Satoh, Atsuhiro and Tanaka, Yasuhito (2018): Sion's minimax theorem and Nash equilibrium of symmetric multiperson zerosum game.

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Abstract
About a symmetric multiperson zerosum 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 zerosum 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 multiperson zerosum game.
Item Type:  MPRA Paper 

Original Title:  Sion's minimax theorem and Nash equilibrium of symmetric multiperson zerosum game 
Language:  English 
Keywords:  multiperson zerosum game, Nash equilibrium,Sion's minimax theorem 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C57  Econometrics of Games and Auctions C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  84533 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  13 Feb 2018 19:57 
Last Modified:  03 Oct 2019 04:55 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/84533 