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摘要翻译：
本文研究了非对称多人零和对策中连续函数的Sion极大极小定理与纳什均衡之间的关系，其中只有一个博弈方不同于其他博弈方，而该对策对其他博弈方是对称的。然后，1。纳什均衡的存在，对于一个玩家以外的玩家是对称的，意味着对于这个玩家和另一个玩家的对，对于另一个玩家对称的Sion的极小极大定理。2.对于一个博弈方和另一个博弈方的对，另一个博弈方对称的Sion极大极小定理表明存在一个对另一个博弈方对称的纳什均衡。因此，它们是等价的。
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英文标题：
《On the relation between Sion's minimax theorem and existence of Nash
equilibrium in asymmetric multi-players zero-sum game with only one alien》
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作者：
Atsuhiro Satoh and Yasuhito Tanaka
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最新提交年份：
2018
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in an asymmetric multi-players zero-sum game in which only one player is different from other players, and the game is symmetric for the other players. Then, 1. The existence of a Nash equilibrium, which is symmetric for players other than one player, implies Sion's minimax theorem for pairs of this player and one of other players with symmetry for the other players. 2. Sion's minimax theorem for pairs of one player and one of other players with symmetry for the other players implies the existence of a Nash equilibrium which is symmetric for the other players. Thus, they are equivalent.
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PDF链接：
https://arxiv.org/pdf/1806.07253
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