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Conditional Beliefs and Higher-Order Preferences

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  • Lee, Byung Soo
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    Abstract

    In this paper, we establish the Bayesian foundations of type structures in which beliefs are lexicographic probability systems (LPS’s)—such as those used in Brandenburger et al. (2008)—rather than standard probability measures as in Mertens and Zamir (1985). This is a setting which the distinction between preferences hierarchies (Epstein and Wang, 1996) and beliefs hierarchies is meaningful and the former has conceptual advantages. Type structures in which beliefs are conditional probability systems (CPS’s) are found to describe fewer hierarchies than LPS type structures can if a nonredundancy requirement is imposed. The two families of type structures are found to be capable of describing the same set of hierarchies in the absence of such a requirement. The existence of “largest”—a notion closely related to universality—LPS/CPS type structures is also shown. Finally, we find that some coherent hierarchies cannot be types but those hierarchies may be needed to express epistemic conditions for iterated elimination of weakly dominated strategies.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 48551.

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    Date of creation: 17 Jul 2013
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    Handle: RePEc:pra:mprapa:48551

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    Keywords: Preferences hierarchies; type structure; weakly dominated strategies; epistemic game theory; lexicographic probability system; conditional probability system;

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    1. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
    2. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, Econometric Society, vol. 64(6), pages 1343-73, November.
    3. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
    4. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
    5. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    6. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, INFORMS, vol. 14(3), pages 159-182, November.
    7. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2008. "Admissibility in Games," Econometrica, Econometric Society, Econometric Society, vol. 76(2), pages 307-352, 03.
    8. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, Econometric Society, vol. 59(1), pages 61-79, January.
    9. Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
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