Statistical Estimation of Mean-Field Equilibria in a Class of Discounted Mean-Field Games

被引：0

作者：

E. Everardo Martinez-Garcia ^{[1
]}

Fernando Luque-Vásquez ^{[1
]}

J. Adolfo Minjárez-Sosa ^{[1
]}

机构：

[1] Universidad de Sonora,Departamento de Matemáticas

来源：

Applied Mathematics & Optimization | 2025年 / 91卷 / 3期

关键词：

Mean field games; Mean field equilibria; Statistical estimation; Discounted criterion; 91A15; 93E20; 62G05;

D O I：

10.1007/s00245-025-10273-3

中图分类号：

学科分类号：

摘要：

This work deals with a class of discrete-time mean-field games evolving according to a stochastic difference equation where the random disturbance distribution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} is unknown or difficult to handle. The mean-field game is defined on Borel spaces and it is assumed possibly unbounded costs. Then, by combining suitable statistical estimation process of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} with the mean-field games theory, we introduce approximation procedures for the mean-field equilibrium under a discounted optimality criterion.

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