (2013) A Solution Concept For Games With Altruism And Cooperation Econometrica 45 (7) (1977), 1623-1630 Quora, 2015 March15

Osborne Martin J. and Rubinstein Ariel (1990) “Bargaining and Markets” ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers

Osborne Martin J. and Rubinstein Ariel (1990) “Bargaining and Markets” ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers John Forbs Nash(1950) TWO-PERSON COOPERATIVE GAMES August 31, 1950 -the RAND Corporation (P-172)

Osborne Martin J. and Rubinstein Ariel (1990) “Bargaining and Markets” ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Osborne, Martin (1994). A Course in Game Theory MIT Press Kalai, Ehud (1977). "Proportional solutions to bargaining situations: Inter-temporal utility comparisons" Econometrica 45 (7):

1623–1630

Kalai, Ehud (1977). "Proportional solutions to bargaining situations: Inter-temporal utility comparisons" Econometrica 45 (7): 1623–1630 Rawls John (1971) A theory of Justice Cambridge, Massachusetts: Belknap Press of Harvard University Press, 1971. Alexander, Jason McKenzie (2000). "Evolutionary Explanations of Distributive Justice" Philosophy of Science 67 (3): 490–516.

AND Alexander, Jason; Skyrms, Brian (1999). "Bargaining with Neighbors: Is Justice Contagious". Journal of Philosophy 96 (11):

588–598. AND Binmore, Kenneth (1998). Game Theory and the Social Contract Volume 2: Just Playing. Cambridge: MIT Press.

AND Binmore, Kenneth (2005). Natural Justice. New York: Oxford University Press.

Kalai Ehud (1975) "Other Solutions to Nash's Bargaining Problems," Econometrica, 1975 (with M. Smorodinsky

Kalai Ehud (2004) “Large Robust Games,” Econometrica, 2004

Kalai Ehud (1988) "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, 1988 (with W.

Stanford)

Capraro Valerio (2013) A Solution Concept For Games With Altruism And Cooperation Econometrica 45 (7) (1977), 1623-1630 Crawford Visent P.(1982) A Theory of Disagreement in Bargaining Econometrica, Volume 50, Issue 3 (May, 1982), 607-638.

Schelling, Thomas C. (1980). The Strategy of Conflict Harvard University Press p. 309

Kalai Ehud (1975) "Other Solutions to Nash's Bargaining Problems," Econometrica, 1975 (with M. Smorodinsky

Kalai Ehud (2004) “Large Robust Games,” Econometrica, 2004

Kalai Ehud (1988) "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, 1988 (with W. Stanford) Kalai Ehud (1993) "Rational Learning Leads to Nash Equilibrium," Econometrica, 1993 ( with E.

Lehrer)

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APPENDIX

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The universe

Earth

The concept of force

In classical mechanics, the concept of a `force’ is based on experimental observations that

everything in the universe seems to have a preferred configuration: – masses appear to attract

each other; objects with opposite charges attract one another; magnets can repel or attract

one another; But we don’t really know why this is (except perhaps the last one).

1. Force is associated with the body till it is in motion. 2. When a body is at rest the force

acting on it is zero. 3. Force is always in the same direction as the velocity of the body. 4. If

the velocity is changing then the force is also changing. 5. Centripetal force and centrifugal

force both act on the body moving uniformly in a circle. 6. The action-reaction forces act on

the same body. 7. The product of mass and acceleration is a force. 8. Only animate things like

people and animals exert forces; passive ones like tables, floors do not exert forces. 9. A force

applied by, say a hand, still acts on the object even after the object leaves the hand360.

The idea of a force is introduced to quantify the tendency of objects to move towards their

preferred configuration. If objects accelerate very quickly towards their preferred

configuration, then we say that there’s a big force acting on them. If they don’t move (or move

at constant velocity), then there is no force. We can’t see a force; we can only deduce its

existence by observing its effect. Specifically, forces are defined through Newton’s laws of

motion 0. A `particle’ is a small mass at some position in space.

1. When the sum of the forces acting on a particle is zero, its velocity is constant;

360 V. G. Jadhao Bhopal, India B. K. Parida “The Concept of Force” -epi-abs6-sindhu.pmd

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2. The sum of forces acting on a particle of constant mass is equal to the product of the mass

of the particle and its acceleration;

3. The forces exerted by two particles on each other are equal in magnitude and opposite in

direction. The second law provides the definition of a force – if a mass m has acceleration a,

the force F acting on it is

F =ma

The win-win-win papakonstantinidis model is defined in this domain:

1. Contact mechanics361 is the study of the deformation of solids that touch

each other at one or more points. The physical and mathematical formulation

of the subject is built upon the mechanics of materials and continuum

361 Johnson, K. L, 1985, Contact mechanics, Cambridge University Press.

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mechanics and focuses on computations involving elastic, visco-elastic, and

plastic bodies in static or dynamic contact. Central aspects in contact

mechanics are the pressures and adhesion acting perpendicular to the

contacting bodies' surfaces (known as the normal direction) and the frictional

stresses acting tangentially between the surfaces. This page focuses mainly

on the normal direction, i.e. on frictionless contact mechanics. Frictional

contact mechanics is discussed separately, focuses mainly on the normal

direction, i.e. on frictionless contact mechanics

2. In linear elasticity the equations describing the deformation of an elastic

body subject only to surface forces (&/or body forces that could be expressed

as potentials) on the boundary are (using index notation the equilibrium

equation:

where is the stress tensor and the Beltrami-Michell compatibility

equations:

1. STRESS TENSOR

2.

o GRAPHS:

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Stresses in a contact area loaded simultaneously with a normal and a tangential force.

Contact of an elastic sphere with an elastic half-space

4. 3D equilibrium of stress tensors

Cauchy stress tensor ,

In continuum mechanics, the Cauchy stress tensor ,true stress tensor,362 or simply called

the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor

consists of nine components that completely define the state of stress at a point inside a

material in the deformed state, placement, or configuration. The tensor relates a unit-length

direction vector n to the stress vectorT(n) across an imaginary surface perpendicular to n:

where,

The Cauchy stress tensor obeys the tensor transformation law under a change in the

system of coordinates. A graphical representation of this transformation law is

the Mohhr’ s circle for stress.

MATRIX

AN EXAMPLE:

)0,4,0(),1,3,2(),3,3,1(,...*)( cbacaxb

362 Fridtjov Irgens (2008), "Continuum Mechanics". Springer

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MATRIX

)()()( egdhcfgdibfheiaA

An example:

202404

)08(3)00(3)40)(1(

)0*34*)2(3)0*10*2(3)4*10*3)(1(

0...4...0...

1...3...2

3...3...1

*)(

caxb

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Now, we have to prove that a space curve with the identically zero torsion363 is contained in a

plane: Let k(s) > 0 be the curvature of the space curve as a function of the arc length

parameter s ∈ (a, b). By the fundamental theorem for plane curves there exists a plane curve

with this curvature function. Considered as a space curve, this curve has the same curvature

function and identically zero torsion. By the fundamental theorem for space curves, this plane

curve can be identified with the original space curve by a rigid motion of the space. Thus the

original curve is contained in a plane364

3. 3D Elasticity365

363 In the elementary differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the plane of curvature. Taken together, the curvature and the torsion of a space curve are analogous to the curvature of a plane curve- the notion of torsion is a manner of characterizing a twist or screw of a moving frame a around a curve 364 https://math.berkeley.edu/~giventh/hw140s.pdf 365 Suvranu De(2014) Introduction to 3D Elasticity MANE 4240 & CIVL 4240 Introduction to Finite Elements

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4.

Now, imagine a group of people acting in harmony in correspondence with the forces of the Earth and the universe.

