Linear quadratic mean field games and their asymptotic solvability
Abstract
We consider linear quadratic (LQ) mean field games (MFGs) and study their asymptotic solvability problems. Roughly, we attempt to answer these questions: When does a sequence of games, with increasing populations, have “well behaved’’ centralized solutions? And how to characterize a necessary and sufficient condition for such nice solution behaviors. We start with a model of homogeneous agents and develop a re-scaling technique for analysis. An important issue in MFGs is the performance of the obtained decentralized strategies in an N-player model, and one usually can obtain an O(N^{-1/2})- Nash equilibrium. By our approach we can improve the estimate from O(N^{-1/2}) to the tightest bound O(1/N).
We will further generalize to a major player model and clarify the relation of different solutions existing in the literature. Finally, this asymptotic solvability formulation can be extended to mean field social optimization.
Zoom Link
https://cityu.zoom.us/j/97232939340?pwd=VU9mNVVNZUNVZDc3NllUTldPN1hNUT09