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首页> 外文期刊>Minimax theory and its applications >Sion's Minimax Theorem and Nash Equilibria of Symmetric Multi-Players Zero-Sum Games with Continuous Strategies
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Sion's Minimax Theorem and Nash Equilibria of Symmetric Multi-Players Zero-Sum Games with Continuous Strategies

机译：锡安的极小极大定理和纳什均衡对称的多人零和游戏连续策略

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摘要

About a symmetric multi-players zero-sum game with continuous strategies 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 may not correspond to Nash equilibrium strategies. However, if it is symmetric, the maximin strategies and the minimax strategies constitute a Nash equilibrium.
机译：关于一个对称的多人零和游戏我们将介绍以下连续策略结果。极大极小定理的巧合战略和极小极大策略了对称纳什均衡的存在。(2)对称纳什均衡的存在证明了锡安的修改版本的吗极大极小定理的巧合极大极小战略和极大极小的策略。他们是等价的。不对称、极大极小策略和极大极小策略的玩家可能不对应于纳什均衡策略。对称的,极大极小策略和极大极小构成纳什均衡策略。

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