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Two-person pairwise solvable games

Author

Listed:
  • Takuya Iimura

    (Tokyo Metropolitan University)

  • Toshimasa Maruta

    (Nihon University)

  • Takahiro Watanabe

    (Tokyo Metropolitan University)

Abstract

A game is solvable if the set of Nash equilibria is nonempty and interchangeable. A pairwise solvable game is a two-person symmetric game in which any restricted game generated by a pair of strategies is solvable. We show that the set of equilibria in a pairwise solvable game is interchangeable. Under a quasiconcavity condition, we derive a complete order-theoretic characterization and some topological sufficient conditions for the existence of equilibria, and show that if the game is finite, then an iterated elimination of weakly dominated strategies leads precisely to the set of Nash equilibria, which means that such a game is both solvable and dominance solvable. All results are applicable to symmetric contests, such as the rent-seeking game and the rank-order tournament, which are shown to be pairwise solvable. Some applications to evolutionary equilibria are also given.

Suggested Citation

  • Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2020. "Two-person pairwise solvable games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 385-409, June.
  • Handle: RePEc:spr:jogath:v:49:y:2020:i:2:d:10.1007_s00182-020-00709-1
    DOI: 10.1007/s00182-020-00709-1
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    References listed on IDEAS

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    Cited by:

    1. Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2019. "Equilibria in games with weak payoff externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 245-258, December.

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    More about this item

    Keywords

    Zero-sum games; Quasiconcavity; Interchangeability; Dominance solvability; Nash equilibrium; Evolutionary equilibrium;
    All these keywords.

    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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