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The existence and uniqueness of monotone pure strategy equilibrium in Bayesian games

  • Mason, Robin
  • Valentinyi, Ãkos

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

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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 0710.

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Date of creation: 29 Oct 2007
Date of revision:
Handle: RePEc:stn:sotoec:0710
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  1. David M. Frankel & Stephen Morris & Ady Pauzner, 2000. "Equilibrium Selection in Global Games with Strategic Complementarities," Econometric Society World Congress 2000 Contributed Papers 1490, Econometric Society.
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  3. Frankel, David M. & Burdzy, Krzysztof & Pauzner, Ady, 2001. "Fast Equilibrium Selection by Rational Players Living in a Changing World," Staff General Research Papers 11923, Iowa State University, Department of Economics.
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  8. Carlsson, H. & van Damme, E.E.C., 1993. "Global games and equilibrium selection," Other publications TiSEM 49a54f00-dcec-4fc1-9488-4, Tilburg University, School of Economics and Management.
  9. Edward L. Glaeser & Jose A. Scheinkman, 2001. "Non-Market Interactions," Harvard Institute of Economic Research Working Papers 1914, Harvard - Institute of Economic Research.
  10. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  11. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  12. In-Koo Cho, 2005. "Monotonicity and Rationalizability in a Large First Price Auction," Review of Economic Studies, Oxford University Press, vol. 72(4), pages 1031-1055.
  13. Ngo Van Long & Antoine Soubeyran, 1999. "Existence and Uniqueness of Cournot Equilibrium: A Contraction Mapping Approach," CIRANO Working Papers 99s-22, CIRANO.
  14. Van Zandt, Timothy & Vives, Xavier, 2003. "Monotone Equilibria in Bayesian Games of Strategic Complementarities," CEPR Discussion Papers 4103, C.E.P.R. Discussion Papers.
  15. Herrendorf, Berthold & Valentinyi, Akos & Waldmann, Robert, 2000. "Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity," Review of Economic Studies, Wiley Blackwell, vol. 67(2), pages 295-307, April.
  16. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  17. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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