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

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  • Coralio Ballester
  • Antoni Calvo-Armengol
  • Yves Zenou

Abstract

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 www.najecon.org in its series NajEcon Working Paper Reviews with number 666156000000000586.

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Date of creation: 10 Mar 2005
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Handle: RePEc:cla:najeco:666156000000000586

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  1. Goyal, S. & Moraga-Gonzalez, J.L., 2000. "R&D Networks," Econometric Institute Research Papers EI 2000-26A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. 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.
  3. 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.
  4. Goyal, Sanjeev & Joshi, Sumit, 2003. "Networks of collaboration in oligopoly," Games and Economic Behavior, Elsevier, vol. 43(1), pages 57-85, April.
  5. Calvó-Armengol, Antoni & Zenou, Yves, 2003. "Social Networks and Crime Decisions: The Role of Social Structure in Facilitating Delinquent Behavior," Working Paper Series 601, Research Institute of Industrial Economics.
  6. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer, vol. 18(1), pages 39-43, March.
  7. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
  8. Akerlof, George A, 1980. "A Theory of Social Custom, of Which Unemployment May be One Consequence," The Quarterly Journal of Economics, MIT Press, vol. 94(4), pages 749-75, June.
  9. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
  10. Kandel, Eugene & Lazear, Edward P, 1992. "Peer Pressure and Partnerships," Journal of Political Economy, University of Chicago Press, vol. 100(4), pages 801-17, August.
  11. Matthew O. Jackson, 2003. "A Survey of Models of Network Formation: Stability and Efficiency," Game Theory and Information 0303011, EconWPA.
  12. Durlauf,S.N., 2003. "Neighborhood effects," Working papers 17, Wisconsin Madison - Social Systems.
  13. 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.
  14. 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.
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