Satoh, Atsuhiro and Tanaka, Yasuhito
(2018):
*Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game.*

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## 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.

Item Type: | MPRA Paper |
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Original Title: | Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game |

Language: | English |

Keywords: | three-players zero-sum 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.uni-muenchen.de/id/eprint/85452 |