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 …

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 …

In this manuscript we propose a structural condition on nonseparable Hamiltonians, which
we term displacement monotonicity condition, to study second-order mean field games …

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 …