抽象凸空间上广义博弈Nash平衡点的存在性  

Existence of Nash equilibrium point in generalized game within an abstract convex space

作　　者：陈治友[1] 夏顺友[2] 

机构地区：[1]贵阳学院数学系,贵州贵阳550005 [2]贵州师范学院数学与计算机科学学院,贵州贵阳550018

出　　处：《辽宁工程技术大学学报（自然科学版）》2012年第5期786-791,共6页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(11161008);贵州省科技基金资助项目(2012GZ71164)

摘　　要：为了在满足H0-条件的抽象凸策略空间中,解决广义博弈中广义最大元对策与约束广义最大元对策的Nash平衡点的存在性问题,根据这两种对策中局中人的最优反应集值映射分别定义了两个对策的最优反应集值映射,利用抽象凸空间中的Fan-Glicksberg-kakutani不动点定理,证明了两个对策的最优反应集值映射均存在不动点,从而获得了广义最大元对策与约束广义最大元对策均存在Nash平衡点的结果.该成果对于用广义最大元方法研究广义博弈中的对策平衡具有一定的参考价值和指导意义.In order to solve the existence problem of Nash equilibrium point for the generalized maximal element game and the restricted generalized maximal element game in an abstract convex game space which satisfies H0-condition,this paper defines the optimal reflection set-valued mappings of two strategies respectively based on two relevant strategy players.In addition,the paper proves the existence of the fixed point in optimal reflection set-valued mappings of two strategies and,therefore,obtains the existence conclusion of Nash equilibrium point for the generalized maximal element game and the restricted generalized maximal element game by applying the Fan-Glicksberg-kakutani fixed point theorem in an abstract convex space.The study results are valuable for future study in the area.

关 键 词：对策论 抽象凸策略空间 H0-条件 广义最大元 最优反应映射 积空间 不动点定理 NASH平衡点 

分 类 号：O177.91[理学—数学]