群体博弈与多目标群体博弈的逼近定理  

Approximation Theorem of Population Games and Multi-objective Population Games

作　　者：王春 杨辉 杨光惠 王国玲 Wang Chun;Yang Hui;GuangYang Hui;Wang Guoling(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913-920,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11271098);贵州省科技计划项目(黔科合基础[2019]1067号);贵州省科技计划项目(黔科合基础-ZK[2022]一般168);贵州省教学改革项目(201908)。

摘　　要：在群体博弈和多目标群体博弈模型下,通过策略扰动,代理人的理性程度被进一步减弱了.由此定义了相应的近似解,并证明了其逼近定理.这不仅使得其逼近过程更符合实际,而且还完善了其Nash平衡状态和弱Pareto-Nash平衡状态求解算法的理论支撑.In population games and multi-objective population games,by perturbation of strategies,we relax rationality of agents further,which is represented by an approximate solution called approximate Nash equilibria and approximate weakly Pareto-Nash equilibria.And we prove their approximation theorem.They not only realistically weaken the condition of approximation theorem,but they also improve the theoretical support for the algorithm of population games.

关 键 词：群体博弈 有限理性 逼近定理 

分 类 号：O225[理学—运筹学与控制论]