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Independence And Heterogeneity In Games Of Incomplete Information

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Author Info
Mason, Robin
Valentinyi, Ãkos

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Abstract

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 playerÂ’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 playerÂ’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. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
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  3. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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  4. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January. [Downloadable!] (restricted)
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  5. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September. [Downloadable!] (restricted)
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  6. Van Zandt, Timothy & Vives, Xavier, 2003. "Monotone Equilibria in Bayesian Games of Strategic Complementarities," CEPR Discussion Papers 4103, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  7. Ngo Van Long & Antoine Soubeyran, 1999. "Existence and Uniqueness of Cournot Equilibrium: A Contraction Mapping Approach," CIRANO Working Papers 99s-22, CIRANO. [Downloadable!]
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  8. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
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  9. Burdzy, Krzysztof & Frankel, David M & Pauzner, Ady, 2001. "Fast Equilibrium Selection by Rational Players Living in a Changing World," Econometrica, Econometric Society, vol. 69(1), pages 163-89, January.
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  10. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
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  11. Diamond, Douglas W & Dybvig, Philip H, 1983. "Bank Runs, Deposit Insurance, and Liquidity," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 401-19, June. [Downloadable!] (restricted)
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  12. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
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  13. Herrendorf, Berthold & Valentinyi, Akos & Waldmann, Robert, 2000. "Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity," Review of Economic Studies, Blackwell Publishing, vol. 67(2), pages 295-307, April.
  14. Edward L. Glaeser & Jose Scheinkman, 2000. "Non-Market Interactions," NBER Working Papers 8053, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Sääskilahti, Pekka, 2006. "Buying Decision Coordination and Monopoly Pricing of Network Goods," MPRA Paper 5106, University Library of Munich, Germany. [Downloadable!]
  2. Mathevet, Laurent, . "A contraction principle for finite global games," Working Papers 1243, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  3. Sääskilahti, Pekka, 2007. "Monopoly pricing of social goods," MPRA Paper 3526, University Library of Munich, Germany. [Downloadable!]
  4. Mathevet, Laurent, 2007. "Supermodular Bayesian implementation: Learning and incentive design," Working Papers 1265, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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