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

Atsuhiro Satoh and Yasuhito Tanaka

MPRA Paper from University Library of Munich, Germany

Abstract: About a symmetric three-players zero-sum game we will show the following results. 1. 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. 2. 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. 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, 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.

Keywords: three-players zero-sum game; Nash equilibrium; Sion's minimax theorem (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2018-03-24
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game (2020)
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