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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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    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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