The same forces in the natural world, logically should determine human behavior

The same rules that allow planets (either our own galaxy system or the more distant galaxy, not to collide (through the

attraction-repulsion forces) achieve coexistence everyone through very sensitive equilibrium of forces (equilibrium of

terror)

What do we want to prove, in relation with the “win-win-win papakonstantinidis equilibrium:

to find and identify a reliable utility function scope (Cu (x) in which maximized, not only for the two negotiators, but

also for the whole society (even for those who do not participate, but that do not even know this deal

DIFFERENTIAL CALCULUS AND INTEGRAL

The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the

concept of the function's integral

w

v

u

u

0

0

0

czyzxz

b

yzyxy

axzxyx

Xzyx

Xzyx

Xzyx

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The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the

concept of the function's integral

The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite

integration of a function is related to its anti-derivative and can be reversed by differentiation. This part of the

theorem is also important because it guarantees the existence of anti-derivatives for continuous functions

The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite

integral of a function can be computed by using any one of its infinitely-many anti-derivatives This part of the

theorem has key practical applications because it markedly simplifies the computation of definite integrals

INTEGRATION: Definitions:

5. Integration

o Mathematics,the operation of finding the integral

of a function or equation, especially solving a differential equation

o Behavior as of an individual, that is in harmony with the environment.

o Psychology, the organization of the constituentelements of the personality into a coordinate

d, harmonious whole.

o Social Integration in social sciences, is the movement of refugees and underprivileged

sections of a society into the mainstream of societies

o Racial Integration, refers to social and cultural behavior

o Economic Integration refers to trade unification between different states

o Educational Integration of students with disabilities

o Regional Integration, a process in which states enter into a regional agreement in order to

enhance regional cooperation through regional institutions and rules

o Horizontal Integration and vertical integration, in microeconomics and strategic

management, refer to a style of ownership and control

o Integration clause, in a contract, a term used to declare the contract the final and complete

understanding of the parties

o Integrated Production

o A step in the process of money laundering366

366 Money laundering is the process of transforming the proceeds of crime into ostensibly legitimate money or other assets.[1] However, in a number of legal and regulatory systems, the term money laundering has become conflated with other forms of financial crime, and sometimes used more generally to include misuse of the financial system (involving things such as securities, digital currencies, credit cards, and traditional currency), including terrorism financing and evasion of international sanctions.(wiki)

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o ECONOMICS

o Integration, in mathematics, the computation of a definite integral, a fundamental concept

of calculus, which allows, among many other uses, computing areas and averaging

continuous functions.

o Indefinite integration, in calculus, the process of calculating indefinite integrals, also known

as anti-derivatives

o Symbolic Integration the computation, mostly on computers, of anti-derivatives and definite

integrals in term of formulas

o Numerical integration, the numerical methods for computing, usually with computers,

definite integrals and, more generally, solutions of differential equations

o Integration is the "Reverse operation" of derivation and gives the basic methods calculating

the integrals. The most important point of the theory we are considering is this: If f (x) is a

function continuous on [a, b], then there is a differentiable function g (x) with the property g

'(x) = f (x) for each x, so the )()( agbg equal to the difference (B-A): the area of the

village A

)}(0],,[:),{( xfybaxyx

..minus the area of the village B

)}(0],,[:),{( xfybaxyx

Integration gives the area under the curve of the function )(xfy Areas can be added so

b

a

c

b

c

a

dxxfdxxfdxxf

thatfollowsitwhichfromcaAcbAbaA

)()()(

........),(),(),(

THE definite integrals:

Let us first look at how we define the area of the passage of X is limited by the graph of a continuous

positive function f (x) defined in the interval [a, b], and the lines x = a, x = b, y = 0, ie.

)}(0],,[:),{( xfybaxyxX

Divide the interval [a, b] into n equal-length intervals n

abx

each of which:

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"..."...........................,

............)(..........

,....2,1..]..,)1([

)(

].)1(...[...]2,[],[],[

limlim

1

1

XOFAREATHEISTHISnumberrealaisandexiststheAlso

XareaofapproachanisxxfthethatoutturnsIt

nkforxkaxkax

xxfE

xnaxnaxaxaxaaba

n

n

k

k

k

n

k

kn

E

DIFFERENTIAL GEOMETRY- DEFINITIONS:

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1. The branch of mathematics that deals with the application of the principles of differential and

integral calculus to the study of curves and surfaces367

2. Differential geometry is a mathematical discipline that uses the techniques of differential

calculus integral calculus linear algebra and multi-linear algebra to study problems in geometry.

The theory of plane and space curves and surfaces in the three-dimensional Euclidian space

formed the basis for development of differential geometry during the 18th century and the 19th

century. Differential Geometry has its origins in the discovery in the 17th century calculus. The

concept of derivative of a function is essentially identical to that of a tangent curve, or even with

the curve

3. DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES368 is the branch of geometry that deals with

smooth curves in the plane and in the Euclidean Space by methods of differential and integral

calculus Starting in antiquity, many concrete curves have been thoroughly investigated using

the synthetic approach Differential Geometry takes another path: curves are represented in a

parametrized form (see at below) and their geometric properties and various quantities

associated with them, such as the curvature and the arc length, are expressed via derivatives and

integrals using vector calculus One of the most important tools used to analyze a curve is the

Frenet frame, a moving frame that provides a coordinate system at each point of the curve that is

"best adapted" to the curve near that point.

4. The theory of curves is much simpler and narrower in scope than the theory of surfaces and its

higher-dimensional generalizations, because a regular curve in a Euclidean space has no intrinsic

geometry. Any regular curve may be parametrized by the arc length (the natural

parameterization) and from the point of view of a bug on the curve that does not know anything

about the ambient space, all curves would appear the same. Different space curves are only

distinguished by the way in which they bend and twist. Quantitatively, this is measured by the

differential-geometric invariants called the curvature and the torsion of a curve. The

367 Dictionary.com 368

Manfredo P. Do Carmo (1976) Differential Geometry of Curves and Surfaces Publisher: Pearson; 1st edition (February 11,

1976)

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fundamental theorem of curves asserts that the knowledge of these invariants completely

determines the curve.

THE TWO (2) FUNDAMENTAL FORMS

In differential geometry the first fundamental form is the inner product i on the tangent space of

a surface in three-dimensional Euclidean Space which is induced canonically form of the dot

product of R3. It permits the calculation of curvature and metric properties of a surface such as

length and area in a manner consistent with the ambient space The first fundamental form is

denoted by the Roman numeral I,

Let X(u, v) be a parametric surface Then the inner product of two tangent vectors is:

where E, F, and G are the coefficients of the first fundamental form.

The first fundamental form may be represented as a symmetry matrix

In differential geometry the fundamental theorem of space curves states that every regular curve in

three-dimensional space, with non-zero curvature, has its shape (and size) completely determined by its

curvature and torsion

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In differential geometry the second fundamental form (or shape tensor) is a quandic form of the

tangent plane of smooth surface in the three-dimensional Euclidean Space usually denoted

by (read "two"). Together with the first fundamental form it serves to define extrinsic

invariants of the surface, its principal curvatures. More generally, such a quadratic form is

defined for a smooth hyper-surface in a Riemannian manifold and a smooth choice of the unit

normal vector at each point.

The equations of a surface S in the Euclidean space with coordinates 321 ,, xxx can be given in

parametric form:

The equations of a surface S in the Euclidean space with coordinates x1, x2, x3 can be given in parametric

form

3.2,1),....,(

..3,2,1)....,(

21

21

iuu

andiuuxx

i

ii

so may also be assessed parametric components of unit

normal vector at any point on the surface S.

5. Since the late 19th century, differential geometry has grown into a field concerned more

generally with the geometric structures on differential manifolds Differential geometry is closely

related to differential topology and the geometric aspects of the theory of differential equations

The differential geometry of surfaces - captures many of the key ideas and techniques

characteristic of this field.

6. Differential geometry arose and developed as a result of and in connection to the mathematical

analysis of curves and surfaces. Mathematical analysis of curves and surfaces had been

developed to answer some of the nagging and unanswered questions that appeared in Calculus,

like the reasons for relationships between complex shapes and curves, series and analytic

functions These unanswered questions indicated greater, hidden relationships and symmetries in

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nature, which the standard methods of analysis could not address. When curves, surfaces

enclosed by curves, and points on curves were found to be quantitatively, and generally, related

by mathematical forms the formal study of the nature of curves and surfaces became a field of

study in its own right, with Monge’s paper in 1795369, and especially, with Gauss’s370 publication

of his article, titled “Disquisitiones Generales Circa Superficies Curvas”, in “Commentationes

Societatis Regiae Scientiarum Gottingesis Recentiores” in 1827. Besides, Gauß371 discovered that

every natural number can be expressed as the sum of one, two or three triangular numbers

«num = » which is one of the basic principles of the "win-win-win

papakonstantinidis model’s math approach»

7. Initially applied to the Euclidean space, further explorations led to non-Euclidean space, and

metric and topological spaces.

6. PARAMETERIZATION

Parameterization (or parameterization) is the process of deciding and defining the parameters necessary

for a complete or relevant specification of a model or geometric object. [citation needed]

Parameterization is also the process of finding parametric equations of a curve, a surface, or, more

generally, a manifold or a variety, defined by an implicit equation. The inverse process is called

implicitization.

