Inequality and Network Structure

G. Iyengar, W. Kets, R. Sethi, S. Bowles

Research output: Working paperDiscussion paperOther research output

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Abstract

This paper explores the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members. We assume that any distribution of value across the network must be stable with respect to coalitional deviations, and that players can form a deviating coalition only if they constitute a clique in the network. We show that if the network is bipartite, there is a unique stable payoff distribution that is maximally unequal in that it does not Lorenz dominate any other stable distribution. We obtain a complete ordering of the class of bipartite networks and show that those with larger maximum independent sets can sustain greater levels of inequality. The intuition behind this result is that networks with larger maximum independent sets are more sparse and hence offer fewer opportunities for coalitional deviations. We also demonstrate that standard centrality measures do not consistently predict inequality. We extend our framework by allowing a group of players to deviate if they are all within distance k of each other, and show that the ranking of networks by the extent of extremal inequality is not invariant in k.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages25
Volume2008-76
Publication statusPublished - 2008

Publication series

NameCentER Discussion Paper
Volume2008-76

Fingerprint

Network structure
Deviation
Clique
Ranking
Social networks
Centrality
Intuition
Stable distribution

Keywords

  • inequality
  • networks
  • coalitional deviations
  • power
  • centrality

Cite this

Iyengar, G., Kets, W., Sethi, R., & Bowles, S. (2008). Inequality and Network Structure. (CentER Discussion Paper; Vol. 2008-76). Tilburg: Microeconomics.
Iyengar, G. ; Kets, W. ; Sethi, R. ; Bowles, S. / Inequality and Network Structure. Tilburg : Microeconomics, 2008. (CentER Discussion Paper).
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Iyengar, G, Kets, W, Sethi, R & Bowles, S 2008 'Inequality and Network Structure' CentER Discussion Paper, vol. 2008-76, Microeconomics, Tilburg.

Inequality and Network Structure. / Iyengar, G.; Kets, W.; Sethi, R.; Bowles, S.

Tilburg : Microeconomics, 2008. (CentER Discussion Paper; Vol. 2008-76).

Research output: Working paperDiscussion paperOther research output

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AU - Sethi, R.

AU - Bowles, S.

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N2 - This paper explores the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members. We assume that any distribution of value across the network must be stable with respect to coalitional deviations, and that players can form a deviating coalition only if they constitute a clique in the network. We show that if the network is bipartite, there is a unique stable payoff distribution that is maximally unequal in that it does not Lorenz dominate any other stable distribution. We obtain a complete ordering of the class of bipartite networks and show that those with larger maximum independent sets can sustain greater levels of inequality. The intuition behind this result is that networks with larger maximum independent sets are more sparse and hence offer fewer opportunities for coalitional deviations. We also demonstrate that standard centrality measures do not consistently predict inequality. We extend our framework by allowing a group of players to deviate if they are all within distance k of each other, and show that the ranking of networks by the extent of extremal inequality is not invariant in k.

AB - This paper explores the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members. We assume that any distribution of value across the network must be stable with respect to coalitional deviations, and that players can form a deviating coalition only if they constitute a clique in the network. We show that if the network is bipartite, there is a unique stable payoff distribution that is maximally unequal in that it does not Lorenz dominate any other stable distribution. We obtain a complete ordering of the class of bipartite networks and show that those with larger maximum independent sets can sustain greater levels of inequality. The intuition behind this result is that networks with larger maximum independent sets are more sparse and hence offer fewer opportunities for coalitional deviations. We also demonstrate that standard centrality measures do not consistently predict inequality. We extend our framework by allowing a group of players to deviate if they are all within distance k of each other, and show that the ranking of networks by the extent of extremal inequality is not invariant in k.

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KW - networks

KW - coalitional deviations

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KW - centrality

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Iyengar G, Kets W, Sethi R, Bowles S. Inequality and Network Structure. Tilburg: Microeconomics. 2008. (CentER Discussion Paper).