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Weak belief and permissibility

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  • Catonini, Emiliano
  • De Vito, Nicodemo

Abstract

We provide epistemic foundations for permissibility (Brandenburger, 1992), a strategic-form solution concept for finite games which coincides with the Dekel-Fudenberg procedure, i.e., the elimination of all weakly dominated strategies, followed by the iterated elimination of strictly dominated strategies. We show that permissibility characterizes the behavioral implications of “cautious rationality and common weak belief of cautious rationality” in the canonical, universal type structure for lexicographic beliefs. For arbitrary type structures, we show that the behavioral implications of these epistemic assumptions are characterized by the solution concept of full weak best response set, a weak dominance analogue of best response set (Pearce, 1984).

Suggested Citation

  • Catonini, Emiliano & De Vito, Nicodemo, 2020. "Weak belief and permissibility," Games and Economic Behavior, Elsevier, vol. 120(C), pages 154-179.
    • Handle: RePEc:eee:gamebe:v:120:y:2020:i:c:p:154-179
    DOI: 10.1016/j.geb.2019.11.007
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    Cited by:

    1. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    2. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    3. Catonini, Emiliano & De Vito, Nicodemo, 2024. "Cautious belief and iterated admissibility," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    4. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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    More about this item

    Keywords

    Epistemic game theory; Permissibility; Dekel-Fudenberg procedure; Infinitely more likely; Lexicographic probability systems; Type structures; Rationality;
    All these keywords.

    JEL classification:

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

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