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Rational behavior under correlated uncertainty

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  • Frick, Mira
  • Romm, Assaf

Abstract

In complete information games, Dekel and Fudenberg (1990) and Börgers (1994) have proposed the solution concept S∞W (one round of elimination of weakly dominated strategies followed by iterated elimination of strongly dominated strategies), motivating it by a characterization in terms of “approximate common certainty” of admissibility. We examine the validity of this characterization of S∞W in an incomplete information setting. We argue that in Bayesian games with a nontrivial state space, the characterization is very sensitive to the way in which uncertainty in the form of approximate common certainty of admissibility is taken to interact with the uncertainty already captured by players' beliefs about the states of nature: We show that S∞W corresponds to approximate common certainty of admissibility when this is not allowed to coincide with any changes to players' beliefs about states. If approximate common certainty of admissibility is accompanied by vanishingly small perturbations to beliefs, then S∞W is a (generally strict) subset of the predicted behavior, which we characterize in terms of a generalization of Hu's (2007) perfect p-rationalizable set.

Suggested Citation

  • Frick, Mira & Romm, Assaf, 2015. "Rational behavior under correlated uncertainty," Journal of Economic Theory, Elsevier, vol. 160(C), pages 56-71.
    • Handle: RePEc:eee:jetheo:v:160:y:2015:i:c:p:56-71
    DOI: 10.1016/j.jet.2015.08.009
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    References listed on IDEAS

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    Cited by:

    1. Tilman Börgers & Jiangtao Li, 2019. "Strategically Simple Mechanisms," Econometrica, Econometric Society, vol. 87(6), pages 2003-2035, November.
    2. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    3. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2022. "Robust refinement of rationalizability with arbitrary payoff uncertainty," Games and Economic Behavior, Elsevier, vol. 136(C), pages 485-504.

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    More about this item

    Keywords

    Rationality; Admissibility; Approximate common certainty; Common p-belief; Incomplete information; Robustness;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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