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

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Abstract
About a symmetric threeplayers zerosum 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 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, without the coincidence of the maximin strategy and the minimax strategy there may exist an asymmetric equilibrium in a symmetric threeplayers zerosum game.
Item Type:  MPRA Paper 

Original Title:  Sion's minimax theorem and Nash equilibrium of symmetric threeplayers zerosum game 
Language:  English 
Keywords:  threeplayers zerosum game, Nash equilibrium, Sion's minimax theorem 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  85452 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  25 Mar 2018 06:58 
Last Modified:  03 Oct 2019 07:16 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/85452 