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On the IENBR-solvability of two-person finite games

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  • Iimura, Takuya

Abstract

We show that a two-person finite game is solved by the iterated elimination of never best responses (IENBR) if and only if it is best response acyclic and strongly solvable in the sense of Nash (1951). Thus the rationalizable strategies (Bernheim, 1984; Pearce, 1984) are equivalent to the Nash equilibrium strategies in two-person finite games if and only if the two conditions are met. We prove this for both mixed strategy games and pure strategy games.

Suggested Citation

  • Iimura, Takuya, 2016. "On the IENBR-solvability of two-person finite games," Economics Letters, Elsevier, vol. 146(C), pages 68-70.
    • Handle: RePEc:eee:ecolet:v:146:y:2016:i:c:p:68-70
    DOI: 10.1016/j.econlet.2016.07.023
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    References listed on IDEAS

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    1. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. Krzysztof Apt & Sunil Simon, 2015. "A classification of weakly acyclic games," Theory and Decision, Springer, vol. 78(4), pages 501-524, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Iterated elimination of never best responses; Rationalizable strategies; Best response acyclic games; Strongly solvable games;
    All these keywords.

    JEL classification:

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

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