Title:
The convergence rate of the equilibrium measure for the LQG Mean Field Game with a Common Noise
Abstract:
The convergence rate of equilibrium measures of N-player mean field games with Brownian common noise to its asymptotic Mean Field Game system is $O(N^{-1/9})$ with respect to 1-Wasserstein distance, obtained by the monograph [Cardaliaguet, Delarue, Lasry, Lions, 2019]. This work studies the convergence rate of the N-player LQG game with a Markov chain common noise towards its asymptotic limit. The approach relies on an explicit coupling of optimal trajectory from N-player game driven by N dimensional Brownian motion with its Mean Field Game counterpart driven by one dimensional Brownian motion. As a result, the convergence rate is $o(N^{-1/2+\epsilon})$.
Biography:
Qingshuo Song’s currently an associate professor at Worcester Polytechnic institute. His research interests include stochastic control theory, and its applications to mathematical finance and various engineering problems. Prior to joining Worcester Polytechnic Institute, he had been working with City University of Hong Kong (as an Associate Professor), University of Michigan and University of Southern California (as a Postdoc). Qingshuo received his BSc from Nankai University, MA and PhD from Wayne State University.
Zoom Meeting Details
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