Sometimes, this may only involve identifying certain parameters or variables. If, for example, the model is

of a wind turbine with a particular interest in the efficiency of power generation, then the parameters of

interest will probably include the number, length and pitch of the blades.

Most often, parameterization is a mathematical process involving the identification of a complete set of

effective coordinates or degrees of freedom of the system, process or model, without regard to their

369Monge, Gaspard.(1795) Une application d'analyse à la géométrie, 1795 2nd Edition Baudouin 370 Gauss(Gauß) Johann Carl Friedrich(1777-1855) (1827). “Commentationes Societatis Regiae Scientiarum Gottingesis

Recentiores” i etc Pars I(Allgemeine Untersuchungen über die unendliche Reihe 1+… Teil I; 30. Januar 1812), Commentationes Societatis Regiae Scientiarum Gottingensis recentiores 2 (classis mathematicae), 1813, S. 3–46 (lateinisch; auch in Gauss: Werke Bond 3 /. 123–162: 371 Gauss also discovered that every natural number can be expressed as the sum of one, two or three triangular numbers (on July 10) and then wrote in his diary the famous by Archimedes word "eureka!" And «num = \ Delta + \ Delta + \ Delta ». On October 1 he published a result on the number of solutions of polynomials with coefficients in finite fields

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utility in some design. Parameterization of a line, surface or volume, for example, implies identification of

a set of coordinates that allows one to uniquely identify any point (on the line, surface, or volume) with an

ordered list of numbers. Each of the coordinates can be defined parametrically in the form of a parametric

curve (one-dimensional) or a parametric equation (2+ dimensions).

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FUNDAMENTAL FORMS OF A GENERAL PARAMETRIC SURFACE

Classical notation

First fundamental: A smooth curve lying in the surface is a map t 7→ (u(t), v(t)) with derivatives

of all orders such that γ(t) = r(u(t), v(t)) is a parametrized curve in R3 .

The second fundamental form of a general parametric surface is defined as follows.

),(.. vurrLet Be a regular parameterization of a surface in 3R where r is a smooth vector

valued function of two variables. It is common to denote the partial derivatives of r with

respect to vu randrbyvandu ......,...... Regularity of the parameterization means

that vu randr .... are linearly independent for any (ump) in the domain of r, and hence span the

tangent plane to S at each point. Equivalently, the cross product vu rr * is a nonzero vector

normal to the surface. The parameterization thus defines a field of unit normal vectors n:

The second fundamental form is usually written as

its matrix in the basis {ru, rv} of the tangent plane is

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The coefficients L, M, N at a given point in the parametric uv-plane are

given by the projections of the second partial derivatives of r at that

point onto the normal line to S

MATRIX:

|A| = ad – bc ("The determinant of A equals a times d minus b times c")

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Although analytical investigations are often restricted to Gaussian fields, phenomena

described by nonlinear laws (such as the dynamics of inflation that produced the cosmic

background radiation) produce non-Gaussian signals. Quite often, the observable signal is

averaged over a large scale, producing approximately Gaussian statistics on account of the

central limit theorem, thus masking the nonlinearity. Nevertheless, the surviving tiny

departures from Gaussianity can carry a crucial signature of the nonlinear microscopic

mechanisms at the heart of the phenomena. As an illustration, consider a low-resolution

measurement of the spatial magnetization of a material well above the critical temperature.

The magnetization fluctuates like a Gaussian random variable—each region contains many

domains oriented up or down in arbitrary proportion. However, a small non-Gaussian

contribution remains, because there is a maximum possible magnetization per unit area that

can be traced all of the way down to the quantization of the spin of the electrons, and hence

the probability distribution cannot exhibit Gaussian tails.

To unveil such elusive effects, one needs an indicator that is sensitive to both short distances

and small signals. The most common tool used to probe the statistics of a random field is to

measure its correlation functions. For example, the statistical properties of a random scalar

field, , with Gaussian statistics, are entirely determined by its two-point correlation

function , and its higher-order correlation functions can be written simply as

the sum of products of two-point correlation functions. The non-factorizability of these

higher-order correlation functions is one of the standard indicators of non-Gaussian

statistics.

Here we focus on a more geometric approach: view the scalar field as the height of a surface

and study its random topography to infer the statistical properties of the signal (Fig. 1, Inset).

The densities of peaks and troughs, or of topological defects in the curvature lines known as

umbilics (Fig. 1), are sensitive indicators of how jagged the height field is at short distances;

as we shall see, they provide an independent pipeline to detect non-Gaussianities, distinct

from multiple-point correlation functions. This geometric approach has been applied

successfully to track the power spectrum of a Gaussian field, and it has been the subject of

extensive theoretical and experimental studies

EIGENVECTOR OR CHARACTERISTIC VECTOR

In linear algebra, an eigenvector or characteristic vector of a square matrix is a vector that

does not change its direction under the associated linear transformation. In other words—if v

is a vector that is not zero, then it is an eigenvector of a square matrix A if Av is a scalar

multiple of v. This condition could be written as the equation:

lvAv

where λ is a scalar known as the eigenvalue or characteristic value associated with the

eigenvector v.

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Geometrically, an eigenvector corresponding to a real, nonzero eigenvalue points in a

direction that is stretched by the transformation and the eigenvalue is the factor by which it is

stretched. If the eigenvalue is negative, the direction is reversed

Eigenvalue (IDIOTIMH) of a linear transformation \ Alpha is the change in meter (possibly in

time) of a vector, which is below the transformation \ Alpha remains unchanged as to the

address An \ Alpha is an n * n matrix, then a nonzero vector x in R ^ n called eigenvector of \

Alpha if the \ Alpha x is a scalar multiple of x. That is, if for some scalar value \ lambda

applies: \ Alpha x = \ lambda x then the scalar value \ lambda called eigenvalue of \ Alpha

and say that x is an eigenvector of \ Alpha corresponding to \ lambda.

There is a correspondence between n by n square matrices and linear transformations from

an n-dimensional vector space to itself. For this reason, it is equivalent to define eigenvalues

and eigenvectors using either the language of matrices or the language of linear

transformations.

In this shear mapping the red arrow changes direction but the blue arrow does not. The blue

arrow is an eigenvector of this shear mapping because it doesn't change direction, and since

its length is unchanged, its eigenvalue is 1.

///////////////////////////////////////////

We prove that the half-integer valued index of an isolated umbilic point on a smooth convex

surface in Euclidean 3-space is less than 2. This follows from a localization of the authors'

proof of the global Caratheodory conjecture.

The link between the two is a semi-local technique that we term "totally real blow-up".

Topologically, given a real surface in a complex surface, the totally real blow-up is the

connect sum of the real surface with an embedded real projective plane. We show that this

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increases the sum of the complex indices of the real surface by 1, and hence cancels isolated

hyperbolic complex points.

This leads to a reduction of the local result to the global result (the non-existence of

embedded Lagrangian surfaces with a single complex point), which proves that the umbilic

index for smooth surfaces is less than 2.

Comparison of our smooth result with that of Hans Hamburger in the real analytic case

(stating that the index of an isolated umbilic point on a real analytic convex surface is less

than or equal to 1) suggests the existence of "exotic" umbilic points of index 3/2372.

Foliation by Umbilic surfaces

Suppose (M,g) denotes a Riemannian manifold with boundary that is a foliation by Umbilic

surfaces. (As an example consider a manifold where the exists a unit parallel vector field) .

Is it realistic to try to show existence of other Umbilic surfaces in this manifold obtained via

Local diffeomorphisms for example tilting the leaves?

To clarify this question consider a manifold which has a unit parallel vector field , i.e a

cylinder.

Now if x3 denotes the transverse coordinate then the { x_3=c } surfaces are umbilic. On the

other hand if one takes the normal coordinates (x1,x2) on a leaf along with x3 as the new

coordinates then x2=c surfaces will also be umbilic!

CURVATURE o Principal curvatures of the surface S at the point p .

o Lines of curvature on a surface.

o Definition of Gaussian curvature and mean curvature.

o Definition of umbilical points on a surface. ▲

o Theorem. If all points of a connected surface S are umbilical points, then S is

contained in a sphere or a plane.\

372 Brendan Guilfoyle, Wilhelm Klingenberg (2012) From Global to Local: an index bound for umbilic points on smooth convex

surfaces Cornell University Library, / Mathematics (Submitted on 25 Jul 2012)

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Curvature tells how the length of a curve changes as the curve is deformed. If an infinitesimal piece of a

planar curve ds is pushed a distance du in the direction of k

the length changes by a factor of kdu1 Indeed, the original arc lies to second order on a circle of

radiusk

1 and the new one on a circle of radius kdu

kduk

1

11

Curvature in 3D

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In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the

case of a line, but this is defined in different ways depending on the context. There is a key distinction

between extrinsic curvature, which is defined for objects embedded in another space (usually a Euclidean

space) in a way that relates to the radius of curvature of circles that touch the object, and intrinsic

curvature, which is defined at each point in a Riemannian manifold. This article deals primarily with the

first concept.

