Mean Field Games: From Many-Player Games to PDEs

Overview

Mean field game theory provides a framework for studying interactions among very large populations of agents doing dynamic optimization. This talk will introduce the basic concepts of mean field games, beginning with the mean field limit that describes systems with infinitely many infinitesimal players. We will discuss how optimal control theory and Hamilton-Jacobi equations lead to partial differential equations approach to the mean field game theory. The talk will conclude with a discussion of some results on the existence of weak solutions to mean field game PDE systems using monotone operator theory.