群体博弈的逼近定理及通有收敛性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1566-1573.

群体博弈的逼近定理及通有收敛性

陈华鑫,贾文生*()

^{贵州大学数学与统计学院贵阳 550025}

收稿日期:2020-08-13 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 贾文生 E-mail:wsjia@gzu.edu.cn
基金资助:
国家自然科学基金(12061020);贵州省科技基金(20201Y284);贵州大学基金(201405);贵州大学基金(201811)

Approximation Theorem and General Convergence of Population Games

Huaxin Chen,Wensheng Jia*()

^{School of Mathematics and Statistics, Guizhou University, Guiyang 550025}

Received:2020-08-13 Online:2021-10-26 Published:2021-10-08
Contact: Wensheng Jia E-mail:wsjia@gzu.edu.cn
Supported by:
the NSFC(12061020);the Science and Technology Foundation of Guizhou Province(20201Y284);the Foundation of Guizhou University(201405);the Foundation of Guizhou University(201811)

摘要/Abstract

摘要：

该文针对群体博弈，研究了表示有限理性的近似解能否收敛到表示完全理性的精确解问题，为群体博弈问题的求解算法提供了一个理论支持.首先在一定的假设条件下，证明了有限理性条件下群体博弈的逼近定理.然后，利用集值分析的方法，在Baire分类的意义下，得到了目标函数扰动情况下群体博弈的解具有通有收敛性的结果.

关键词: 群体博弈, 逼近定理, 通有收敛性, 有限理性

Abstract:

In this paper, we study whether the approximate solution of bounded rationality converges to the exact solution of complete rationality, which provides a theoretical support for the algorithm of population games. Firstly, under certain assumptions, the approximation theorem of population games under bounded rationality is proved. Then, by using the method of set-valued analysis and in the sense of Baire classification, we obtain the result that the solution of population games with perturbations on the objective function has generic convergence.

Key words: Population games, Approximation theorem, Generic convergence, Bounded rationality

中图分类号:

O225

陈华鑫,贾文生. 群体博弈的逼近定理及通有收敛性[J]. 数学物理学报, 2021, 41(5): 1566-1573.

Huaxin Chen,Wensheng Jia. Approximation Theorem and General Convergence of Population Games[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1566-1573.

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