n人非合作博弈纳什均衡解的存在性  

The existence of Nash equilibria for a class of n-person noncooperative games

作　　者：卢婧琦 洪世煌[1] 江俊 LU Jingqi;HONG Shihuang;JIANG Jun(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2022年第6期80-83,共4页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(71771068,71471051)。

摘　　要：讨论一类n人非合作博弈纳什均衡的存在性。首先给出集值映射局部包含性的概念,根据这一性质,在不假设策略集的紧(凸)性及支付函数的拟凸性的前提下,给出了纳什均衡存在性的充分条件,从而推广了某些已有文献的结论。最后,通过实例验证了所得结论的适用性。This paper discusses the existence of Nash equilibria for a class of n-person noncooperative games. Firstly, the concept of local inclusion of set-valued mapping is given. Then, by using this property, a sufficient condition for the existence of Nash equilibrium in the game is given without assuming the compactness(or convexity) of the strategy sets and the quasi-convexity of the payoff functions. Thus, some conditions of the existing literature are weakened. A specific example is given to illustrate the applicability of our results.

关 键 词：纳什均衡 博弈论 集值分析 解的存在性 

分 类 号：O225[理学—运筹学与控制论]