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Cautious Belief and Iterated Admissibility

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  • Emiliano Catonini
  • Nicodemo De Vito

Abstract

We define notions of cautiousness and cautious belief to provide epistemic conditions for iterated admissibility in finite games. We show that iterated admissibility characterizes the behavioral implications of "cautious rationality and common cautious belief in cautious rationality" in a terminal lexicographic type structure. For arbitrary type structures, the behavioral implications of these epistemic assumptions are characterized by the solution concept of self-admissible set (Brandenburger, Friedenberg and Keisler 2008). We also show that analogous conclusions hold under alternative epistemic assumptions, in particular if cautiousness is "transparent" to the players. KEYWORDS: Epistemic game theory, iterated admissibility, weak dominance, lexicographic probability systems. JEL: C72.

Suggested Citation

  • Emiliano Catonini & Nicodemo De Vito, 2023. "Cautious Belief and Iterated Admissibility," Papers 2305.15330, arXiv.org.
    • Handle: RePEc:arx:papers:2305.15330
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    References listed on IDEAS

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    1. Asheim, Geir B. & Sovik, Ylva, 2005. "Preference-based belief operators," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 61-82, July.
    2. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    3. Kin Chung Lo, 1999. "Nash equilibrium without mutual knowledge of rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 621-633.
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    More about this item

    Keywords

    epistemic game theory; iterated admissibility; weak dominance; lexicographic probability systems. jel: c72.;
    All these keywords.

    JEL classification:

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

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