Motivated by the models of epidemic control in large populations, we consider a Stackelberg
mean field game model between a principal and a mean field of agents whose states evolve …

These notes are an introduction to Mean Field Game (MFG) theory, which models differential
games involving infinitely many interacting players. We focus here on the Partial Differential …

Mean field games (MFGs) describe the limit, as n tends to infinity, of stochastic differential
games with n players interacting with one another through their common empirical …

We study a sequence of symmetric n-player stochastic differential games driven by both
idiosyncratic and common sources of noise, in which players interact with each other …

We consider N-player and mean field games in continuous time over a finite horizon, where
the position of each agent belongs to {-1,1\}. If there is uniqueness of mean field game …

We force uniqueness in finite state mean field games by adding a Wright–Fisher common
noise. We achieve this by analyzing the master equation of this game, which is a degenerate …

This is an expanded version of the lecture given at the AMS Short Course on Mean Field
Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of …

We consider an n-player symmetric stochastic game with weak interactions between the
players. Time is continuous, and the horizon and the number of states are finite. We show …

We consider a game for a continuum of non-identical players evolving on a finite state
space. Their heterogeneous interactions are represented with a graphon, which can be …

We show the convergence of finite state symmetric N-player differential games, where
players control their transition rates from state to state, to a limiting dynamics given by a finite …