Inequality and Network Structure

CentER Discussion Paper Series No. 2008-76

25 Pages Posted: 16 Sep 2008  

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Willemien Kets

Northwestern University; Tilburg University - CentER for Economic Research

Rajiv Sethi

Columbia University, Barnard College - Department of Economics; Santa Fe Institute

Samuel Bowles

Santa Fe Institute; University of Massachusetts

Date Written: August 6, 2008

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.

Keywords: inequality, networks, coalitional deviations, power, centrality

JEL Classification: C71, D30, D85

Suggested Citation

Iyengar, Garud and Kets, Willemien and Sethi, Rajiv and Bowles, Samuel, Inequality and Network Structure (August 6, 2008). CentER Discussion Paper Series No. 2008-76. Available at SSRN: https://ssrn.com/abstract=1268765 or http://dx.doi.org/10.2139/ssrn.1268765

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States
+1 212-854-4594 (Phone)
+1 212-854-8103 (Fax)

Willemien Kets (Contact Author)

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Tilburg University - CentER for Economic Research ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Rajiv Sethi

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Columbia University, Barnard College - Department of Economics ( email )

3009 Broadway
New York, NY 10027
United States
212-854-5140 (Phone)
212-854-8947 (Fax)

Samuel Bowles

Santa Fe Institute ( email )

1399 Hyde Park Rd
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu

University of Massachusetts ( email )

Amherst, MA 01002
United States
413-545-2590 (Phone)

HOME PAGE: http://www-unix.oit.umass.edu/~bowles/

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