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Correlated Equilibrium via Hierarchies of Beliefs

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  • Du, Songzi

Abstract

We study a model of correlated equilibrium where every player takes actions based on his hierarchies of beliefs (belief on what other players will do, on what other players believe about others will do, etc.) intrinsic to the game. Our model does away with messages from outside mediator that are usually assumed in the interpretation of correlated equilibrium. We characterize in every finite, complete information game the exact sets of correlated equilibria (both subjective and objective) that can be obtained conditioning on hierarchies of beliefs; the characterizations rely on a novel iterated deletion procedure. If the procedure ends after k rounds of deletion for a correlated equilibrium obtained from hierarchies of beliefs, then players in the equilibrium need to reason to at most k-th order beliefs. Further conceptual and geometric properties of the characterizations are studied.

Suggested Citation

  • Du, Songzi, 2009. "Correlated Equilibrium via Hierarchies of Beliefs," MPRA Paper 16926, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:16926
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    File URL: https://mpra.ub.uni-muenchen.de/16926/1/MPRA_paper_16926.pdf
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    References listed on IDEAS

    as
    1. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    2. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
    3. Robert J. Aumann & Jacques H. Dreze, 2008. "Rational Expectations in Games," American Economic Review, American Economic Association, vol. 98(1), pages 72-86, March.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
    6. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    7. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    8. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    9. Adam Brandenburger & Amanda Friedenberg, 2014. "Intrinsic Correlation in Games," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 4, pages 59-111 World Scientific Publishing Co. Pte. Ltd..
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    More about this item

    Keywords

    game theory; correlated equilibrium; higher order beliefs; purification; intrinsic correlation;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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