主从群体博弈合作均衡的通有稳定性  

Generic Stability of Cooperative Equilibria for Leader-Follower Population Games

作　　者：武文俊 杨光惠 房才雅 杨辉 Wu Wenjun;Yang Guanghui;Fang Caiya;Yang Hui(College of Mathematics and Statistics,Guizhou University,Guiyang 550025;Guizhou Provincial Key Laboratory for Games Decision-Making and Control Systems,Guiyang 550025)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州省博弈决策与控制系统重点实验室,贵阳550025

出　　处：《数学物理学报（A辑）》2023年第3期921-929,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11271098);贵州大学引进人才科研项目([2017]59);贵州省科技计划项目(黔科合基础[2019]1067号);贵州省教学改革项目(2019008)。

摘　　要：该文研究了一个领导者和多个群体跟随者构成的主从群体博弈合作均衡的存在性及稳定性.首先,当群体跟随者间存在合作行为时,定义了主从群体博弈的合作均衡;其次,给出了一个合作均衡的存在性定理,并通过算例说明了合作均衡的存在性及与Nash均衡是不同的均衡.最后,应用集值分析中的Fort定理证明了在Baire分类意义下,得到了支付函数扰动的情况下,大多数主从群体博弈的合作均衡点集都是通有稳定的.In this paper,we study the existence and generic stability of cooperative equilibria in leader-follower population games with a leader and multiple population followers.Firstly,a cooperative equilibrium of leader-follower population games is defined in consideration of cooperative behavior among population followers.Secondly,we prove the existence of cooperative equilibria,and an example is illustrated that cooperative equilibria exist and are different from the classical Nash equilibria.Finally,using Fort's theorem,we prove that in the sense of Baire category most cooperative equilibria of leader-follower population games are of generic stability under perturbations of payoff functions.

关 键 词：主从群体博弈 合作均衡 存在性 通有稳定性 

分 类 号：O225[理学—运筹学与控制论]