Curvature of curves on a surface

The Curvatures of Curves on a Surface:

Normal and

Geodesic Curvatures

If a is a curve, parametrized by its arc-length, then its curvature is

)()( tatk

The curvature tells us the geometry of the curve (especially it tells us how the curve is turned).

Let a be a unit-speed curve

acurvetheto

VECTORBINORMALthecalledistBThentxNtTtBLet

vectornormalprincipalthecalledistNtTtTtNLet

acurvethetoVECTORTANGENTunitthecalledisTtatT

......

.........)..(,..)..()()(..

...........)..(.)(/)()(..

....................)...()(

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Note that the vectors },,{ BNT are perpendicular to each other. They form an orthonormal basis373

for3R

In particular

setlorthonormaanisB

jifor

jiforvv

othereachtoorthogonalarevectorstheofall

normalizedbeenallhavethey

vv

lengthahaveBinvectorstheall

kiallforvvvvB

ji

ji

ik

.........

.....,1

..,0

..............

........

1*

1.................

,..2,1......1....... 21

Let M be a surface in 3R and let MP be a point. Let )(MTPv be a unit tangent vector. We

want to introduce the concept of the normal curvature of M at P in the direction v.

To do so, take any arc-length parametrized curve α in M such that vaPa )0(,)0( (passing

through the point P and having v as its tangent vector at P) The value of the normal curvature of a at

the point P (i.e. t = 0) is independent of the choice of α, only depends on the unit-tangent vector v

The intersection of a normal plane and the surface will form a curve called a normal section and

the curvature of this curve is the normal curvature.

NOTES:

In mathematics, an implicit equation is a relation of the form R(x1,..., xn) = 0, where R is a function of

several variables (often a polynomial). For example, the implicit equation of the unit circle is

373 Lay, David C. (2006). Linear Algebra and Its Applications (3rd ed.) In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other

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0122 yx

This implicit equation defines f as a function of x only if -1 ≤ x ≤ 1 and one considers only non-negative

(or non-positive) values for the values of the function. An implicit function is a function that is defined

implicitly by an implicit equation, by associating one of the variables (the value) with the others (the

arguments)

In the mathematical field of algebraic geometry, a singular point of an algebraic variety V374 is

a point P that is 'special' (so, singular), in the geometric sense that at this point the tangent

space at the variety may not be regularly defined. In case of varieties defined over the reals,

this notion generalizes the notion of non-local flatness375. A point of an algebraic variety

which is not singular is said to be regular. An algebraic variety which has no singular point is

said to be non singular or smooth376.

For example, the plane algebraic curve (a cubic curve) of equation 0)1(22 xxy which

is plotted below, crosses itself at the origin (0,0) and the origin is thus a double point of the

curve. It is singular because a single tangent may not be correctly defined there377.

The canonical example of extrinsic curvature is that of a circle, which everywhere has

curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence

have higher curvature. The curvature of a smooth curve is defined as the curvature of its

osculating circle at each point.

374 Mazur, Barry(1959). On embeddings of spheres Bulletin of the American Mathematical Society, Vol. 65 (1959), no. 2, pp. 59-

65 375 LOCAL FLATNESS: Suppose a d dimensional manifold N is embedded into an n dimensional manifold M (where d < n).

If we say N is locally flat at x if there is a neighborhood of x such that the topological

pair is homeomorphic to the pair , with a standard inclusion of as a subspace of . That

is, there exists a homeomorphism such that the image of coincides with .

376 Brown, Morton (1962), Locally flat imbeddings of topological manifolds. Annals of Mathematics, Second series, Vol. 75

(1962), pp. 331-341. 377 John Milnor (1969) Singular Points of Complex Hyper-surfaces Annals of Mathematics Studies 61 Princeton University Press

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In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a

point P that is 'special' (so, singular), in the geometric sense that at this point the tangent

space at the variety may not be regularly defined. In case of varieties defined over the reals,

this notion generalizes the notion of non-local flatness. A point of an algebraic variety which

is not singular is said to be regular. An algebraic variety which has no singular point is said to

be non singular or smooth.

A curve can be described, and thereby defined, by a pair of scalar fields: curvature and

torsion, both of which depend on some parameter which parameterizes the curve but which

can ideally be the arc length of the curve. From just the curvature and torsion, the vector fields

for the tangent, normal, and bi-normal vectors can be derived using the Frenet-Serret

formulas378. Then, integration of the tangent field (done numerically, if not analytically) yields

the curve

378 Toulouse Frenet(1847) The doctoral thesis there which he submitted in 1847. His thesis was entitled Sur les fonctions qui

servent à déterminer l'attraction des sphéroides quelconques. Programme d'une thèse sur quelque propriétés des courbes à

double courbure and published in Toulose in 1847 – Serret Joseph Alfred (1851) Traité de trigonométrie Paris: Gautier-

Villars, 1880: In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along

a continuous, differentiable curve in three-dimensional Euclidean space ℝ3, or the geometric properties of the curve itself

irrespective of any motion. More specifically, the formulas describe the derivatives of the so-called tangent, normal, and

binormal unit vectors in terms of each other. The formulas are named after the two French mathematicians who independently

discovered them: Jean Frédéric Frenet, in his thesis of 1847, and Joseph Alfred Serret in 1851.

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the Frenet-Serret formulas

Definition of Gaussian Curvature379

For an intuitive understanding, imagine a flat sheet of paper (or just grab one in your hand). It

has zero Gaussian curvature. If you take that sheet and bend it or roll it up into a tube or twist

it into a cone, its Gaussian curvature stays zero.

Indeed, since paper isn't particularly elastic, pretty much anything you can do to the sheet that

still lets you flatten it back into a flat sheet without wrinkles or tears will preserve its Gaussian

curvature. Now take that sheet and wrap it over a sphere. You'll notice that you have to wrinkle

the sheet, especially around the edges, to make it conform to the sphere's surface. That's

because a sphere has positive Gaussian curvature, and so the circumference of a circle drawn

on a sphere is less than π π times its diameter. The wrinkles on the paper are where you have

to fold it to get rid of that excess circumference.

Similarly, if you tried to wrap the sheet of paper over a saddle-shaped surface, you'd find that

you would have to tear it (or crumple it in the middle) to make it lie on the surface. That's

because, on a surface with negative Gaussian curvature, the circumference of a circle is longer

than ππ times its diameter, and so, to make a flat sheet lie along such a surface, you either

have to tear it to increase the circumference, or wrinkle it in the middle to reduce the radius.

Indeed, in nature, plants can produce curved or wrinkled leaves simply by altering the rate at

which the edges of the leaf grow as compared to the center, which alters the Gaussian

curvature of the resulting surface, as in this picture of ornamental kale

:

379 The normal (or Gaussian) distribution is a very common continuous probability distribution Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known The normal distribution is remarkably useful because of the central limit theorem In its most general form, under some conditions (which include finite variance ), it states that averages of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of random variables is sufficiently large.

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If we focus on a more geometric approach, then it’s easy to note that: : view the scalar field as the height of a surface and study its random topography to infer the statistical properties of the signal (Fig. 1, Inset). The densities of peaks and troughs, or of topological defects in the curvature lines known as umbilics (Fig. 1), are sensitive indicators of how jagged the height field is at short distances; as we shall see, they provide an independent pipeline to detect non-Gaussianities, distinct from multiple-point correlation functions. This geometric approach has been applied successfully to track the power spectrum of a Gaussian field, and it has been the subject of extensive theoretical and experimental studies

The Gaussian curvature: DEFINITION

Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a foundational result

in differential geometry proved by Carl Friedrich Gauss that concerns the

curvature of surfaces.

Gauss presented the theorem in this way (translated from Latin):

The Gaussian curvature is the ratio of the solid angle subtended by the normal projection of a

small patch divided by the area of that patch.

The fact that this ratio is based totally on the definition of distance within the surface

(independent of the embedding of the surface; that is, bending and twisting, etc.) is

Gauss' Theorema Egregium

The Gaussian curvature of surfaces

The theorem says that the Gaussian curvature of a surface does not change if one bends the

surface without stretching it. In other words, Gaussian curvature can be determined entirely by

measuring angles, distances and their rates on the surface itself, without further reference to

the particular way in which the surface is embedded in the ambient 3-dimensional Euclidean

space. Thus the Gaussian curvature is an intrinsic invariant of a surface.

