相关论文: Closed-loop convergence for mean field games with …

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

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 address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…

This paper studies linear quadratic graphon mean field games (LQ-GMFGs) with common noise, in which a large number of agents are coupled via a weighted undirected graph. One special feature, compared with the well-studied graphon mean field…

Here, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct…

The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on $\mathbb R^{d}$. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria), as Borel probability…

In this paper, we consider a mean field game model inspired by crowd motion where agents aim to reach a closed set, called target set, in minimal time. Congestion phenomena are modeled through a constraint on the velocity of an agent that…

We introduce a notion of weak solution of the master equation without idiosyncratic noise in Mean Field Game theory and establish its existence, uniqueness up to a constant and consistency with classical solutions when it is smooth. We work…

In this paper we provide the existence of classical solutions to stationary mean field game systems in the whole space $\mathbb{R}^N$, with coercive potential, aggregating local coupling, and under general conditions on the Hamiltonian,…

We consider a class of extended mean field games with common noises, where there exists a strictly terminal constraint. We solve the problem by reducing it to an unconstrained control problem by adding a penalized term in the cost…

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…

The objective of this paper is to provide an equivalent of the theory developed in P.~Cardaliaguet, F.~Delarue, J.M.~Lasry, P.L.~Lions \cite{CDLL}, following the approach of control on Hilbert spaces introduced by the authors in…

This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…

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…

We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to…

This paper studies the existence and approximation of equilibria for general time-inconsistent mean field game (MFG) problems in continuous time. To handle the intricate nonlocal equilibrium Hamilton-Jacobi-Bellman (EHJB) system arising…

We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…

In this paper, we study the long-time behavior of mean field game (MFG) systems influenced by a common noise. While classical results establish the convergence of deterministic MFG towards stationary solutions under suitable monotonicity…

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.…

We consider the mean field game of cross--holding introduced in \citeauthor*{DjeteTouzi} \cite{DjeteTouzi} in the context where the equity value dynamics are affected by a common noise. In contrast with \cite{DjeteTouzi}, the problem…