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Interim Partially Correlated Rationalizability

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  • Tang, Qianfeng
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    Abstract

    In game theory, there is a basic methodological dichotomy between Harsanyi's "game-theoretic" view and Aumann's "Bayesian decision-theoretic" view of the world. We follow the game-theoretic view, propose and study interim partially correlated rationalizability for games with incomplete information. We argue that the distinction between this solution concept and the interim correlated rationalizability studied by Dekel, Fudenberg and Morris (2007) is fundamental, in that the latter implicitly follows Aumann's Bayesian view. Our main result shows that two types provide the same prediction in interim partially correlated rationalizability if and only if they have the same infinite hierarchy of beliefs over conditional beliefs. We also establish an equivalence result between this solution concept and the Bayesian solution--a notion of correlated equilibrium proposed by Forges (1993).

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26810.

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    Date of creation: 11 Nov 2010
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    Handle: RePEc:pra:mprapa:26810

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    Keywords: Games with incomplete information; Rationalizability; Common knowledge; Hierarchies of beliefs.;

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    1. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
    2. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
    3. Eddie Dekel & Drew Fudenberg, 2006. "Topologies on Type," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1417, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, Springer, vol. 61(4), pages 329-344, December.
    5. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 189-198, February.
    6. Jeffrey C. Ely & Marcin Peski, 2005. "Hierarchies of Belief and Interim Rationalizability," Levine's Bibliography 122247000000000817, UCLA Department of Economics.
    7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 1029-50, July.
    8. Tang, Qianfeng, 2010. "The Bayesian Solution and Hierarchies of Beliefs," MPRA Paper 26811, University Library of Munich, Germany.
    9. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(5), pages 2115-2145, September.
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    Cited by:
    1. Tang, Qianfeng, 2010. "The Bayesian Solution and Hierarchies of Beliefs," MPRA Paper 26811, University Library of Munich, Germany.

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