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Thus the formula of the preceding article leads itself to the remarkable Theorem. If a curved

surface is developed upon any other surface whatever, the measure of curvature in each point

remains unchanged.

The theorem is "remarkable" because the starting definition of Gaussian curvature makes

direct use of position of the surface in space. So it is quite surprising that the result

does not depend on its embedding in spite of all bending and twisting deformations

undergone.

In modern mathematical language, the theorem may be stated as follows:

The Gaussian Curvature of a surface is invariant under local isometric

A sphere of radius R has constant Gaussian curvature which is equal to 1/R2. At the same

time, a plane has zero Gaussian curvature. As a corollary of Theorema Egregium, a piece of

paper cannot be bent onto a sphere without crumpling. Conversely, the surface of a sphere

cannot be unfolded onto a flat plane without distorting the distances. If one were to step on

an empty egg shell, its edges have to split in expansion before being flattened. Mathematically

speaking, a sphere and a plane are not isometric, even locally. This fact is of enormous

significance for cartography: it implies that no planar (flat) map of Earth can be perfect, even

for a portion of the Earth's surface. Thus every cartographic projection necessarily distorts at

least some distances (APPENDIX)

Surfaces in3R are examined:

o sphere: SPHEREvkavjuaviuavur .....cos......sin..cos..sin.sin.),(

o torus: TORUSukbvjviubavur ....sin.).sin.)(cos.cos.(),(

o CYLINDERukvjviavur ...).sin.(cos),(

PRINCIPAL CURVATURES

In differential geometry, the two principal curvatures at a given point of a surface are the

eigenvalues of the shape operator at the point. They measure how the surface bends by

different amounts in different directions at that point At each point p of a differentiable

surface in 3-dimensional Euclidean space one may choose a unit normal vector. A normal

plane at p is one that contains the normal vector, and will therefore also contain a unique

direction tangent to the surface and cut the surface in a plane curve, called normal section.

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This curve will in general have different curvatures for different normal planes at p. The

principal curvatures at p, denoted k1 and k2, are the maximum and minimum values of this

SMOOTH SURFACE

:DEFINITION

tindependenlinearyaredv

rrvand

du

rrupoeachatordersallof

sderivativehasvuzvuyvuxvureomorphismaisUVr

thatsuchRVsetopenanfromRVrmapaandXUoodneighbourha

haspoeachthatsuchRXsubsetaisRinsurfacesmootheA

........int..........

....))..,(),,(),,((),(..hom......:

................:............

..int........................

23

33

DEFINITION (2) A surface parameterized in variables and is called smooth if the tangent

vectors in the and directions satisfy

where is a cross product

Smooth manifolds and smooth maps

The principal curvature of a surface

The major and minor axes of the small ellipses represent the direction and relative size of

maximum and minimum curvature at the center, equivalent to the direction of maximum and

minimum polarization for an optical field. The curvature lines are always tangent to the

direction of maximal curvature. At some points the curvature is the same along all directions

(the equivalent polarization is circular); these are called umbilical points, of which there are

three types, all shown in this image: (Upper Left) Lemon; (Upper Right) star; (Lower Right)

monstar. The circles demonstrate their topological indices: for a star, for the other

two. The lemon has one (locally) straight curvature line terminating at it (indicated with a thick

line), the other two have three. (Inset) Computer-generated Gaussian surface with periodic

boundary conditions, a small square of which served as the source of this picture

In this paper, we introduce the key physical concepts and mathematical techniques necessary

to study the stochastic geometry of signals that can be described as a Gaussian random field

plus a perturbation that we wish to track. We first show how to treat non-Gaussianities within

a local approximation and calculate how the statistics of extrema change when a nonlinear

transformation is applied locally to a Gaussian field . Then we consider the case

of fields that cannot be probed directly, by calculating the statistics of umbilical points, which

are topological defects of the lines of principal curvature Finally, we turn to a class of

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nonlinear diffusion and go beyond the local approximation by considering the effects of

spatial gradients that couple values of the field at different locations. As an illustration, we

solve explicitly for the nonlocal non-Gaussianities generated dynamically by the

deterministic Kardar-Parisi-Zhang (KPZ) equation, which models surface growth

The surface normal is a vector function

The unit normal is a smooth vector function of the coordinate of the point on the surface so

),,( zyx nnnn is a smooth function of ).,( zyx that satisfies the equation of surface. A

surface is generally parametrized through two variables, e.g., ),( vur The smooth typically

means twice continuously differentiable

A surface (in 3R ) can be given

3

2

............))..,(),,(),,((),(,..

......

............)..(),(),(

RINTOAfrommapaisvuzvuyvuxvurso

RAsubsetafrom

parametersarevanduwhereuvzzuvyyuvxx

Whenever you fix any parameter, say, u , you'll obtain a curve on your surface, so, if it is

possible (if these functions are differentiable) you can define tangent vectors uv rr , (they are

partial derivatives of rr with respect to respective parameters) for these curves. In some good

cases these two vectors will not be parallel and thus will form the base of a tangent plane (but

it doesn't always exist, consider the top of a cone) to your surface at any given

point ),( vu Then you can calculate the normal vector of unit length at any point ),( vu by

computing the cross product of uv randr .. dividing it by its length. In this way you'll obtain a

function ),( vun it must be continuous differentiable380

DEFINITION 4 SMOOTH MANIFOLD

Another word for a C^infty (infinitely differentiable) manifold, also called a differentiable

manifold. A smooth manifold is a topological manifold together with its "functional structure"

(Bredon 1995) and so differs from a topological manifold because the notion of

differentiability exists on it. Every smooth manifold is a topological manifold, but not

necessarily vice versa. (The first nonsmooth topological manifold occurs in four dimensions.)

Milnor (1956) showed that a seven-dimensional hypersphere can be made into a smooth

manifold in 28 ways.

380

Mathematics, http://math.stackexchange.com/questions/448979/what-is-a-smooth-surface#comment964707_448979

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GRAPH

Lines of curvature on an ellipsoid showing umbilic points

configurations of lines of curvature near umbilics

Star

Monstar

Lemon

Computer representation of an Umbilic Torus

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The classification of umbilics is closely linked to the classification of real cubic

forms .

A cubic form will have a number of root lines such that the cubic form is zero for all

real . There are a number of possibilities including:

Three distinct lines: an elliptical cubic form, standard model .

Three lines, two of which are coincident: a parabolic cubic form, standard

model .

A single real line: a hyperbolic cubic form, standard model .

Three coincident lines, standard model

The equivalence classes of such cubics under uniform scaling form a three-dimensional real

projective space and the subset of parabolic forms define a surface – called the umbilic

bracelet by Christopher Zeeman Taking equivalence classes under rotation of the coordinate

system removes one further parameter and a cubic forms can be represent by the complex

cubic form with a single complex parameter . Parabolic

forms occur when , the inner deltoid, elliptical forms are inside the

deltoid and hyperbolic one outside. If and is not a cube root of unity then the

cubic form is a right-angled cubic form which play a special role for umbilics.

If then two of the root lines are orthogonal

Fundamental Forms in determining the metric properties of a surface

There are three types of so-called fundamental forms381. The most important are the first

and second (since the third can be expressed in terms of these). The fundamental forms are

extremely important and useful in determining the metric properties of a surface, such as Line

element line element, area element, normal curvature Gaussian curvature and mean curvature

. Let be a regular surface with points in the tangent space of . Then the first

fundamental form is the inner product of tangent vectors,

(1)

For , the second fundamental form is the symmetric bilinear form on the tangent

space ,

381 Mary Gray 1997, Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition CRC Press, 29 Δεκ

1997

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papakonstantinidis Page 312

(2)

where is the shape operator . The third fundamental form is given by

(3)

The first and the second fundamental forms satisfy

(4)

(5)

where is a regular patch and and are the partial derivatives of with respect

to parameters and , respectively. Their ratio is simply the normal curvature

(6)

for any nonzero tangent vector. The third fundamental form is given in terms of the first and

second forms by

(7)

where is the mean curvature and is the Gaussian curvature

The first fundamental form (or line element) is given explicitly by the Riemannian metric

Riemannian metric

(8)

It determines the arc length of a curve on a surface. The coefficients are given by

(9)

(10)

(11)

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The coefficients are also denoted , , and . In curvilinear coordinates

(where ), the quantities

(12)

(13)

are called scale factors

The second fundamental form is given explicitly by

where

(15)

(16)

(17)

and are the direction cosines of the surface normal. The second fundamental form can also

be written

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

where is the NORMAL VECTOR

(14)

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papakonstantinidis Page 314

(26)

(27)

(28)

The torsion of a space curve sometimes also called the "second curvature" (Kreyszig 1991,

p. 47) 382 , is the rate of change of the curve's osculating plane . The torsion is positive for

a right-handed curve, and negative for a left-handed curve. A curve with curvature is

planar iff .

