Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game
by Atsuhiro Satoh; Yasuhito Tanaka
International Journal of Mathematics in Operational Research (IJMOR), Vol. 16, No. 2, 2020

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.

Online publication date: Mon, 16-Mar-2020

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