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In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints,…

Mean-Field Game (MFG) serves as a crucial mathematical framework in modeling the collective behavior of individual agents interacting stochastically with a large population. In this work, we aim at solving a challenging class of MFGs in…

Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…

In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…

The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game…

The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many…

This article focuses two issues related to the first-order discounted mean field games system. The first is the time discretization problem. The time discretization approach enables us to prove the existence of solutions (u,m) of the…

This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon…

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…

Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential games with $n$ players interacting with one another through their common empirical distribution. Under suitable smoothness assumptions that…

This article presents the variant of the approach introduced in the recent work of Bensoussan, Wong, Yam and Yuan [13] to the generic first-order mean field game problem. A major contribution here is the provision of new crucial a priori…

We present results of existence, regularity and uniqueness of solutions of the master equation associated with the mean field planning problem in the finite state space case, in the presence of a common noise. The results hold under…

This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…

The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…

Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such…

In this paper, the existence of non-trivial time periodic solutions of first order mean field games is proved. It is assumed that there is a non-trivial periodic orbit contained in the Mather set. The whole system is autonomous with a…

The Schr\"odinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a differential equation whose flow can be split with benefit into…

The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite general assumptions. Remarkably, this is achieved without…