Related papers: A fully-discrete Semi-Lagrangian scheme for a firs…
We introduce a mean field game model for pedestrians moving in a given domain and choosing their trajectories so as to minimize a cost including a penalization on the difference between their own velocity and that of the other agents they…
We study the regularity and well-posedness of the local, first-order forward-backward mean field games system, assuming a polynomially growing cost function and a Hamiltonian of quadratic growth. We consider systems and terminal data that…
We consider a convexity constrained Hamilton-Jacobi-Bellman-type obstacle problem for the value function of a zero-sum differential game with asymmetric information. We propose a convexity-preserving probabilistic numerical scheme for the…
We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation's gradient flow structure with respect to the Wasserstein distance. The scheme inherits…
In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset $\Gamma$ of full space $\mathbb{R}^m$. The decentralized strategies and consistency…
We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master…
We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…
In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…
Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the…
We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state…
The aim of this paper is to study the long time behavior of solutions to deterministic mean field games systems on Euclidean space. This problem was addressed on the torus ${\mathbb T}^n$ in [P. Cardaliaguet, {\it Long time average of first…
This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…
Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These…
Convergence of the policy iteration method for discrete and continuous optimal control problems holds under general assumptions. Moreover, in some circumstances, it is also possible to show a quadratic rate of convergence for the algorithm.…
We study the wellposedness of the master equation for a second-order mean field games with the Grushin type diffusion. In order to do this, we obtain the properties of its solution by investigating a degenerate mean field games system for…
The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain…
We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and…
This paper establishes the existence of equilibria result of a class of mean field games with singular controls. The interaction takes place through both states and controls. A relaxed solution approach is used. To circumvent the tightness…
This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…
The standard formulation of the PDE system of Mean Field Games (MFG) requires the differentiability of the Hamiltonian. However in many cases, the structure of the underlying optimal problem leads to a convex but nondifferentiable…