Institutions and Games

Samuel BowlesUniversity of Siena & Santa Fe Institute

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Contracts

Individuals

Exogenous Enforcement

Endogenous Enforcement

Exogenous Preferences

Neoclassical (Walrasian) econ

Stiglitz, Holmstrom, Williamson, implementation theory

Endogenous Preferences

Hayek, Sen, Mill, evolutionary bargaining models

Post-Walrasian

Smith, Marx, Akerlof,

Other taxonomies would be illuminating, for example, concerning the content of preferences, e.g. self regarding or other regarding) and the role of positive feedbacks (generalized increasing returns) etc Background reading: Bowles, S. and H. Gintis. 2000. "Walrasian Economics in Retrospect." Quarterly Journal of Economics, 115:4, pp. 1411-39.

One roadmap of economics

• Try to answer a question that people are already asking. What’s the question?

• This means explaining something about how the world works that is not now understood. Whats the method?

• Purely theoretical investigations are very risky.• Empirical methods are important: econometrics,

history, experiments, agent based modeling, ethnography

Coordination failures and the classical constitutional conundrum?

• What are they?• Coordination failure: non cooperative interaction leading to

a result that is not P-efficient. • The conundrum: How can social interactions be structured

so that people are free to choose their own actions while avoiding outcomes that none would have chosen?

• Modern fields of econ addressing this question: welfare economics, implementation theory, optimal contract theory

• Game theory is the fundamental analytical tool for the study of economic institutions.

• The Pareto criterion (and its discontents)?

Questions for today

• What is it about the structure of payoffs in social interactions that makes Pareto inferior outcomes likely, while in others P-inferior outcomes are less difficult to avoid?

• How can (classical) game theory illuminate the way that institutions may address the classical conundrum?

• Postponed until later: behavioral foundations and evolutionary game theory: – Preferences

– Institutions as evolved rather than designed

– The practical (meaning evolutionary) relevance of NE

The classical conundrum: Hume’s meadow

• Two neighbors may agree to drain a meadow, which they possess in common; because 'tis easy for them to know each others mind; and each must perceive, that the immediate consequence of his failing in his part, is the abandoning of the whole project. But 'tis very difficult and indeed impossible, that a thousand persons shou'd agree in any such action; it being difficult for them to concert so complicated a design, and still more difficult for them to execute it; while each seeks a pretext to free himself of the trouble and expense, and wou'd lay the whole burden on others.

David Hume, A Treatise of Human Nature, (1739)

The classical constitutional conundrum: Rousseau’s stag hunt

This is how men could imperceptibly acquire some crude idea of mutual commitments and the advantages to be had in fulfilling them... Were it a matter of catching a deer, everyone was quite aware that he must faithfully keep to his post in order to achieve this purpose; but if a hare happened to pass within reach of one of them, no doubt he would have pursued it without giving it a second thought, and that, having obtained his prey he cared very little about causing his companions to miss theirs.

Jean-Jacques Rousseau, Discourse on the Origin and Foundations of Inequality among Men (1755)

Why do coordination failures occur, generically?

• The reason why uncoordinated activities of individuals pursuing their own ends often produce outcomes that all would seek to avoid is that each person’s actions affect the well-being of others and these effects are often not included in whatever optimizing process or rule of thumb which results in the actions taken by the relevant actors.

• More simply: actors to not take appropriate account of the effects of their actions on others.

• The problem thus concerns both preferences and constraints (e.g. people do not care about others, and they are not constrained to act as if they did care)

Preferences, beliefs and constraints (defined in ch 3)

• NB institutions are group level phenomena, while preferences and beliefs are facts about individuals:– Beliefs: an individual’s understanding of the relationship

between her actions and consequent outcomes.– Preferences: an individual’s evaluation of the outcomes.– Constraints: define the set of feasible actions

• Institutions constitute part of the constraints (you have to pay for the goods you acquire) and (as we will see) they also influence the evolution of beliefs and preferences.

Institutions

• What are they?• Institutions: the laws, informal rules, and conventions which

give a durable structure to social interactions among the members of a population based on – centrally deployed coercion (laws), – social sanction (informal rules) and – mutual expectations (conventions)

which make conforming to the institution a best response for virtually all members of the relevant group, given individual beliefs and preferences.

Tragedy of the Fishers: A Prisoners Dilemma Eye Jay 6 hours 8 hoursFish 6 hours 1,1 0, 1+Fish 8 hours 1+, 0 u, u

Coordination typically involves problems of both allocation and distribution as in the PD game.

What is the allocation problem here? What is the distribution problem?

Pure conflict and pure common interest games. What are they?

