The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …

This book brings together several recent developments on the regularity theory for mean-
field game systems. We detail several classes of methods and present a concise overview of …

We analyze a (possibly degenerate) second order mean field games system of partial
differential equations. The distinguishing features of the model considered are (1) that it is …

We deal with systems of PDEs, arising in mean field games theory, where viscous Hamilton–
Jacobi and Fokker–Planck equations are coupled in a forward-backward structure. We …

The theory of mean field games (MFGs) studies the limiting behaviors of large systems
where the agents interact with each other in a certain symmetric way. The running and …

Mean field games are studied in the framework of controlled martingale problems, and
general existence theorems are proven in which the equilibrium control is Markovian. The …

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 …

We consider a first-order system of mean field games with local coupling in the deterministic
limit. Under general structure conditions on the Hamiltonian and coupling, we prove …

Here, we consider numerical methods for stationary mean-field games (MFG) and
investigate two classes of algorithms. The first one is a gradient-flow method based on the …

In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians
and power-like local dependence on the measure. We establish existence of classical …