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The Bayesian Solution and Hierarchies of Beliefs

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  • Tang, Qianfeng
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    Abstract

    The Bayesian solution is a notion of correlated equilibrium proposed by Forges (1993), and hierarchies of beliefs over conditional beliefs are introduced by Ely and Pęski (2006) in their study of interim rationalizability. We study the connection between the two concepts. We say that two type spaces are equivalent if they represent the same set of hierarchies of beliefs over conditional beliefs. We show that the correlation embedded in equivalent type spaces can be characterized by partially correlating devices, which send correlated signals to players in a belief invariant way. Since such correlating devices also implement the Bayesian solution, we establish that the Bayesian solution is invariant across equivalent type spaces.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26811.

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    Date of creation: 09 Nov 2010
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    Handle: RePEc:pra:mprapa:26811

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    Related research

    Keywords: Games with incomplete information; Correlated equilibrium; The Bayesian solution; Common knowledge; Hierarchies of beliefs.;

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    References

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    1. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics.
    2. Jeffrey C. Ely & Marcin Peski, . "Hierarchies Of Belief And Interim Rationalizability," Discussion Papers 1388, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. FORGES, Françoise, 2006. "Correlated equilibrium in games with incomplete information revisited," CORE Discussion Papers 2006041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Tang, Qianfeng, 2010. "Interim Partially Correlated Rationalizability," MPRA Paper 26810, University Library of Munich, Germany.
    5. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    6. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
    7. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
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    Cited by:
    1. Tang, Qianfeng, 2010. "Interim Partially Correlated Rationalizability," MPRA Paper 26810, University Library of Munich, Germany.

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