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 …

In this paper we propose two new monotonicity conditions that could serve as sufficient
conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for …

This paper presents a class of evolutive Mean Field Games with multiple solutions for all
time horizons T and convex but non-smooth Hamiltonian H, as well as for smooth H and T …

In this paper we investigate maximal L q-regularity for time-dependent viscous Hamilton–
Jacobi equations with unbounded right-hand side and superlinear growth in the gradient …

We consider mean field game systems in time-horizon (0, T), where the individual cost
functional depends locally on the density distribution of the agents, and the Hamiltonian is …

The classical Kuramoto model is studied in the setting of an infinite horizon mean field
game. The system is shown to exhibit both synchronization and phase transition …

Abstract Recently, R. Carmona, Q. Cormier, and M. Soner proposed a Mean Field Game
(MFG) version of the classical Kuramoto model, which describes synchronization …

We consider time-dependent viscous mean-field games systems in the case of local,
decreasing and unbounded couplings. These systems arise in mean-field game theory, and …

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with
common noises and their corresponding $ N $-player games. The theory of mean field game …

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 …