Non-cooperative and cooperative games with a very large number of players have many
applications but remain generally intractable when the number of players increases …

We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb
{R}^ d\times\mathcal {P} _2 (\mathbb {R}^ d), $ where $\mathcal {P} _2 (\mathbb {R}^ d) $ is …

This paper continues the study of the mean field game (MFG) convergence problem: In what
sense do the Nash equilibria of n-player stochastic differential games converge to the mean …

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 paper studies the convergence problem for mean field games with common noise. We
define a suitable notion of weak mean field equilibria, which we prove captures all …

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 …