Convergence Rate of LQG Mean Field Games with Common Noise

TL;DR

This paper analyzes how quickly the trajectories and empirical measures of players in an N-player LQG Nash game with common noise converge, using a decomposition approach within the Mean Field Game framework.

Contribution

It establishes three different convergence rates for the trajectories and empirical measures in LQG mean field games with common noise, advancing understanding of their convergence properties.

Findings

Three distinct convergence rates are derived.

The methodology uses a decomposition of the equilibrium path.

The study applies the MFG framework to analyze convergence.

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 Game framework.