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Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game

Author

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  • Atsuhiro Satoh
  • Yasuhito Tanaka

Abstract

About a symmetric three-players zero-sum game we will show the following results. A modified version of Sion's minimax theorem with the coincidence of the maximin strategy and the minimax strategy are proved by the existence of a symmetric Nash equilibrium. The existence of a symmetric Nash equilibrium is proved by the modified version of Sion's minimax theorem with the coincidence of the maximin strategy and the minimax strategy. Thus, they are equivalent. However, without the coincidence of the maximin strategy and the minimax strategy there may exist an asymmetric equilibrium in a symmetric three-players zero-sum game.

Suggested Citation

  • Atsuhiro Satoh & Yasuhito Tanaka, 2020. "Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 16(2), pages 279-289.
    • Handle: RePEc:ids:ijmore:v:16:y:2020:i:2:p:279-289
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    Cited by:

    1. Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Nash equilibrium of partially asymmetric three-players zero-sum game with two strategic variables," Papers 1809.02465, arXiv.org.
    2. Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "The equivalence of mini-max theorem and existence of Nash equilibrium in asymmetric three-players zero-sum game with two groups," MPRA Paper 87249, University Library of Munich, Germany.

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    JEL classification:

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

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