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

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-06-04 DOI:10.1007/s00245-025-10273-3

E. Everardo Martinez-Garcia, Fernando Luque-Vásquez, J. Adolfo Minjárez-Sosa

引用次数: 0

Abstract

This work deals with a class of discrete-time mean-field games evolving according to a stochastic difference equation where the random disturbance distribution \(\theta \) 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 \(\theta \) with the mean-field games theory, we introduce approximation procedures for the mean-field equilibrium under a discounted optimality criterion.

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一类折现平均场对策中平均场均衡的统计估计

本文研究一类根据随机差分方程演化的离散时间平均场博弈，其中随机扰动分布\(\theta \)是未知的或难以处理的。在Borel空间上定义了平均场博弈，并假设其代价可能无界。然后，将\(\theta \)的适当统计估计过程与平均场博弈理论相结合，引入了贴现最优性准则下的平均场平衡的近似过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.