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Rational belief hierarchies

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  • Tsakas Elias

    (METEOR)

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    Abstract

    We consider agents whose language can only express probabilistic beliefs that attach a rationalnumber to every event. We call these probability measures rational. We introduce the notion of arational belief hierarchy, where the first order beliefs are described by a rational measure overthe fundamental space of uncertainty, the second order beliefs are described by a rational measureover the product of the fundamental space of uncertainty and the opponent''s first order rationalbeliefs, and so on. Then, we derive the corresponding (rational) type space model, thus providinga Bayesian representation of rational belief hierarchies. Our first main result shows that thistype-based representation violates our intuitive idea of an agent whose language expresses onlyrational beliefs, in that there are rational types associated with non-rational beliefs over thecanonical state space. We rule out these types by focusing on the rational types that satisfycommon certainty in the event that everybody holds rational beliefs over the canonical statespace. We call these types universally rational and show that they are characterized by a boundedrationality condition which restricts the agents'' computational capacity. Moreover, theuniversally rational types form a dense subset of the universal type space. Finally, we show thatthe strategies rationally played under common universally rational belief in rationalitygenerically coincide with those satisfying correlated rationalizability.

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    Bibliographic Info

    Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 004.

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    Date of creation: 2012
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    Handle: RePEc:unm:umamet:2012004

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    Keywords: microeconomics ;

    References

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    1. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers, David K. Levine 9817a118e65062903de7c3577, David K. Levine.
    2. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information, EconWPA 9609002, EconWPA, revised 17 Sep 1996.
    3. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
    4. HEIFETZ, Aviad & MEIER, Martin & SCHIPPER, Burkhard C., 2004. "Interactive unawareness," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    14. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, Elsevier, vol. 67(2), pages 503-525, November.
    15. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 27(2), pages 265-298, May.
    16. Joseph Y. Halpern, 2000. "Alternative Semantics for Unawareness," Game Theory and Information, EconWPA 0004010, EconWPA.
    17. Eliaz, Kfir, 2003. "Nash equilibrium when players account for the complexity of their forecasts," Games and Economic Behavior, Elsevier, Elsevier, vol. 44(2), pages 286-310, August.
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    20. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, Elsevier, vol. 136(1), pages 286-301, September.
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