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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
Date of revision:
Handle: RePEc:bge:wpaper:178
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  1. 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.
  2. 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.
  3. Durlauf, Steven N., 2004. "Neighborhood effects," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 50, pages 2173-2242 Elsevier.
  4. Sumit Joshi, 2000. "Networks of Collaboration in Oligopoly," Econometric Society World Congress 2000 Contributed Papers 0623, Econometric Society.
  5. 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.
  6. 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.
  7. Matthew O. Jackson, 2003. "A Survey of Models of Network Formation: Stability and Efficiency," Game Theory and Information 0303011, EconWPA.
  8. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
  9. repec:oup:qjecon:v:94:y:1980:i:4:p:749-75 is not listed on IDEAS
  10. 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.
  11. repec:oup:qjecon:v:115:y:2000:i:3:p:905-953 is not listed on IDEAS
  12. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
  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. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer, vol. 18(1), pages 39-43, March.
  15. 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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