The theory of mean field games aims at studying deterministic or stochastic differential
games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field …

The mean-field framework was developed to study systems with an infinite number of
rational agents in competition, which arise naturally in many applications. The systematic …

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 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 turnpike property in contemporary macroeconomics asserts that if an economic planner
seeks to move an economy from one level of capital to another, then the most efficient path …

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 …

This paper analyzes the convergence of optimal control problems for an evolution equation
in a finite time-horizon 0,T toward the limit steady state ones as T→∞. We focus on linear …

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 …

We address the numerical approximation of mean field games with local couplings. For
power-like Hamiltonians, we consider a stationary system and also a system involving …