Convergence rate of LQG mean field games with common noise

Jiamin Jian (), Qingshuo Song () and Jiaxuan Ye ()
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Jiamin Jian: Worcester Polytechnic Institute
Qingshuo Song: Worcester Polytechnic Institute
Jiaxuan Ye: Worcester Polytechnic Institute

Mathematical Methods of Operations Research, 2024, vol. 99, issue 3, No 2, 233-270

Abstract: 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.

Keywords: Mean field games; N-Player Nash game; Convergence rate; Wasserstein distance (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00186-024-00863-2

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