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Independence and heterogeneity in games of incomplete information

  • Mason, Robin
  • Valentinyi, Akos

This paper provides a sufficient condition for existence and uniqueness of equilibrium, which is in monotone pure strategies, in games of incomplete information. First, we show that if each player’s incremental ex post payoff is uniformly increasing in its own action and type, and its type is sufficiently uninformative of the types of its opponents (independence), then its expected payoff satisfies a strict single crossing property in its own action and type, for any strategy profile played by its opponents. This ensures that a player’s best response to any strategy profile is a monotone pure strategy. Secondly, we show that if, in addition, there is sufficient heterogeneity of the conditional density of types, then the best response correspondence is a contraction mapping. This ensures equilibrium existence and uniqueness. In contrast to existing results, our uniqueness result does not rely on strategic complementarities; this allows for a wider range of applications. Keywords; incomplete information, heterogeneity, existence, unique pure strategy equilibrium JEL classification: C72; D82

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Paper provided by Economics Division, School of Social Sciences, University of Southampton in its series Discussion Paper Series In Economics And Econometrics with number 0307.

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Date of creation: 01 Jul 2003
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Handle: RePEc:stn:sotoec:0307
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  1. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  2. Frankel, David M. & Burdzy, Krzysztof & Pauzner, Ady, 2001. "Fast Equilibrium Selection by Rational Players Living in a Changing World," Staff General Research Papers Archive 11923, Iowa State University, Department of Economics.
  3. David M. Frankel & Stephen Morris & Ady Pauzner, 2001. "Equilibrium Selection in Global Games with Strategic Complementarities," Cowles Foundation Discussion Papers 1336, Cowles Foundation for Research in Economics, Yale University.
  4. Edward L. Glaeser & Jose A. Scheinkman, 2001. "Non-Market Interactions," Harvard Institute of Economic Research Working Papers 1914, Harvard - Institute of Economic Research.
  5. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
  6. Berthold Herrendorf & Akos Valentinyi & Robert Waldmann, 2000. "Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 295-307.
  7. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 14-23.
  8. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  9. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  10. Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07.
  12. Carlsson, H. & van Damme, E.E.C., 1990. "Global games and equilibrium selection," Discussion Paper 1990-52, Tilburg University, Center for Economic Research.
  13. Van Long, Ngo & Soubeyran, Antoine, 2000. "Existence and uniqueness of Cournot equilibrium: a contraction mapping approach," Economics Letters, Elsevier, vol. 67(3), pages 345-348, June.
  14. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-97, June.
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