广义集值博弈问题非合作均衡点的存在性和稳定性  

Existence and stability of noncooperative equilibrium points of generalized set payoffs games problems

作　　者：赵巧灵 张宇 王佳 ZHAO Qiaoling;ZHANG Yu;WANG Jia(College of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming 650221,China;Office of Educational Academic Affairs,Yunnan University of Finance and Economics,Kunming 650221,China)

机构地区：[1]云南财经大学统计与数学学院,云南昆明650221 [2]云南财经大学教务处,云南昆明650221

出　　处：《纯粹数学与应用数学》2024年第3期526-536,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(11901511);云南省基础研究(202101AT070216);云南财经大学研究生创新研究项目(2022YUFEYC072).

摘　　要：利用Kakutani-Fan-Glicksberg不动点定理和集最优值函数的半连续性结果,得到了广义集值博弈问题非合作均衡点的存在性定理.并给出例子解释此定理推广了已有文献中的结果.进一步,还研究了当支付函数和可行约束映射受扰动后,此非合作均衡点集的稳定性定理.By using the Kakutani-Fan-Glicksberg fixed-point theorem and the continuity results of optimal valued function of set-valued mappings,an existence theorem of noncooperative equilibrium point for generalized set payoff game problems is obtained.An example is given to explain our result extends the ones in the literatures.Furthermore,when the payoff functions and feasible constraint mappings are disturbed,stability theorem of the equilibrium point set is obtained.

关 键 词：集支付 向量优化 通有稳定性 不动点定理 

分 类 号：O225[理学—运筹学与控制论]