Convergence rate of LQG mean field games with common noise

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Mathematical Methods of Operations Research Pub Date : 2024-06-25 DOI:10.1007/s00186-024-00863-2

Jiamin Jian, Qingshuo Song, Jiaxuan Ye

引用次数: 0

Abstract

This paper focuses on exploring the convergence properties of a generic player’s trajectory and empirical measures in an N-player Linear-Quadratic-Gaussian Nash game, where Brownian motion serves as the common noise. The study establishes three distinct convergence rates concerning the representative player and empirical measure. To investigate the convergence, the methodology relies on a specific decomposition of the equilibrium path in the N-player game and utilizes the associated mean field games framework.

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具有共同噪声的 LQG 平均场博弈的收敛率

本文重点探讨了 N 人线性-二次方-高斯纳什博弈中一般博弈者的轨迹和经验度量的收敛特性，其中布朗运动是常见噪声。该研究确定了代表棋手和经验度量的三种不同收敛率。为了研究收敛性，该方法依赖于对 N 人博弈中均衡路径的特定分解，并利用相关的均值场博弈框架。

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

Mathematical Methods of Operations Research 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience. All papers are refereed. The emphasis is on originality, quality, and importance.