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Epistemically Robust Strategy Subsets

Author

Listed:
  • Geir B. Asheim

    () (Department of Economics, University of Oslo, P.O. Box 1095 Blindern, NO-0317 Oslo, Norway)

  • Mark Voorneveld

    () (Department of Economics, Stockholm School of Economics, Box 6501, SE-113 83 Stockholm, Sweden)

  • Jörgen W. Weibull

    () (Department of Economics, Stockholm School of Economics, Box 6501, SE-113 83 Stockholm, Sweden
    Institute for Advanced Study in Toulouse, 31000 Toulouse, France
    Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden)

Abstract

We define a concept of epistemic robustness in the context of an epistemic model of a finite normal-form game where a player type corresponds to a belief over the profiles of opponent strategies and types. A Cartesian product X of pure-strategy subsets is epistemically robust if there is a Cartesian product Y of player type subsets with X as the associated set of best reply profiles such that the set Y i contains all player types that believe with sufficient probability that the others are of types in Y − i and play best replies. This robustness concept provides epistemic foundations for set-valued generalizations of strict Nash equilibrium, applicable also to games without strict Nash equilibria. We relate our concept to closedness under rational behavior and thus to strategic stability and to the best reply property and thus to rationalizability.

Suggested Citation

  • Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-16, November.
  • Handle: RePEc:gam:jgames:v:7:y:2016:i:4:p:37-:d:83690
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    References listed on IDEAS

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    More about this item

    Keywords

    epistemic game theory; epistemic robustness; rationalizability; closedness under rational behavior; mutual p -belief;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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