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Admissibility and event-rationality

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  • Barelli, Paulo
  • Galanis, Spyros

Abstract

We develop an approach to providing epistemic conditions for admissible behavior in games. Instead of using lexicographic beliefs to capture infinitely less likely conjectures, we postulate that players use tie-breaking sets to help decide among strategies that are outcome-equivalent given their conjectures. A player is event-rational if she best responds to a conjecture and uses a list of subsets of the other playersʼ strategies to break ties among outcome-equivalent strategies. Using type spaces to capture interactive beliefs, we show that event-rationality and common belief of event-rationality (RCBER) imply S∞W, the set of admissible strategies that survive iterated elimination of dominated strategies. By strengthening standard belief to validated belief, we show that event-rationality and common validated belief of event-rationality (RCvBER) imply IA, the iterated admissible strategies. We show that in complete, continuous and compact type structures, RCBER and RCvBER are nonempty, hence providing epistemic criteria for S∞W and IA.

Suggested Citation

  • Barelli, Paulo & Galanis, Spyros, 2013. "Admissibility and event-rationality," Games and Economic Behavior, Elsevier, vol. 77(1), pages 21-40.
  • Handle: RePEc:eee:gamebe:v:77:y:2013:i:1:p:21-40
    DOI: 10.1016/j.geb.2012.08.012
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    References listed on IDEAS

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    Cited by:

    1. Aviad Heifetz & Martin Meier & Burkhard Schipper, 2017. "Comprehensive Rationalizability," Working Papers 174, University of California, Davis, Department of Economics.
    2. Keisler, H. Jerome & Lee, Byung Soo, 2011. "Common assumption of rationality," MPRA Paper 34441, University Library of Munich, Germany.
    3. Yang, Chih-Chun, 2015. "Weak assumption and iterative admissibility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 87-101.
    4. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

    More about this item

    Keywords

    Epistemic game theory; Admissibility; Iterated weak dominance; Common knowledge; Rationality; Completeness;

    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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