群体博弈的逼近定理及通有收敛性

Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1566-1573.

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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)

Abstract

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

CLC Number:

O225

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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Approximation Theorem and General Convergence of Population Games

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