NetworkNetwork formation with Chenghong Luo formation with

myopic and Ana Mauleon

Vincent Vannetelbosch

y pfarsighted 

l

Vannetelbosch

Working Paper,

players g

2018

Part 1 Introduction to Pairwise Stability Part 1. Introduction to Pairwise Stability

and Efficiency

1. Pairwise Stability

O tli

a w se Stab ty

2. Efficiency

3. Conflict between Efficiency and Pairwise Outline Stability

Part 2. Network formation with myopic

and farsighted players

1. Introduction to Farsightedness

2 M i F i ht d N t k 2. Myopic-Farsighted Network

Pairwise

Pairwise Stability

YesYes NoNo/Indif.

Improving Path

Improving Cycle

Effi i Efficiency

Conflict between Stability andStability and Efficiency

Jackson, 2008

Cost-benefit structure with only Myopic players

Network typology

Efficiency Pairwise Stability Conflict

Distance‐based Utility

Complete network

Unique Strongly Unique No

Star Network

Unique Strongly Yes

UtilityEmpty Network

Unique Strongly Not Unique Yes

No links or at least

Any Yesat least two links per player

Any No Yes

Conflict between Pairwise Stability andPairwise Stability and 

Efficiency with Distance‐based Utility

Jackson and Wolinsky, 1996

Conflict between Pairwise b l d ffStability and Efficiency 

with Distance‐based Utility

Jackson,2008 (p.165)

Farsighted Players: forward looking, no errors

Farsighted Improving Path. Farsighted Players anticipate

further changes along the path and compare the ultimate

network to the current one (not necessarily a sequence of

Farsighted

adjacent networks)

Farsightedly Pairwise Stable Network. If there is no

farsighted improving path from g to some other network g’,

such that each pair of consecutive networks along the the Farsighted Players

such that each pair of consecutive networks along the the

sequence are adjacent.

Farsightedly Strongly Stable. If there is no farsighted

improving path from g to some other network g’.p g p g g

Existence of Farsightedly Pairwise Stable Network:

Consistent Set. All deviations away from the network are

expected to farsightedly lead back to some network in the

set that is not improving for the original deviating coalition.

Conflict betweenConflict between Pairwise Stability and Efficiency

FARSIGHTED PLAYERS

Form and delete links based on the improvement the end

Myopic‐

Form and delete links based on the improvement the end network offers relative to the current network

MYOPIC PLAYERSMyopicFarsighted Model

MYOPIC PLAYERS

Form and delete links based on the improvement the resulting network offers relative to the current network

Only Pairwise deviations!

Empirical evidences of a mixed population p p p(Kirchsteiger, Mantovani, Mauleon, Vannetelbosch, 2006)

Myopic‐F i ht d Farsighted 

Improving Path

Myopic‐F i ht d

Farsighted Stable Set

PROPOSITION(1.1)

R l (1)Results (1)PROPOSITION(1.2)

Proposition(1.1) P f ‐ Proof –

Internal Stability

Proposition(1.1) P f‐ Proof –

External Stability

COROLLARYCOROLLARY

R l (2)Results (2)PROPOSITION(2)

C l i

Main Result: resolution of conflict between Stability

and Efficiency

M i Li it A i /H i i b fi Conclusion Main Limit: Asymmetries/Heterogeneity in benefits

and costs would imply that a conflict between stability

and efficiency could rise again (transfers?)

AppendixAppendixExtra contents

Ob ti

Assumption of perfect information/perception

Pairwise Adjustments (no coalitions)

T i i i f P f ( i f ili Observations Transitivity of Preferences (existence of a utility

function)

Assumption of utility additivity (measure of efficiency)

What isWhat is Farsightedness? Consistent with its multidimensional nature, empathy appears to be

supported by a number of neural networks involving several regions including frontal regions, the insula and temporal regions .including frontal regions, the insula and temporal regions .

Emotional Empathy: ability supports our tendency to react emotionally to the pain and distress of others and to recognize their emotions.

Cognitive Empathy: ability to engage in the cognitive process of adopting another's psychological point of view.

From “The neuropsychology of empathy: evidence from lesion studies” – Simone, Shamay, Tsoory - in Revue de neuropsychologie 2015/4 (Volume 7), pages 237 à 243