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Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common…

Analysis of PDEs · Mathematics 2026-02-26 Benjamin Moll , Lenya Ryzhik

Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that…

Optimization and Control · Mathematics 2023-05-24 Han Huang , Jiajia Yu , Jie Chen , Rongjie Lai

In this paper, we study first-order stationary monotone mean-field games (MFGs) with Dirichlet boundary conditions. While for Hamilton--Jacobi equations Dirichlet conditions may not be satisfied, here, we establish the existence of…

Analysis of PDEs · Mathematics 2018-04-20 Rita Ferreira , Diogo Gomes , Teruo Tada

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…

Multiagent Systems · Computer Science 2021-05-18 Sarah Perrin , Mathieu Laurière , Julien Pérolat , Matthieu Geist , Romuald Élie , Olivier Pietquin

The intersection of Mean Field Games (MFGs) and Reinforcement Learning (RL) has fostered a growing family of algorithms designed to solve large-scale multi-agent systems. However, the field currently lacks a standardized evaluation…

Machine Learning · Computer Science 2026-02-16 Lorenzo Magnino , Jiacheng Shen , Matthieu Geist , Olivier Pietquin , Mathieu Laurière

The standard formulation of the PDE system of Mean Field Games (MFG) requires the differentiability of the Hamiltonian. However in many cases, the structure of the underlying optimal problem leads to a convex but nondifferentiable…

Numerical Analysis · Mathematics 2025-02-17 Yohance A. P. Osborne , Iain Smears

This paper studies an inverse problem for a multipopulation mean field game (MFG) system where the objective is to reconstruct the running and terminal cost functions of the system that couples the dynamics of different populations. We…

Analysis of PDEs · Mathematics 2025-02-17 Kui Ren , Nathan Soedjak , Kewei Wang

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

In this paper, we study two kinds of inverse problems for Mean Field Games (MFGs) with common noise. Our focus is on MFGs described by a coupled system of stochastic Hamilton-Jacobi-Bellman and Fokker-Planck equations. Firstly, we establish…

Analysis of PDEs · Mathematics 2024-12-12 Qi Lü , Zhonghua Liao

We propose a control-theoretic framework for evolutionary clustering based on Mean Field Games (MFG). Moving beyond static or heuristic approaches, we formulate the problem as a population dynamics game governed by a coupled…

Numerical Analysis · Mathematics 2026-03-31 Alessio Basti , Fabio Camilli , Adriano Festa

We provide an existence result for stationary fractional mean field game systems, with fractional exponent greater than 1/2. In the case in which the coupling is a nonlocal regularizing potential, we obtain existence of solutions under…

Analysis of PDEs · Mathematics 2017-05-30 Annalisa Cesaroni , Marco Cirant , Serena Dipierro , Matteo Novaga , Enrico Valdinoci

We consider the one-dimensional stationary first-order mean-field game (MFG) system with the coupling between the Hamilton-Jacobi equation and the transport equation. In both cases that the coupling is strictly increasing and decreasing…

Analysis of PDEs · Mathematics 2018-05-29 Yiru Cai , Haobo Qi , Yi Tan , Xifeng Su

We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…

Analysis of PDEs · Mathematics 2020-09-28 Pierre Cardaliaguet , Panagiotis Souganidis

Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications,…

Machine Learning · Statistics 2025-12-02 Jiajia Yu , Junghwan Lee , Yao Xie , Xiuyuan Cheng

We study mean-field control (MFC) problems with common noise using the control randomisation framework, where we substitute the control process with an independent Poisson point process, controlling its intensity instead. To address the…

Optimization and Control · Mathematics 2024-12-31 Robert Denkert , Idris Kharroubi , Huyên Pham

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…

Optimization and Control · Mathematics 2014-03-25 Jianhui Huang , Shujun Wang

Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy…

Optimization and Control · Mathematics 2021-12-10 Xin Guo , Renyuan Xu , Thaleia Zariphopoulou

We study mean-field games of optimal stopping (OS-MFGs) and introduce an entropy-regularized framework to enable learning-based solution methods. By utilizing randomized stopping times, we reformulate the OS-MFG as a mean-field game of…

Optimization and Control · Mathematics 2025-09-24 Jodi Dianetti , Roxana Dumitrescu , Giorgio Ferrari , Renyuan Xu

Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…

Methodology · Statistics 2017-04-25 Dimitris Bertsimas , Martin S. Copenhaver , Rahul Mazumder

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…

Optimization and Control · Mathematics 2020-01-31 Samer Dweik , Guilherme Mazanti