Related papers: Nonsmooth mean field games with state constraints

We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable…

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

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 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…

We present a novel framework for mean field games with finite state space and common noise, where the common noise is given through shocks that occur at random times. We first analyze the game for up to $n$ shocks, in which case we are able…

The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…

In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of 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 consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both…

We propose and analyze a framework for mean-field Markov games under model uncertainty. In this framework, a state-measure flow describing the collective behavior of a population affects the given reward function as well as the unknown…

We study a family of mean field games arising in modeling the behavior of strategic economic agents which move across space maximizing their utility from consumption and have the possibility to accumulate resources for production (such as…

The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of…

This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…

We discuss a class of explicitly solvable mean field type control problems/mean field games with a clear economic interpretation. More precisely, we consider long term average impulse control problems with underlying general one-dimensional…

This paper introduces and analyses some models in the framework of Mean Field Games describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games,…

We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment…

The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…

In this paper, we present a model of a game among teams. Each team consists of a homogeneous population of agents. Agents within a team are cooperative while the teams compete with other teams. The dynamics and the costs are coupled through…

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…