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

Satoh, Atsuhiro and Tanaka, Yasuhito (2017): Sion's minimax theorem and Nash equilibrium of symmetric multi-person zero-sum game.

Abstract

We will show that Sion's minimax theorem is equivalent to the existence of Nash equilibrium in a symmetric multi-person zero-sum game. If a zero-sum game is asymmetric, maximin strategies and minimax strategies of players do not correspond to Nash equilibrium strategies. However, if it is symmetric, the maximin strategy and the minimax strategy constitute a Nash equilibrium.

• Item Type: MPRA Paper
• Language: English
• Keywords: multi-person zero-sum game, Nash equilibrium, Sion's minimax theorem.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

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