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A new epistemic characterization of ε-proper rationalizability

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  • Perea, Andrés
  • Roy, Souvik

Abstract

For a given ε>0, the concept of ε-proper rationalizability (Schuhmacher, 1999) is based on two assumptions: (1) every player is cautious, i.e., does not exclude any opponent's choice from consideration, and (2) every player satisfies the ε-proper trembling condition, i.e., the probability he assigns to an opponent's choice a is at most ε times the probability he assigns to b whenever he believes the opponent to prefer b to a. In this paper we show that a belief hierarchy is ε-properly rationalizable in the complete information framework, if and only if, there is an equivalent belief hierarchy within the incomplete information framework that expresses common belief in the events that (1) players are cautious, (2) the players' beliefs about the opponent's utilities are “centered around the original utilities” in some specific way parametrized by ε, and (3) players rationalize each opponent's choice by a utility function that is as close as possible to the original utility function.

Suggested Citation

  • Perea, Andrés & Roy, Souvik, 2017. "A new epistemic characterization of ε-proper rationalizability," Games and Economic Behavior, Elsevier, vol. 104(C), pages 309-328.
    • Handle: RePEc:eee:gamebe:v:104:y:2017:i:c:p:309-328
    DOI: 10.1016/j.geb.2017.04.009
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    References listed on IDEAS

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    1. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    2. 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.
    3. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396.
    4. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
    5. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 377-399, April.
    7. Andrés Perea & Willemien Kets, 2016. "When Do Types Induce the Same Belief Hierarchy?," Games, MDPI, vol. 7(4), pages 1-17, October.
    8. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915.
    9. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 453-478.
    10. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 599-615.
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    Cited by:

    1. Shuige Liu, 2018. "Characterizing Permissibility, Proper Rationalizability, and Iterated Admissibility by Incomplete Information," Papers 1811.01933, arXiv.org.
    2. Shuige Liu, 2018. "Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model," Papers 1801.08767, arXiv.org.
    3. Shuige Liu, 2018. "Characterizing Assumption of Rationality by Incomplete Information," Papers 1801.04714, arXiv.org.

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    More about this item

    Keywords

    Epistemic game theory; Incomplete information; Proper rationalizability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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