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The Bayesian Solution and Hierarchies of Beliefs

  • Tang, Qianfeng
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    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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    File URL: https://mpra.ub.uni-muenchen.de/26811/1/MPRA_paper_26811.pdf
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    File URL: https://mpra.ub.uni-muenchen.de/26902/2/MPRA_paper_26902.pdf
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    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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    1. repec:dau:papers:123456789/157 is not listed on IDEAS
    2. Francoise Forges, 2006. "Correlated equilibrium in games with incomplete information revisited," Post-Print hal-00360743, HAL.
    3. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
    4. Jeffrey C. Ely & Marcin Peski, 2005. "Hierarchies of Belief and Interim Rationalizability," Levine's Bibliography 122247000000000817, UCLA Department of Economics.
    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. Tang, Qianfeng, 2010. "Interim Partially Correlated Rationalizability," MPRA Paper 26810, University Library of Munich, Germany.
    7. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    8. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
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