The torsion can be defined by

(1)

where is the unit normal vector and is the unit bi-normal vector. Written explicitly in

terms of a parameterized vector function ,

(2)

(3)

(Gray 1997, p. 192)383, where denotes a scalar triple product384 and is the radius of

curvature

The quantity is called the radius of torsion and is denoted or .

▲

382. Kreyszig, E. (1991)"Torsion." §14 in Differential Geometry. New York: Dover, pp. 37-40, 1991.

383 Gray, A. (1997)"Drawing Space Curves with Assigned Curvature." §10.2 in Modern Differential Geometry of Curves and

Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 222-224, 1997 384 Papakonstantinidis, 2015”corresponding in the “win-win-win” concept

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Definition The maximum normal curvature k1 and the minimum normal curvature k2 are called the

principal curvatures of the surface S at the point p . The corresponding (orthogonal) directions are called

the principal directions at p

22 yxz

Quadric surfaces are the graphs of quadratic equations in three Cartesian variables in space. Like the

graphs of quadratics in the plane, their shapes depend on the signs of the various coefficients in their

quadratic equations.

Spheres and Ellipsoids: A sphere is the graph of an equation of the form x2 + y2 + z2 = p2 for some real

number p. The radius of the sphere is p (see the figure below). Ellipsoids are the graphs of equations of

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the form ax2 + by2 + cz2 = p2, where a, b, and c are all positive. In particular, a sphere is a very special

ellipsoid for which a, b, and c are all equal.

x2 + y2 + z2 = 4

Paraboloids

Surfaces whose intersections with planes perpendicular to any two of the coordinate axes are parabolas in

those planes are called paraboloids. An example is shown in the figure below -- this is the graph

of z = x2 + y2.

The surface in the following figure is the graph of z = x2 - y2. In this case, the intersections with planes

perpendicular to the x- and y-axes are still parabolas, but the two sets of parabolas differ in the direction

in which they point. For reasons we will see, this surface is called a hyperbolic paraboloid -- and, for

obvious reasons, it is also called a "saddle surface."

SPHERE

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DEFINITION: A point p on a surface S where the two principal curvatures are equal, 21 kk is called an

umbilical point. This includes the planar points, where 021 kk

Examples. All points of a sphere are umbilical points. The point (0, 0, 0) is an umbilical point on the

paraboloid22 yxz

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we normally describe a sphere like this, with radius r:

Parametrically we can describe the coordinates for a point on the spheres surface like this:

A parametrized curve means that:

0).',.'..(.........

..........,.

.....,,,,....

0.'.''

..

,,......)..(),(

vutoequivalentisconditionthis

sotindependenlineararerr

thatimpliessurfaceaofdefinitionthe

vrur

and

ordersallofsderivativehavetvtu

vu

vu

SPHERE

22222

222

sin

..............

..,...0..,...sin...

...

..sin....cos....cos..sin....

.,....sin....sin...sin....cos..

..cos..sin..cos..sin..sin.),(

vduadva

formlfundamentafirstthegetwesoand

arrGrrFvarrE

thatso

vkavjaviuar

vjuaviuar

gives

vkavjuaviuavur

vvvuuu

v

u

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papakonstantinidis Page 319

Umbilical Points385

DEFINITIONS:

DEFINITION: A point p on a surface S where the two principal curvatures are equal, 21 kk

is called an umbilical point. This includes the planar points, where 021 kk

Examples. All points of a sphere are umbilical points. The point (0, 0, 0) is an umbilical

point on the paraboloid 22 yxz

385 Peter T. Sander, and Steven W. Zucker, “S in gu l ar i t ie s o f P r in c i pa l D i r e c t io n F ie ld s f r om 3 - D I m age s ”

DEFINITION 1

An umbilical point, (also called simply an umbilic), is a point on a surface at which the curvature is the same in any direction.

all the normal curvatures are equal in all directions and hence principal directions are indeterminate (MIT DEC 2009) Thus, the orthogonal net of lines of curvatures become singular at an umbilic

A principal curve on a surface is a curve whose velocity always points in a principal direction, that is, a

direction in which the normal curvature is a maximum or a minimum. In Section 19.1, we derive the

differential equation for the principal curves on a patch in R3 and give examples of its solution. As in

Section 18.2, the idea then is to re-parameterize a surface with specified coordinate curves.

An umbilic point on a surface is a point at which the principal curvatures are equal, so that at such

a point it is not possible to distinguish principal directions. Every point of a sphere is an umbilic

point. If a regular surface M C R3 consists entirely of umbilic points, then it is (perhaps not

surprisingly) part of a plane or sphere. For surfaces such as an ellipsoid

with a, b, c distinct, the umbilic points are isolated and can be considered to be degenerate principal

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As well as being mathematically interesting in its own right the differential geometry of curved surfaces is important in a number of physical problems. This work takes into consideration the

classification and statistics of the simplest singular points386 on a surface Σ that do not depend on the orientation of Σ in space. These are the 'umbilic points', defined as places where the two principal curvatures of Σ are equal. In optics Σ might be a smooth wave-front produced for example by transmission of a plane wave through an irregular refracting medium or reflection from an undulating surface. Then the normals to Σ are the rays of geometrical optics; the rays through umbilic points on Σ pass through the singular 'anastigmatic points' of the 'focal surface' that consists of the envelope of all

the rays. It is near these focal points that the wave attains its greatest intensity (Berry 1976)387.

Conclusions (Berry 1975):

386 In mathematics a singularity is in general a point at which a given mathematical object is not defined, or a point of an

exceptional set where it fails to be well- behaved in some particular way, such as differentiability

For example, the function on the real line has a singularity at x = 0, where it seems to "explode" to ±∞ and is not

defined. The function g(x) = |x| (see absolute value) also has a singularity at x = 0, since it is not differentiable there. Similarly,

the graph defined by y2 = x also has a singularity at (0,0), this time because it has a "corner" (vertical tangent) at that point. The

algebraic set defined by in the (x, y) coordinate system has a singularity (singular point) at

(0, 0) because it does not admit a tangent there. 387

Berry M V and Hannay J H (1977) Umbilic points on Gaussian random surfaces”- J. Phys A: Math. Gen., Vol. 10, No. 11,

1977. Printed in Great Britain 1977

curves. In fact, each looks very much like a navel, hence the name. The four umbilic points on an ellipsoid (with a, b, c distinct) are easy to locate visually, provided one draws the ellipsoid

An obvious example of a surface consisting entirely of umbilical points is a sphere

Actually, spheres and planes are the only surfaces, all of whose points are umbilical The number of umbilics on a surface is often finite and they are isolated

Umbilics has generic futures and may act as fingerprints for shape recognition

At un umbilic the directions of principal curvature can no longer be evaluated by second order derivatives and higher order derivatives are necessary to compute the lines of curvature, near the umbilic

This is also the domain of "win-win-win papakonstantinidis model": This is the proposal of a new form of social welfare, based on the interaction of human behavior in relation with the choices that people make in order to take a decision:

A s m o o t h c u r v e l y i n g i n t h e s u r f a c e i s a m a p t — (u(t),v(t)) w i t h d e r i v a t i v e s o f a l l o r d e r s s u c h t h a t :

3.........))..(),(()( Rincurveedparametrizistvturt

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“a figure of any given shape determined by the ratio u is e qu a l l y l i k e l y to be found in any

orientation388. (see at the scheme below)

Dupin’s Theorem:

In three mutually orthogonal systems of surfaces, the lines of curvature on any surface in one

of the systems are its intersections with the surfaces of the other two systems.

