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Consistency of beliefs and epistemic conditions for Nash and correlated equilibria

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  • Barelli, Paulo
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    Abstract

    A consistency condition (action-consistency) on the interim beliefs of players in a game is introduced. Action-consistency is weaker than common priors and, unlike common priors, is characterized by a "no-bets" condition on verifiable events. Using action-consistency, we provide epistemic conditions to Nash and correlated equilibria weakening the common knowledge restrictions in Aumann and Brandenburger [Aumann, R., Brandenburger, A., 1995. Epistemic conditions for Nash equilibrium. Econometrica 63, 1161-1180] and Aumann [Aumann, R., 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55, 1-18].

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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 67 (2009)
    Issue (Month): 2 (November)
    Pages: 363-375

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    Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:363-375

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    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Common prior assumption Universal beliefs space Epistemic conditions for equilibria Common knowledge;

    References

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    1. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Topologies on Types," Harvard Institute of Economic Research Working Papers 2093, Harvard - Institute of Economic Research.
    2. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    3. Barton L. Lipman, 1997. "Finite Order Implications of Common Priors," Game Theory and Information 9703005, EconWPA.
    4. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    5. Hu, Tai-Wei, 2007. "On p-rationalizability and approximate common certainty of rationality," Journal of Economic Theory, Elsevier, vol. 136(1), pages 379-391, September.
    6. Zvika Neeman, 1993. "Common Beliefs and the Existence of Speculative Trade," Discussion Papers 1052, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Ng, Man-Chung, 2003. "On the duality between prior beliefs and trading demands," Journal of Economic Theory, Elsevier, vol. 109(1), pages 39-51, March.
    8. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
    9. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
    10. Werlang, Sérgio Ribeiro da Costa & Chin-Chiu Tan, Tommy, 1987. "The Bayesian Foundations of Solution Concepts of Games," Economics Working Papers (Ensaios Economicos da EPGE) 111, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    11. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
    12. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
    13. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    14. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
    15. Ben Polak, 1999. "Epistemic Conditions for Nash Equilibrium, and Common Knowledge of Rationality," Econometrica, Econometric Society, vol. 67(3), pages 673-676, May.
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    18. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    20. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
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    Cited by:
    1. Bach Christian W. & Tsakas Elias, 2012. "Pairwise interactive knowledge and Nash equilibrium," Research Memorandum 008, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Jose Alvaro Rodrigues-Neto, 2011. "The Cycles Approach," ANU Working Papers in Economics and Econometrics 2011-547, Australian National University, College of Business and Economics, School of Economics.
    3. Hellman, Ziv, 2013. "Weakly rational expectations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 496-500.
    4. Paulo Barelli, 2010. "Consistent Beliefs in Extensive Form Games," Games, MDPI, Open Access Journal, vol. 1(4), pages 415-421, October.

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