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Independence and Heterogeneity in Games of Incomplete Information

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  • Mason, Robin
  • Valentinyi, Akos

Abstract

This Paper provides a sufficient condition for the existence and uniqueness of equilibrium in monotone pure strategies, in games of incomplete information. First, we show that if each player's incremental ex post pay-off 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 pay-off 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. Our approach allows us to establish these results in a wide range of applications, including cases where there are no existing existence results.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 4177.

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Date of creation: Jan 2004
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Handle: RePEc:cpr:ceprdp:4177

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Keywords: existence; heterogeneity; incomplete information; unique pure strategy equilibrium;

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References

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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.
  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.
  3. 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.
  4. Hans Carlsson & Eric van Damme, 1993. "Global Games and Equilibrium Selection," Levine's Working Paper Archive 122247000000001088, David K. Levine.
  5. Edward L. Glaeser & Jose A. Scheinkman, 2001. "Non-Market Interactions," Harvard Institute of Economic Research Working Papers 1914, Harvard - Institute of Economic Research.
  6. Ngo Van Long & Antoine Soubeyran, 1999. "Existence and Uniqueness of Cournot Equilibrium: A Contraction Mapping Approach," CIRANO Working Papers 99s-22, CIRANO.
  7. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  8. 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.
  9. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  10. 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.
  11. 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.
  12. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  13. 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.
  14. 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.
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Cited by:
  1. Laurent Mathevet, 2010. "A contraction principle for finite global games," Economic Theory, Springer, vol. 42(3), pages 539-563, March.
  2. Sääskilahti, Pekka, 2007. "Monopoly pricing of social goods," MPRA Paper 3526, University Library of Munich, Germany.
  3. Makris, Miltiadis, 2008. "Complementarities and macroeconomics: Poisson games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 180-189, January.
  4. Sääskilahti, Pekka, 2006. "Buying Decision Coordination and Monopoly Pricing of Network Goods," MPRA Paper 5106, University Library of Munich, Germany.

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