Cooperative

Non-cooperative

Common Interest Conflict

Wage bargaining

Language evolution

Labor discipline

Rules of the roadProperty rights (modern)

Contractual exchange

Evolution of norms Repayment of loans

Property rights (pre-state)

Crop shares

Tragedy of the Fishers: A Prisoners Dilemma Eye Jay 6 hours 8 hoursFish 6 hours 1,1 0, 1+Fish 8 hours 1+, 0 u, u

Common and conflicting interest

The degree of common interest: (1- u)/(1+)..or in this case the gain from cooperation by contrast to mutual defection relative to the gain from defecting on a cooperator Or more generally, the maximum difference between the payoffs possible when both choose the same action divided by the maximum difference when they choose different actions (SW to NE distance compared to SE to NW difference).

Risk dominance may be a better predictor of outcomes than payoff dominance (what do these terms mean?)

• Risk dominant strategy: in a 2x2 game the best response when one believes that the other is equally likely to play his two strategies is the risk dominant strategy. Planting late is risk dominant (p = fraction planting early).

• Risk dominant equilibrium: both players play their risk dominant strategies.

l

e

2

0

3

4

p* 1.00

Risk dominantequilibriium

Payoff dominantequilibrium

Basin of attractionof the risk dominantequilibrium

e a rly la te

e a rly 4 ,4 0 ,3

la te 3 ,0 2 ,2

l

e

2

0

3

4

p* 1.00

Figure 1.4 Planting late is risk dominant. Note: p = the fraction planting early; p* = 2/3 so l > e if p = ½.

Planting in Palanpur

Risk dominance and risk-dominant equilibria

P - in fe rio r N ashe x is ts

N o P- in fe r io r N a sh

N o P-o p tim u m is N a sh P riso ne rs ' d ile m m a R o c k , p a p er, sc isso rs

A P -op t im um is N ash A ssu ra nc e ga m e In v is ib le ha nd

A taxonomy of coordination failures (considering only pure strategies)

The mathematical representation of institutions

NB: Institutions: the laws, informal rules, and conventions which give a durable structure to social interactions. Three ways of representing institutions:

• As games (e.g principal agent models of wage setting)• As Nash equilibria of games (driving on the right as a

mutual best response) • As NE that are accessible and stable (has a ‘large basin

of attraction’) in a plausible dynamic (crop shares of one half as stochastically stable states)

Game theory and the theory of institutions: advantages and shortcomings• Advantages over non-strategic

approaches:– Explicit representation of

information and action sets– Subject-subject (strategic) vs

Subject object• Shortcomings (on which, more

later)– Limitations of the Nash

equilibrium (evolutionarily irrelevant equilibria)

– Cognitively implausible ‘refinements’

Desiderata for game theory: many important games are …

• Overlapping: one plays in many games simultaneously• Recursive: the structure of the game in subsequent periods

is an outcome of past play• Constitutive: past play of a game influences the preferences

and beliefs (and therefore payoffs and equilibrium strategies) in subsequent play

• Asymmetric: when members of different classes, species, sexes, nations, races, age cohorts, etc interact, strategy sets typically differ (and payoffs).

• Other than the last, game theory has not yet adequately modeled the other desiderata

Why are coordination failures common? Why are P-improvements not implemented?

• No NE is P-efficient (PD)

• There exists a P-efficient NE that is a P-improvement over the status quo but it is inaccessible (AG)– It is not risk dominant

– Coordinating actions is impossible (‘if we knew how to do that, we would not be poor.’)

• The transformation of the game to support an accessible P-efficient NE may require institutional innovations that subject one or more parties to the risk of a utility loss.

• There may be no mutually acceptable process to determine the sharing of the gains to cooperation. (UG: process-based utility)

• Next time read ch 2 and review discussion questions. (pp 56-76 will be discussed next time)

1

0 1

c

a

d

b

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2

1

• c’

•

•

The idea: if c' rather than c were the payoff to RU, the game would exhibit less conflict of interest. Or the degree of conflict of interest,

= 1- ( + )/2or the size of the infeasible set of outcomes (acde), relative to the stakes of the game (which by the normalization of payoffs is unity). (p 196-197 see also Axelrod (1970) and Wood (2004).)

Dividing a cake or finding a common language? Degree of conflict of interest in a game

U D

L a: 1,0 b:,

R c: , d: 0,1

, , , all [0,1]

DSE

Comparing the two measures for the standard PD game

common interest: (1- u)/(1+) = (b-c)/(a-d)

conflict of interest = 1- ( + )/2 = (a-b)/(a-d)

Both are normalized on (a-d) but captures the gains from cooperation, while captures the incentive to defect on a cooperator.

A question for later: is cooperation more difficult to sustain by means of game repetition if payoffs exhibit a high level of conflict (low level of common interest)?

C D

C b,b d,a

D a,d c,c