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Self-Admissible Sets

In: The Language of Game Theory Putting Epistemics into the Mathematics of Games

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  • Adam Brandenburger
  • Amanda Friedenberg

Abstract

Best-response sets (Pearce [1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger, Friedenberg, and Keisler [2008]) characterizes “rationality and common assumption of rationality.” We analyze the behavior of SAS's in some games of interest — Centipede, the Finitely Repeated Prisoner's Dilemma, and Chain Store. We then establish some general properties of SAS's, including a characterization in perfect-information games.

Suggested Citation

  • Adam Brandenburger & Amanda Friedenberg, 2014. "Self-Admissible Sets," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 8, pages 213-249, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814513449_0008
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    Cited by:

    1. Hans Carlsson & Philipp Christoph Wichardt, 2019. "Strict Incentives and Strategic Uncertainty," CESifo Working Paper Series 7715, CESifo.
    2. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    3. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 126-144.
    4. Michal Król, 2012. "‘Everything must go!’- Cournot as a Stable Convention within Strategic Supply Function Competition," Economics Discussion Paper Series 1217, Economics, The University of Manchester.
    5. Tsakas, E., 2010. "Belief hierarchies in standard state space models and epistemic equivalence of belief spaces," Research Memorandum 048, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2019. "Comprehensive rationalizability," Games and Economic Behavior, Elsevier, vol. 116(C), pages 185-202.
    7. Catonini, Emiliano & De Vito, Nicodemo, 2024. "Cautious belief and iterated admissibility," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    8. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.

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    More about this item

    Keywords

    Game Theory; Epistemic Game Theory; Foundations; Applied Mathematics; Social Neuroscience; Rationalizability; Nash Equilibrium; Probability; Uncertainty;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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