Related papers: Stationary focusing Mean Field Games
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…
Mean field games (MFG) and mean field control problems (MFC) are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative games with a…
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…
In a game theoretic framework, we study energy markets with a continuum of homogenous producers who produce energy from an exhaustible resource such as oil. Each producer simultaneously optimizes production rate that drives her revenues, as…
We study a sequence of symmetric $n$-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empirical distribution. The unique Nash equilibrium…
We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…
We study mean field games for large non--exchangeable populations with moderate local interactions and common noise. The finite--player system is driven by two complementary interaction mechanisms : a graphon--type structure, which encodes…
We look at the long time behavior of potential Mean Field Games (briefly MFG) using some standard tools from weak KAM theory. We first show that the time-dependent minimization problem converges to an ergodic constant $-\lambda$, then we…
We study an ergodic mean field game problem with state constraints. In our model the agents are affected by idiosyncratic noise and use a (singular) feedback control to prevent the Brownian motion from exiting the domain. We characterize…
We consider mean field games with ergodic cost in the framework of a general discrete time controlled Markov processes. The state space of the processes is given by a general $\sigma$-compact Polish space. Under certain conditions, we show…
This paper is devoted to a class of finite horizon deterministic mean field games with Grushin type dynamics, state constraints and nonlocal coupling. First, we consider the optimal control problem that each agent aims to solve when the…
We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent's dynamics can spend finite time both in the interior of the edges and at the vertices. The…
We study the local in time existence of a regular solution of a nonlinear parabolic backward-forward system arising from the theory of Mean-Field Games (briefly MFG). The proof is based on a contraction argument in a suitable space that…
We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon $T$ goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations with state constraints from the viewpoint of weak KAM theory,…
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…
This paper focuses on linear-quadratic (LQ for short) mean-field games described by forward-backward stochastic differential equations (FBSDEs for short), in which the individual control region is postulated to be convex. The decentralized…
We introduce the notion of stable solution in mean field game theory: they are locally isolated solutions of the mean field game system. We prove that such solutions exist in potential mean field games and are local attractors for learning…
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…
The standard solution concept for stochastic games is Markov perfect equilibrium (MPE); however, its computation becomes intractable as the number of players increases. Instead, we consider mean field equilibrium (MFE) that has been…
We consider stochastic mean field games for which the state space is a network. In the ergodic case, they are described by a system coupling a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation, whose unknowns are the invariant…