T-凸空间中Fan Ky点与Nash平衡点存在定理  

The existence theorems of Fan Ky's points and Nash equilibrium points on T-convex spaces

作　　者：陈治友[1] CHEN Zhi-you(College of Mathematics and Information Science,Guiyang University,Guiyang 550005,China)

机构地区：[1]贵阳学院数学与信息科学学院,贵州贵阳550005

出　　处：《高校应用数学学报（A辑）》2020年第1期108-114,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11561013;11761023);贵州省科技基金(黔科合J字[2014]2005);贵州省科技合作计划(黔科合LH字[2015]7298)。

摘　　要：充分利用KKM方法和经典的集值分析方法,在不具有线性结构的T-凸空间中,建立并证明了弱Fan Ky点存在引理,并借助该引理获得了两个Fan Ky点存在定理;最后,作为对Fan Ky点存在定理的应用,在T-凸策略空间中建立并证明了n人非合作博弈Nash平衡点存在定理.In this paper,by making full use of the KKM method and the classical multivalued analysis method,the existence lemma of weak Fan Ky's points is established and proved in T-convex spaces without a linear structure.Based on this lemma,two existence theorems of Fan Ky's points are obtained.As an application of the existence theorems of Fan Ky's points,the existence theorem of Nash equilibrium points for n-person non-cooperative game is established and proved in T-convex strategy spaces.

关 键 词：T-凸空间 Fan Ky点 弱Fan Ky点 NASH平衡点 

分 类 号：O177.91[理学—数学]