Related papers: A Lagrange-Galerkin scheme for first order mean fi…
The paper is concerned with the deterministic limit of mean field games with the nonlocal coupling. It is assumed that the dynamics of mean field games are given by nonlinear Markov processes. This type of games includes stochastic mean…
We address the numerical solution of second-order Mean Field Game problems through Newton iterations in infinite dimensions, introduced in [14], where quadratic convergence of the method was rigorously established. Building upon this…
Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +$\infty$, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a…
The mean-field game system is treated as an Euler Lagrange system corresponding to an optimal control problem governed by Fokker-Planck equation.
The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…
We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…
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 paper introduces a new method based on Deep Galerkin Methods (DGMs) for solving high-dimensional stochastic Mean Field Games (MFGs). We achieve this by using two neural networks to approximate the unknown solutions of the MFG system…
Explicit, unconditionally stable, high-order schemes for the approximation of some first- andsecond-order linear, time-dependent partial differential equations (PDEs) are proposed.The schemes are based on a weak formulation of a…
In this article, we introduce a method to approximate solutions of some variational mean field game problems with congestion, by finite sets of player trajectories. These trajectories are obtained by solving a minimization problem similar…
This paper investigates the well-posedness of a type of state constraint ergodic Mean Field Game system in a bounded domain in which the Hamilton-Jacobi-Bellman equation is paired with an infinite Dirichlet boundary condition. In this…
The second order Mean Field Games system (MFGS) in a bounded domain with the lateral Cauchy data is considered. This means that both Dirichlet and Neumann boundary data for the solution the MFGS are given. Two H\"older stability estimates…
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…
This work focuses on the rate of convergence for singular perturbation problems for first-order Hamilton-Jacobi equations. As an application we derive the rate of convergence for singularly perturbed two-players zero-sum deterministic…
Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…
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 provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with…
We study the intermediate asymptotic behavior of solutions to the first-order mean field games system with a local coupling, when the initial density is a compactly supported function on the real line, and the coupling is of power type.…
The goal of this paper is to show existence of short-time classical solutions to the so called Master Equation of \emph{first order} Mean Field Games, which can be thought of as the limit of the corresponding master equation of a stochastic…