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Sion's minimax theorem and Nash equilibrium of symmetric multi-person zero-sum game

Atsuhiro Satoh () and Yasuhito Tanaka ()

MPRA Paper from University Library of Munich, Germany

Abstract: About a symmetric multi-person zero-sum game we will show the following results. 1. Sion's minimax theorem plus the coincidence of the maximin strategy and the minimax strategy are proved by the existence of a symmetric Nash equilibrium. 2. The existence of a symmetric Nash equilibrium is proved by Sion's minimax theorem plus the coincidence of the maximin strategy and the minimax strategy. Thus, they are equivalent. If a zero-sum game is asymmetric, maximin strategies and minimax strategies of players do not correspond to Nash equilibrium strategies. If it is symmetric, the maximin strategies and the minimax strategies constitute a Nash equilibrium. However, with only the minimax theorem there may exist an asymmetric equilibrium in a symmetric multi-person zero-sum game.

Keywords: multi-person zero-sum game; Nash equilibrium; Sion's minimax theorem (search for similar items in EconPapers)
JEL-codes: C57 C72 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
Date: 2018-02-13
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Working Paper: Sion's minimax theorem and Nash equilibrium of symmetric multi-person zero-sum game (2017) Downloads
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