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

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  • Coralio Ballester
  • Antoni Calvó-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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Bibliographic Info

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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Keywords: Social Networks; peer effects; centrality measures; policies;

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References

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  1. Goyal, Sanjeev & Moraga-Gonzalez, Jose Luis, 2001. "R&D Networks," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 686-707, Winter.
  2. Matthew O. Jackson, 2003. "A Survey of Models of Network Formation: Stability and Efficiency," Game Theory and Information, EconWPA 0303011, EconWPA.
  3. Antoni Calvó-Armengol & Matthew O. Jackson, 2004. "The Effects of Social Networks on Employment and Inequality," American Economic Review, American Economic Association, American Economic Association, vol. 94(3), pages 426-454, June.
  4. Kandel, Eugene & Lazear, Edward P, 1992. "Peer Pressure and Partnerships," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 100(4), pages 801-17, August.
  5. Eli Berman, 2000. "Sect, Subsidy, And Sacrifice: An Economist'S View Of Ultra-Orthodox Jews," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 115(3), pages 905-953, August.
  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.
  7. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1005-1028, September.
  8. Ballester, Coralio & Calvó-Armengol, Antoni & Zenou, Yves, 2004. "Who's Who in Crime Network. Wanted the Key Player," Working Paper Series, Research Institute of Industrial Economics 617, Research Institute of Industrial Economics.
  9. Sanjeev Goyal & Sumit Joshi, 2000. "Networks of Collaboration in Oligopoly," Tinbergen Institute Discussion Papers, Tinbergen Institute 00-092/1, Tinbergen Institute.
  10. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 102(5), pages 841-77, October.
  11. George A. Akerlof, 1978. "A theory of social custom, of which unemployment may be one consequence," Special Studies Papers, Board of Governors of the Federal Reserve System (U.S.) 118, Board of Governors of the Federal Reserve System (U.S.).
  12. Durlauf,S.N., 2003. "Neighborhood effects," Working papers, Wisconsin Madison - Social Systems 17, Wisconsin Madison - Social Systems.
  13. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer, Springer, vol. 18(1), pages 39-43, March.
  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, University of Chicago Press, vol. 100(2), pages 271-91, April.
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