序空间中的极大元定理及其在博弈中的应用  

The maximal element theorem in ordered spaces with applications to games

作　　者：岳洁晴 洪世煌[1] 贾科克 YUE Jieqing;HONG Shihuang;JIA Keke(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）》2023年第4期72-75,96,共5页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(71771068)。

摘　　要：运用不动点定理及偏序集中归纳集的性质,获得了乘积序空间中集值映射的1个极大元定理。同时,将该定理应用于非合作非货币化博弈,得到1个广义Nash均衡点存在性定理,并用实例验证了该存在性定理的可行性。In this paper,a maximal element theorem is established by applying the fixed point theorem and the properties of the inductive set for set-valued function on partially ordered set.Moreover,this result is used to establish an existence theorem of the extended Nash equilibriums for the nonmonetized noncooperative games.Finally,a practical example is given to verify the feasibility of the existence theorem.

关 键 词：偏序集 极大元定理 不动点定理 NASH均衡 

分 类 号：O225[理学—运筹学与控制论]