摘要翻译：
研究了连续函数的Sion极大极小定理与两群零和对称的五人对策的纳什均衡之间的关系。我们将显示以下结果。1.每组中对称的纳什均衡的存在意味着每组中一对游戏的Sion极大极小定理。2.对于每组中的一对游戏，Sion的极大极小定理暗示了在每组中存在一个对称的纳什均衡。因此，它们是等价的。这类博弈的一个例子是两个寡头垄断下的每一集团的相对利润最大化博弈，使得每一集团中的企业具有相同的成本函数并使其在每一集团中的相对利润最大化，并且每一集团中的企业的需求函数对称。
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英文标题：
《Sion's mini-max theorem and Nash equilibrium in a five-players game with
  two groups which is zero-sum and symmetric in each group》
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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：General Economics        一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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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 a five-players game with two groups which is zero-sum and symmetric in each group. We will show the following results.   1. The existence of Nash equilibrium which is symmetric in each group implies Sion's minimax theorem for a pair of playes in each group. 2. Sion's minimax theorem for a pair of playes in each group imply the existence of a Nash equilibrium which is symmetric in each group.   Thus, they are equivalent. An example of such a game is a relative profit maximization game in each group under oligopoly with two groups such that firms in each group have the same cost functions and maximize their relative profits in each group, and the demand functions are symmetric for the firms in each group.
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PDF链接：
https://arxiv.org/pdf/1809.02466