Browder type fixed point theorems and Nash equilibria in generalized games

被引：5

作者：

Liu, Jiuqiang ^{[1
,2
]}

Wang, Mingyu ^{[1
]}

Yuan, Yi ^{[3
]}

机构：

[1] Xian Univ Finance & Econ, China Xian Inst Silk Rd Res, Xian 710100, Shaanxi, Peoples R China

[2] Eastern Michigan Univ, Dept Math, Ypsilanti, MI 48197 USA

[3] Xian Univ Finance & Econ, Coll Business, Xian 710100, Shaanxi, Peoples R China

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2020年 / 22卷 / 03期

关键词：

Browder fixed point theorem; Fan-Knaster-Kuratowski-Mazurkiewicz theorem; generalized games; Nash equilibrium; MAXIMAL ELEMENTS; EXISTENCE;

D O I：

10.1007/s11784-020-00806-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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).

引用

页数：16

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