Representation of the cubic expansion near an umbilic point: the win-win-win domain

Representation of the cubic expansion near an umbilic point by figures in the Argand diagram, generated by the resultant

of three rotating vectors, one turning three times as fast as the other. The ratio U of the lengths of these vectors

determines the shape of each figure and the resulting sector angles determine the chance that the umbilic is elliptic (for U

< 1) and lemon (for U > 1).(Berry, 1976)389

388 Berry, M V, 1975, Surface Science, Vol 1, 291-327, ‘Liquid Surfaces’, IAEA-SMR-15/9 389 Berry, M V, 1976, , ‘Waves and Thom’s theorem” Advances in Physics, 25, 1-26

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Necessary Condition for Equilibrium: The necessary conditions for equilibrium are: (i) the vector sum of all external forces is zero. (ii) the sum of the moments of all external forces about any line is zero. EQUATIONS OF EQUILIBRIUM: When a body is in equilibrium, the net force and the net moment equal zero, i.e. F = 0 and M = 0 These two vector equations can be written as six scalar equations of equilibrium. These are FX = 0 FY = 0 FZ = 0 MX = 0 MY = 0 MZ = 0 6 equations for 3D equilibrium Note: The moment equations can be determined about any point. Usually, choosing the point where the maximum number of unknown forces are present simplifies the solution

▲

SPHERE

DEFINITION 2

In the differential geometry of surfaces in three dimensions, umbilics or umbilical

points are points on a surface that are locally spherical. At such points the normal

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curvature in all directions are equal, hence, both principal curvatures are equal, and every

tangent vector is a principal direction390

The sphere is the only surface with non-zero curvature where every point is umbilic.

A flat umbilic is an umbilic with zero Gaussian curvature.

An umbil ic point U on a surface Σ is a place where the two principal

curvatures of Σ are equal . U is a singularity of Σ in three different senses: ( i )

it is the source of elliptic (E) or hyperbolic (H) umbilic catastrophes in the

envelope of normals ( ' focal surface' ) of Σ ; ( i i ) it has index 2

1 depending on

whether the principal curvature directions of Σ (defining the lines of

curvature) rotate by during a circuit of U; ( i i i ) i t has a pattern of the

'star' (S) , ' lemon' (L) or 'monstar' (M) type depending on the configuration

of l ines of curvature near U 391.

DEFINITION 3: In the differential geometry of surfaces in three dimensions, umbilics or

umbilical points are points on a surface that are locally spherical. At such points the normal

curvature in all directions are equal, hence, both principal curvatures are equal, and every

tangent vector is a principal direction. The name "umbilic" comes from the Latin umbilicus -

navel392

Umbilic points generally occur as isolated points in the elliptical region of the surface; that is,

where the Gaussian curvature is positive.

The sphere is the only surface with non-zero curvature where every point is umbilic. A flat

umbilic is an umbilic with zero Gaussian curvature. The monkey saddle is an example of a

surface with a flat umbilic and on the plane every point is a flat umbilic.

The three main types of umbilic points are elliptical umbilics, parabolic umbilics and

390 http://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node183.html 391Berry M V and Hannay J H (1977) Umbilic points on Gaussian random surfaces”- J. Phys A: Math. Gen., Vol. 10, No. 11, 1977. Printed in Great Britain 1977 392 Darboux Gaston (1887,1889,1896), Leçons sur la théorie génerale des surfaces: Volume I, Volume II, Volume III, Volume IV, Gauthier-Villars

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hyperbolic umbilics.

Elliptical umbilics have the three ridge lines393 passing through the umbilic and hyperbolic

umbilics have just one.

Parabolic umbilics are a transitional case with two ridges one of which is singular. Other

configurations are possible for transitional cases. These cases correspond to the D4−, D5 and

D4+ elementary catastrophes

Umbilics can also be characterised by the pattern of the principal direction vector field

around the umbilic which typically form one of three configurations: star, lemon, and

lemonstar (or monstar). The index of the vector field is either −½ (star) or ½ (lemon,

monstar). Elliptical and parabolic umbilics always have the star pattern, whilst hyperbolic

umbilics can be star, lemon, or monstar (Darboux)394

Table: Four (4) types of explicit quadratic surfaces according to α and β

Other configurations are possible for transitional cases. We note “configurations of lines of

curvature near umbilics” as follow:

393 Porteous Ian (2001) Geometric Differentiation, Chapter 11 Ridges and Ribs, pp 182–97, Cambridge University Press: A

smooth surface in three dimensions has a ridge point when a line of curvature has a local maximum or minimum of principle

curvature The set of ridge points form curves on the surface called ridges The ridges of a given surface fall into two families,

typically designated red and blue, depending on which of the two principal curvatures has an extremum.

At umbilical points the colour of a ridge will change from red to blue. There are two main cases: one has three ridge lines

passing through the umbilic, and the other has one line passing through it. 394 Darboux Fred (2009) Function in a Hypersurface of a Riemannian Manifold with Semi-Symmetric Metric Connection” Oscillator with Discontinuity by Variational Approach", 1, No. 10, 2009 (Darboux classification)

Signs of α and β Types of surfaces Types of points at p

αβ<0 Hyperbolic paraboloid Hyperbolic point

αβ>0, and α # β Elliptic paraboloid Elliptic point

a=β Paraboloid of revolution Umbilical Point

α=0 or β=0 Parabolic cylinder Parabolic Point

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At such points the normal curvature in all directions are equal, hence, both principal

curvatures are equal, and every tangent vector is a principal direction. The name "umbilic"

comes from the Latin umbilicus - navel.

Lines of curvature on an ellipsoid showing umbilic points

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Paraboloid of revolution395:

Umbilic Points on a connected smooth surface problem396

Every point on S is umbilical → S is a plane or sphere

If every point in a surface 3RS is umbilical then it is contained in a

sphere or a plane. But this proof only works for open sets of S.

395 With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis. It is

the shape of the parabolic reflections, used in mirrors antenna, dishes, and the like; and is also the shape of the surface of a

rotating This shape is also called a circular paraboloid.

396 MATHEMATICS -wikilexikon

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In Manfredo's Differential Geometry of Curves and Surfaces397 is a proof that if this is true in

a neighborhood of pp, for all p∈Sp∈S, then the surface is contained in a plane or sphere. It is

the second part of the proof.

But at certain point he says "Since S is connected, given any other point rr in S there is a

continuous curve in rapathatsuchSIaS )1(,...)0(........:,

EXAMPLE:

Lemma A point p on a regular surface3RS is an umbilic point if and only if the shape

operator of M at p is a multiple of the identity.

Proof: Let Sp denote the shape operator of M at p. Then Sp is a multiple of the identity if

and only if all of the normal curvatures of M at p coincide. This is true if and only if the

maximum and minimum of the normal curvatures, namely, k1(p) and k2(p), coincide. Write

k(p) = k1(p) = k2(p); then Sp = k(p)I, where I denotes the identity map on Mp.

A topological space X is called locally398 path connected if every x∈X is contained in a

neighborhood U which is path connected.

If X is locally path connected, then it is connected if f it is path connected. We know that path

connected implies connected always. To see the reverse implication in this case:

Suppose X was not path connected. Then we can write X as a disjoint union of (at least two)

397 Manfredo P.Do Carmo (1976) Differential Geometry of Curves and Surfaces 1st Differential Geometry of Curves and

Surfaces 1st Edition

398Coppin, C. A. (1972), "Continuous Functions from a Connected Locally Connected Space into a Connected Space with a Dispersion Point", Proceedings of the American Mathematical Society (American Mathematical Society) 32 (2): 625–626

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path-connected components But each path component must be open, by the locally path

connected criteria.

Now, any manifold is locally homeomorphic to Rn, and since Rn is locally path connected, we

have that any manifold is locally path connected.

And so for a manifold, connectedness does imply path-connectedness

A differentiable manifold is a type of manifold that is locally399 similar enough to a linear

space to allow one to do calculus. Any manifold can be described by a collection of charts,

also known as an atlas. One may then apply ideas from calculus while working within the

individual charts, since each chart lies within a linear space to which the usual rules of calculus

apply. If the charts are suitably compatible (namely, the transition from one chart to another is

differentiable), then computations done in one chart are valid in any other differentiable

chart400

A non-differentiable atlas of charts for the globe The results of calculus may not be

compatible between charts if the atlas is not differentiable. In the center and right charts the

Tropic of Cancer is a smooth curve, whereas in the left chart it has a sharp corner. The notion

of a differentiable manifold refines that of a manifold by requiring the functions that

transform between charts to be differentiable

The near-Gaussian fields under investigation are not always directly accessible experimentally.

For example, the mass distribution along the line of sight responsible for weak gravitational

lensing is believed to be mostly composed of dark matter, and hence it cannot be detected

directly If the projected gravitational potential over a flat patch of the sky is taken to be the

height of a 2D surface the measurable shear field is given by the lines of principal curvature At

399 In mathematics, more specifically topology, a local homeomorphism is intuitively a function, f, between topological spacesthat preserves local structure.

