一类主从博弈Nash均衡点的存在性和稳定性  

The Existence and Stability of Nash Equilibrium Points for Single-Leader-Multi-Follower Games

作　　者：蔡江华 贾文生 刘露萍 CAI Jianghua;JIA Wensheng;LIU Luping(School of Mathematics and Statistics,Guizhou University,Guiyang Guizhou 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵州贵阳550025

出　　处：《江西师范大学学报（自然科学版）》2019年第3期277-281,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11561013);人社部留学归国人员择优(人社[2015]192);贵州省联合基金(黔科联合[2014]7643);贵州大学人才引进基金(贵大[2014]05);贵州大学培育基金(黔科合平台人才[2017]5788)资助项目

摘　　要：针对单个领导者与多个跟随者的主从博弈,在较弱的条件下,利用Berge极大值定理、Fan-Glicksberg不动点定理,证明了一类主从博弈Nash均衡点的存在性,推广和改进了已有的一些结果.在均衡点的稳定性方面,从最佳回应拓扑的角度证明了此类主从博弈存在Nash均衡点集的本质连通区.Aiming at the leader-follower game between single leader and multiple followers,the existence of Nash equilibrium point for single-leader-multi-follower games is proved by using the Berge maximum theorem and the Fan-Glicksberg fixed point theorem under the weak condition,and some of the new results have promotion and improvement.In terms of the stability of equilibrium point,it is proved from the viewpoint of best response topology that the single-leader-multi-follower games have the essential components of the Nash equilibrium point sets.

关 键 词：主从博弈 NASH 均衡点 伪连续 本质连通区 拟凹 

分 类 号：O225[理学—运筹学与控制论]