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

  • Ballester, Coralio
  • Calvó-Armengol, Antoni
  • Zenou, Yves

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 own concavity 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 in 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 identified 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 C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5329.

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Date of creation: Oct 2005
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Handle: RePEc:cpr:ceprdp:5329
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  1. Iannaccone, Laurence R, 1992. "Sacrifice and Stigma: Reducing Free-Riding in Cults, Communes, and Other Collectives," Journal of Political Economy, University of Chicago Press, vol. 100(2), pages 271-91, April.
  2. Ballester, Coralio & Calvó-Armengol, Antoni & Zenou, Yves, 2004. "Who's Who in Crime Networks: Wanted - The Key Player," CEPR Discussion Papers 4421, C.E.P.R. Discussion Papers.
  3. Goyal, S. & Joshi, S., 2000. "Networks of Collaboration in Oligopoly," Econometric Institute Research Papers EI 9952-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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  6. Antoni Calvó-Armengol & Yves Zenou, 2003. "Social Networks and Crime Decisions: The Role of Social Structure in Facilitating Delinquent Behavior," Working Papers 52, Barcelona Graduate School of Economics.
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  12. Eli Berman, 2000. "Sect, Subsidy, And Sacrifice: An Economist'S View Of Ultra-Orthodox Jews," The Quarterly Journal of Economics, MIT Press, vol. 115(3), pages 905-953, August.
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