群体博弈与多目标群体博弈的逼近定理

数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 913-920.

群体博弈与多目标群体博弈的逼近定理

王春,杨辉^*(),杨光惠,王国玲

贵州大学数学与统计学院贵阳 550025; 贵州省博弈决策与控制系统重点实验室贵阳 550025

收稿日期:2022-04-25 修回日期:2023-02-12 出版日期:2023-06-26 发布日期:2023-06-01
通讯作者: 杨辉 E-mail:huiyang@gzu.edu.cn
基金资助:
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);贵州省教学改革项目(201908);贵州省科技计划项目(黔科合基础)(ZK[2022]General168)

Approximation Theorem of Population Games and Multi-objective Population Games

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

Received:2022-04-25 Revised:2023-02-12 Online:2023-06-26 Published:2023-06-01
Contact: Hui Yang E-mail:huiyang@gzu.edu.cn
Supported by:
NSFC(11271098);Guizhou Provincial Science and Technology Foundation([2019]1067);Educational Reform Foundation of Guizhou Procince(201908);Guizhou Provincial Science and Technology Projects(ZK[2022]General168)

摘要/Abstract

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.

关键词: 群体博弈, 有限理性, 逼近定理

Abstract:

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.

Key words: Population games, Bounded rationality, Approximation theorem

中图分类号:

O225

王春,杨辉,杨光惠,王国玲. 群体博弈与多目标群体博弈的逼近定理[J]. 数学物理学报, 2023, 43(3): 913-920.

Wang Chun,Yang Hui,GuangYang Hui,Wang Guoling. Approximation Theorem of Population Games and Multi-objective Population Games[J]. Acta mathematica scientia,Series A, 2023, 43(3): 913-920.

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