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 …

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 investigate time-dependent mean-field games with superquadratic Hamiltonians and a
power dependence on the measure. Such problems pose substantial mathematical …

In this paper, we consider mean-field games where the interaction of each player with the
mean field takes into account not only the states of the players but also their collective …

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 …

In this paper, we prove the existence of classical solutions for time-dependent mean-field
games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the …

We consider second-order ergodic Mean-Field Games systems in the whole space RN with
coercive potential and aggregating nonlocal coupling, defined in terms of a Riesz interaction …

We consider time-dependent mean-field games with congestion that are given by a
Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are …

Here, we establish the existence of weak solutions to a wide class of time-dependent
monotone mean-field games (MFGs). These MFGs are given as a system of degenerate …