400 Donalson Simon (1983) "An application of gauge theory to four-dimensional topology" Journal of Differential

Geometry 18 (2): 279–315

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some special points called umbilics, the curvature is equal in all directions, so the shear field

cannot be defined and it must vanish. More precisely, a point on a surface with

height function is an umbilic if the second derivatives satisfy the two

conditions and . The ratio between different types of umbilical points

(which is a universal number for an isotropic Gaussian field) serves as an indicator of non-

Gaussianities in lieu of the extrema, which cannot be detected. A similar reasoning can be

applied to study polarization singularities in the cosmic microwave background and

topological defects in a nematic or superfluid near criticality

o Inspection of fig 1 reveals that there are three types of umbilics: lemons, monstars,

and stars. Note that these umbilics are topological defects in the curvature-line field.

The topological index of any umbilic is equal to ±1/2, if the curvature-line field

rotates counterclockwise (clockwise) by an angle π along any closed path encircling

only that umbilic in the counterclockwise direction.

o A star has three curvature lines terminating at it and a topological index of .

o A lemon has only one line and index .

o A monstar has index , like a lemon, but three lines terminating at it, like a star. A

striking feature of isotropic Gaussian fields is that the monstar fraction, the relative

density of monstars with respect to all umbilics, equals ; this is a

universal number independent of the power spectrum Any deviation from this special

value is therefore a sure sign of non-Gaussian effects.

UMBILICS: SURFACES IN 3D SPACE

UMBILICAL, SPHERICAL AND PLANAR POINTS, SURFACES CONSISTING OF UMBILICS; SURFACES OF REVOLUTION, LINES OF

CURVATURE, PARAMETERIZATIONS FOR WHICH COORDINATE LINES ARE LINES OF CURVATURE, DUPIN'S THEOREM,

CONFOCAL SECOND ORDER SURFACES; RULED AND DEVELOPABLE SURFACES: EQUIVALENT DEFINITIONS, BASIC

EXAMPLES, RELATIONS TO SURFACES WITH K=0, STRUCTURE THEOREM.

A REGULAR PARAMETERIZED SURFACE 3: Rr (Ω IS AN OPEN SUBSET OF THE PLANE) HAS TWO PRINCIPAL

CURVATURES ),(...)..,( 21 vukandvuk AT EACH POINT ),( vurp OF THE SURFACE.

o IF ),(..)..,(),( 121 vukthenvukvuk IS THE MINIMUM OF NORMAL CURVATURES IN DIFFERENT

DIRECTIONS AT P, WHILE ),(2 vuk IS THE MAXIMUM OF THEM.

o IF ),(),( 21 vukvuk THEN THE PRINCIPAL DIRECTIONS CORRESPONDING TO

),(..)..,( 21 vukandvuk ARE UNIQUELY DEFINED, HOWEVER IF ),(),( 21 vukvuk THEN THE

NORMAL CURVATURE IS CONSTANT IN ALL DIRECTIONS AND EVERY DIRECTION IS PRINCIPAL.

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DEFINITION A POINT ),( vurp OF A SURFACE IS CALLED A UMBILICAL POINT OR UMBILIC IF THE PRINCIPAL

CURVATURES AT P ARE EQUAL. A UMBILICAL POINT Ρ IS SAID TO BE SPHERICAL IF 0),(),( 21 vukvuk AND

PLANAR IF 0),(),( 21 vukvuk

THE FOLLOWING THEOREM GIVES A CHARACTERIZATION OF THOSE SURFACES WHICH HAVE ONLY UMBILICAL POINTS: THEOREM A CONNECTED REGULAR SURFACE ALL POINTS OF WHICH ARE UMBILICAL IS CONTAINED IN A PLANE OR

SPHERE. PROOF: First we show that the principal curvature function kkk 21 is constant along the surface. Fixing a parameterization r, we have vvuu krNandkrN ..... since

vu randr .... are principal directions as any tangent vector is.

Differentiating the first equation with respect to v, the second with respect to u, we get:

uvvuuvuvuvuv krrkNandkrrkN .....

from which tconsiskifeikkifonlyholdcanequationlastthe

tindependenlinearlyarerandrSincerkrk

vu

vuvuuv

tan.........,..0...............

,...............

The Carathéodory conjecture explanation

The Carathéodory conjecture is a mathematical conjecture attributed to Constantin

Carathéodory by Hans Ludwig Hamburger in a session of the Berlin Mathematical Society in

1924, [1]. Other early references are the Invited Address [3] of Stefan Cohn-Vossen to

the International Congress of Mathematicians of 1928 in Bologna and the book [2]

by Wilhelm Blaschke. Carathéodory never committed the Conjecture into writing. In [1],John

Edensor Littlewood mentions the Conjecture and Hamburger's contribution [10] as an

example of a mathematical claim that is easy to state but difficult to prove. Dirk

Struik describes in [5] the formal analogy of the Conjecture with the Four Vertex Theorem for

plane curves. Modern references for the Conjecture are the problem list of Shing-Tung Yau in

[6] and the book [7] of Marcel Berger, as well as the books [18] and [19], [20], [21].

Mathematical content

The Conjecture claims that any convex, closed and sufficiently smooth surface in three

dimensional Euclidean space needs to admit at least two umbilic points. In the sense of the

Conjecture, the spheroid with only two umbilic points and the sphere, all points of which are

umbilic, are examples of surfaces with minimal and maximal numbers of umbilics. For the

conjecture to be well posed, or the umbilic points to be well-defined, the surface needs to be

at least twice differentiable.

Mathematical research on an approach by a local index estimate

For analytic surfaces, an affirmative answer to this conjecture was given in 1940 by Hans

Ludwig Hamburger in a long paper published in three parts [10]. The approach of Hamburger

was via a local index estimate for isolated umbilics, which he showed to imply the Conjecture

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in his earlier work [8], [9]. In 1943, a shorter proof was proposed by Gerrit Bol [11], see also

[23], but, in 1959, Tilla Klotz found and corrected a gap in Bol's proof in [10]. Her proof, in

turn, was announced to be incomplete in Hanspeter Scherbel's dissertation [13] (no results of

that dissertation related to the Carathéodory conjecture were published for decades, at least

nothing was published up to June 2009). Among other publications we refer to papers [14]—

[16].

All the proofs mentioned above are based on a reduction of the Carathéodory conjecture to

the following Loewner conjecture: the index of every isolated umbilic point is never

greater than one. Roughly speaking, the main difficulty lies in resolution of singularities

generated by umbilical points. All the above-mentioned authors resolve the singularities by

induction on 'degree of degeneracy' of the umbilical point, but none of them was able to

present the induction process clearly.

In 2002, Vladimir Ivanov revisited the work of Hamburger on analytic surfaces with the

following stated intent [17]:

"First, considering analytic surfaces, we assert with full responsibility that Carathéodory was

right. Second, we know how this can be proved rigorously. Third, we intend to exhibit here a

proof which, in our opinion, will convince every reader who is really ready to undertake a

long and tiring journey with us."

Umbilical points and maxima/minima of a function : regular smooth manifolds,

Two new methods are developed to solve a global and partial matching problem with no a

priori information on correspondence or initial transformation and no scaling effects, namely

the KH and the umbilic method. The KH method establishes a correspondence between two

objects by utilizing the Gaussian and mean curvatures. The umbilic method uses the

qualitative properties of umbilical points to find correspondence information between two

objects. These two methods are extended to deal with uniform scaling effects. The umbilic

method is enhanced with an algorithm for scaling factor estimation using the quantitative

properties of umbilical points. The KH method is used as a building block of an optimization

scheme based on the golden section search which recovers iteratively an optimum scaling

factor. Since the golden section search only requires an initial interval for the scaling factor,

the solution process is simplified compared to iterative optimization algorithms, which require

good initial estimates of the scaling factor and the rigid body transformation. The matching

algorithms are applied to problems of copyright protection. A suspect model is aligned to an

original model through matching methods so that similarity between two geometric models

can be assessed to determine if the suspect model contains part(s) of the original model.

Three types of tests, the weak, intermediate and strong tests, are proposed for similarity

assessment between two objects. The weak and intermediate tests are performed at node

points obtained through shape intrinsic wire framing. The strong test relies on isolated

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umbilical points which can be used as fingerprints of an object for supporting an ownership

claim to the original model. The three tests are organized in two decision algorithms so that

they produce systematic and statistical measures for a similarity decision between two objects

in a hierarchical manner. Based on the systematic statistical evaluation of similarity, a decision

can be reached whether the suspect model is a copy of the original model