Related papers: Mean Field Games of Controls: Finite Difference Ap…
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…
In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…
This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…
This paper introduces a framework of Constrained Mean-Field Games (CMFGs), where each agent solves a constrained Markov decision process (CMDP). This formulation captures scenarios in which agents' strategies are subject to feasibility,…
We study the singular perturbation problem for mean field game systems with control of acceleration. For such a problem we analyze the behavior of solutions as the acceleration costs vanishes. In this setting the Hamiltonian fails to be…
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…
We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…
We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…
This work studies non-cooperative Multi-Agent Reinforcement Learning (MARL) where multiple agents interact in the same environment and whose goal is to maximize the individual returns. Challenges arise when scaling up the number of agents…
We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative…
We study a class of deterministic mean field games and related optimal control problems, with a finite time horizon and in which the state space is a network. An agent controls her velocity, and, when she occupies a vertex, she can either…
Mean Field Games (MFG) provide a theoretical frame to model socio-economic systems. In this letter, we study a particular class of MFG which shows strong analogies with the {\em non-linear Schr\"odinger and Gross-Pitaevski equations}…
The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games for which the interaction between the players is of mean-field type. We implement the Mean-Field Games strategy…
We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…
We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is…
The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many…
This paper studies a mean field game inspired by crowd motion in which agents evolve in a compact domain and want to reach its boundary minimizing the sum of their travel time and a given boundary cost. Interactions between agents occur…
Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a…