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

Meeting ID: 972 3293 9340

Password: 151920