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 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 …

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 …

We apply the tensor train (TT) decomposition to construct the tensor product polynomial
chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with …

We consider stationary viscous mean-field games (MFG) systems in the case of local,
decreasing and unbounded coupling. These systems arise in ergodic MFG theory and …

Here, we consider stationary monotone mean-field games (MFGs) and study the existence
of weak solutions induced by monotonicity. First, we introduce a regularized problem that …

A standard assumption in mean-field game (MFG) theory is that the coupling between the
Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in …

We consider a class of quasilinear elliptic systems of PDEs consisting of N Hamilton–Jacobi–
Bellman equations coupled with N divergence form equations, generalising to N> 1 …

This paper studies an inverse problem for a multipopulation mean field game (MFG) system
where the objective is to reconstruct the running and terminal cost functions of the system …