In this paper, we present two generalizations of the well-known Browder fixed point theorem, one of which is equivalent to the well-known Fan–Knaster–Kuratowski–Mazurkiewicz theorem. As applications, we apply these fixed point theorems to derive existence theorems for Nash equilibria in generalized games which generalize some existing existence theorems in the literature, including the well-known equilibrium existence theorem by Arrow and Debreu (Econometrica 22:265–290, 1954) and the existence theorem by Cubiotti (Int J Game Theory 26:267–273, 1997).

中文翻译：

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广义博弈中的Browder型不动点定理和Nash均衡

在本文中，我们给出了著名的Browder不动点定理的两种推广，其中之一等效于著名的Fan-Knaster-Kuratowski-Mazurkiewicz定理。作为应用，我们应用这些不动点定理来推导广义博弈中的纳什均衡的存在定理，这些博弈论概括了文献中的一些现有存在定理，包括著名的Arrow and Debreu平衡存在定理（计量经济学22：265–290，1954年）。 ）和Cubiotti的存在性定理（Int J Game Theory 26：267-273，1997）。