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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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File URL: http://eprints.soton.ac.uk/167733/1/0307.pdf
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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. Morris, S & Song Shin, H, 1996. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," Economics Papers 126, Economics Group, Nuffield College, University of Oxford.
  2. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  4. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07.
  5. Philip J. Reny & Shmuel Zamir, 2004. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Econometrica, Econometric Society, vol. 72(4), pages 1105-1125, 07.
  6. 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.
  7. Edward L. Glaeser & Jose Scheinkman, 2000. "Non-Market Interactions," NBER Working Papers 8053, National Bureau of Economic Research, Inc.
  8. 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.
  9. Van Zandt, Timothy & Vives, Xavier, 2003. "Monotone Equilibria in Bayesian Games of Strategic Complementarities," CEPR Discussion Papers 4103, C.E.P.R. Discussion Papers.
  10. 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.
  11. 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.
  12. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  13. Ngo Van Long & Antoine Soubeyran, 1999. "Existence and Uniqueness of Cournot Equilibrium: A Contraction Mapping Approach," CIRANO Working Papers 99s-22, CIRANO.
  14. repec:ner:tilbur:urn:nbn:nl:ui:12-154416 is not listed on IDEAS
  15. 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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