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Interim Bayesian Nash equilibrium on universal type spaces for supermodular games

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  • Van Zandt, Timothy
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    Abstract

    We prove the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information. There are two main differences from the earlier proofs and from general existence results for non-supermodular Bayesian games: (a) we use the interim formulation of a Bayesian game, in which each player's beliefs are part of his or her type rather than being derived from a prior; (b) we use the interim formulation of a Bayesian Nash equilibrium, in which each player and every type (rather than almost every type) chooses a best response to the strategy profile of the other players. There are no restrictions on type spaces and action sets may be any compact metric lattices.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 145 (2010)
    Issue (Month): 1 (January)
    Pages: 249-263

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    Handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:249-263

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    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

    Keywords: Supermodular games Incomplete information Universal type spaces Interim Bayesian Nash equilibrium;

    References

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    1. Jeffrey C. Ely & Marcin Peski, 2005. "Hierarchies of Belief and Interim Rationalizability," Levine's Bibliography 122247000000000817, UCLA Department of Economics.
    2. Van Zandt, Timothy & Vives, Xavier, 2003. "Monotone Equilibria in Bayesian Games of Strategic Complementarities," CEPR Discussion Papers 4103, C.E.P.R. Discussion Papers.
    3. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07.
    4. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    5. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
    6. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
    7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
    8. 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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    Cited by:
    1. Takashi Kamihigashi & Kevin REFFETT & Kevin REFFETT, 2014. "Partial Stochastic Dominance," Discussion Paper Series DP2014-23, Research Institute for Economics & Business Administration, Kobe University.
    2. Luciano De Castro, 2012. "Correlation of Types in Bayesian Games," Discussion Papers 1556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    4. Eric Hoffmann, 2013. "Global Games Selection in Games with Strategic Substitutes or Complements," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201308, University of Kansas, Department of Economics.

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