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Existence of pure equilibria in symmetric two-player zero-sum games

Author

Listed:
  • Mehmet S. Ismail

    (King’s College London)

  • Ronald Peeters

    (University of Otago)

Abstract

This paper contributes to the literature on pure equilibria in symmetric zero-sum games in two main ways. First, we introduce new sufficient conditions, including interchangeability and weak quasiconcavity, for the existence of such equilibria. Second, we uncover relationships between these newly introduced conditions and existing ones. For instance, we demonstrate that the class of weakly quasiconcave games generalizes the class of quasiconcave games and ordinal potential games. Additionally, we show that exact potential games satisfy the interchangeability condition. However, no logical relationship exists between interchangeability and (weak) quasiconcavity.

Suggested Citation

  • Mehmet S. Ismail & Ronald Peeters, 2025. "Existence of pure equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(1), pages 1-18, June.
    • Handle: RePEc:spr:jogath:v:54:y:2025:i:1:d:10.1007_s00182-025-00938-2
    DOI: 10.1007/s00182-025-00938-2
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    References listed on IDEAS

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    More about this item

    Keywords

    Saddle points; Symmetric two-player zero-sum games; Pure strategy equilibrium; Potential games; Quasiconcave games;
    All these keywords.

    JEL classification:

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

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