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Correlated Equilibrium via Hierarchies of Beliefs

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  • Du, Songzi
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    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.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16926.

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    Date of creation: 15 Aug 2009
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    Handle: RePEc:pra:mprapa:16926

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

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    1. AUMANN, Robert J. & DREZE, Jacques H., . "Rational expectations in games," CORE Discussion Papers RP -2011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Brandenburger, Adam & Friedenberg, Amanda, 2008. "Intrinsic correlation in games," Journal of Economic Theory, Elsevier, vol. 141(1), pages 28-67, July.
    3. Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. 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).
    5. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
    8. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
    9. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
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