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Best-reply sets

Author

Listed:
  • Jonathan Weinstein

    (Washington University in St. Louis)

Abstract

We provide results concerning, in a given normal-form game, which sets of actions are best replies to some belief. Proposition 1 states that for any set S of actions, there is a belief under which all actions in S are simultaneously best replies if and only if no mixture of actions in S is strictly dominated. Similarly, Proposition 2 states that for any set S of actions, there is a full-support belief under which all actions in S are best replies if and only if no mixture of actions in S is weakly dominated. One important consequence is Corollary 1: a two-player game has a totally mixed Nash equilibrium if and only if neither player has a pair of mixed strategies such that one weakly dominates the other.

Suggested Citation

  • Jonathan Weinstein, 2020. "Best-reply sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 105-112, April.
    • Handle: RePEc:spr:etbull:v:8:y:2020:i:1:d:10.1007_s40505-019-00169-1
    DOI: 10.1007/s40505-019-00169-1
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    References listed on IDEAS

    as
    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    2. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    3. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
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    More about this item

    Keywords

    Game theory; Normal-form games; Best replies; Rationalizability;
    All these keywords.

    JEL classification:

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

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