Related papers: Second-order monotonicity conditions and mean fiel…

We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that…

We study a stationary first--order mean field game on the $d$--dimensional torus. The system couples a Hamilton--Jacobi equation for the value function with a transport equation for the density of players. Our goal is to give a detailed and…

We consider the variational approach to prove the existence of solutions of second order stationary Mean Field Games on a bounded domain $\Omega\subseteq \mathbb{R}^{d}$, with Neumann boundary conditions, and with and without density…

We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows…

This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…

This manuscript constructs global in time solutions to the $master\ equations$ for potential Mean Field Games. The study concerns a class of Lagrangians and initial data functions, which are $displacement\ convex$ and so, it may be in…

We introduce a model of anonymous games with the player dependent action sets. We propose several learning procedures based on the well-known Fictitious Play and Online Mirror Descent and prove their convergence to equilibrium under the…

In an extended mean field game the vector field governing the flow of the population can be different from that of the individual player at some mean field equilibrium. This new class strictly includes the standard mean field games. It is…

Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…

This paper studies the convergence of mean field games with finite state space to mean field games with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain…

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…

For a general nonlinear control system, we study the problem of small time local attainability of a target which is the closure of an open set. When the target is smooth and locally the sublevel set of a smooth function, we develop second…

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 a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a…

In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the…

Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…

We investigate time dependent, first order Mean Field Games on the torus comparing, in a broad and general framework, the classical differential formulation , given by a Hamilton Jacobi equation coupled with a continuity equation, with a…

This paper studies the monotonicity of equilibrium costs and equilibrium loads in nonatomic congestion games, in response to variations of the demands. The main goal is to identify conditions under which a paradoxical non-monotone behavior…