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Correlated equilibrium and higher order beliefs about play

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  • Du, Songzi

Abstract

We study a refinement of correlated equilibrium in which playersʼ actions are driven by their beliefs and higher order beliefs about the play of the game (beliefs over what other players will do, over what other players believe others will do, etc.). For any finite, complete-information game, we characterize the behavioral implications of this refinement with and without a common prior, and up to any a priori fixed depth of reasoning. In every finite game “most” correlated equilibrium distributions are consistent with this refinement; as a consequence, this refinement gives a classification of “most” correlated equilibrium distributions based on the maximum order of beliefs used by players in the equilibrium. On the other hand, in a generic two-player game any non-degenerate mixed-strategy Nash equilibrium is not consistent with this refinement.

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  • Du, Songzi, 2012. "Correlated equilibrium and higher order beliefs about play," Games and Economic Behavior, Elsevier, vol. 76(1), pages 74-87.
    • Handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:74-87
    DOI: 10.1016/j.geb.2012.05.008
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    References listed on IDEAS

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    2. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
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    4. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
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    Cited by:

    1. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.

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    More about this item

    Keywords

    Correlated equilibrium; Higher order beliefs; Intrinsic correlation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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