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Who's Who in Networks. Wanted: The Key Player

  • Coralio Ballester
  • Antoni Calvó-Armengol
  • Yves Zenou

Finite population non-cooperative games with linear-quadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an ownconcavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. This Bonacich-Nash linkage implies that aggregate equilibrium increases with network size and density. We then analyze a policy that consists of targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identifed with an inter-centrality measure, which takes into account both a player's centrality and her contribution to the centrality of the others.

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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 178.

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Date of creation: Jul 2004
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Handle: RePEc:bge:wpaper:178
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  1. Eli Berman, 1998. "Sect, Subsidy, and Sacrifice: An Economist's View of Ultra-Orthodox Jews," NBER Working Papers 6715, National Bureau of Economic Research, Inc.
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  9. Antoni Calvó-Armengol & Matthew O. Jackson, 2004. "The Effects of Social Networks on Employment and Inequality," American Economic Review, American Economic Association, vol. 94(3), pages 426-454, June.
  10. Antoni Calvó-Armengol & Yves Zenou, 2004. "Social Networks And Crime Decisions: The Role Of Social Structure In Facilitating Delinquent Behavior," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(3), pages 939-958, 08.
  11. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
  12. Ballester, Coralio & Calvó-Armengol, Antoni & Zenou, Yves, 2004. "Who's Who in Crime Network. Wanted the Key Player," Working Paper Series 617, Research Institute of Industrial Economics.
  13. Matthew O. Jackson, 2003. "A survey of models of network formation: Stability and efficiency," Working Papers 1161, California Institute of Technology, Division of the Humanities and Social Sciences.
  14. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
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