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We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…

Optimization and Control · Mathematics 2025-01-23 Alain Bensoussan , Ho Man Tai , Tak Kwong Wong , Sheung Chi Phillip Yam

In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

Optimization and Control · Mathematics 2024-06-18 Gokce Dayanikli , Mathieu Lauriere

In this paper, we consider a class of mean field games in which the optimal strategy of a representative agent depends on the statistical distribution of the states and controls. We prove some existence results for the forward-backward…

Analysis of PDEs · Mathematics 2020-07-13 Z Kobeissi

Recent advances in multiagent learning have seen the introduction ofa family of algorithms that revolve around the population-based trainingmethod PSRO, showing convergence to Nash, correlated and coarse corre-lated equilibria. Notably,…

Computer Science and Game Theory · Computer Science 2022-08-30 Paul Muller , Mark Rowland , Romuald Elie , Georgios Piliouras , Julien Perolat , Mathieu Lauriere , Raphael Marinier , Olivier Pietquin , Karl Tuyls

Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However, high order methods have not been thoroughly investigated. In…

Numerical Analysis · Mathematics 2023-08-16 Guosheng Fu , Siting Liu , Stanley Osher , Wuchen Li

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled objects in interaction. Though these models are much simpler than the underlying differential games they describe in some limit, their…

Physics and Society · Physics 2020-07-15 Thibault Bonnemain , Thierry Gobron , Denis Ullmo

In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality…

Optimization and Control · Mathematics 2009-03-10 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players. Considering the limit when the number of players is infinite, Nash equilibria are studied by considering the interaction of a typical…

Optimization and Control · Mathematics 2021-06-14 Mathieu Lauriere

This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…

Optimization and Control · Mathematics 2020-08-12 Haoyang Cao , Xin Guo

This paper develops a linear programming approach for mean field games with reflected jump-diffusion dynamics. We first prove the equivalence between the mean field equilibria in the linear programming formulation and those in the weak…

Optimization and Control · Mathematics 2025-11-14 Zongxia Liang , Xiang Yu , Keyu Zhang

In this paper, we study a priori estimates for a first-order mean-field planning problem with a potential. In the theory of mean-field games (MFGs), a priori estimates play a crucial role to prove the existence of classical solutions. In…

Analysis of PDEs · Mathematics 2020-03-06 Tigran Bakaryan , Rita Ferreira , Diogo Gomes

In this article, we study a simplified version of a density-dependent first-order mean field game, in which the players face a penalization equal to the population density at their final position. We consider the problem of finding an…

Optimization and Control · Mathematics 2026-02-04 P. Jameson Graber , Brady Zimmerman

In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…

Optimization and Control · Mathematics 2026-03-27 François Delarue , Pierre Lavigne

Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer (2018) and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting…

Probability · Mathematics 2021-11-05 Luciano Campi , Maddalena Ghio , Giulia Livieri

We propose and investigate a discrete-time mean field game model involving risk-averse agents. The model under study is a coupled system of dynamic programming equations with a Kolmogorov equation. The agents' risk aversion is modeled by…

Optimization and Control · Mathematics 2020-12-29 J. Frédéric Bonnans , Pierre Lavigne , Laurent Pfeiffer

We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a primal-dual problem so that we are able to train the model via…

Machine Learning · Computer Science 2021-03-16 Shaojun Ma , Haomin Zhou , Hongyuan Zha

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…

Optimization and Control · Mathematics 2022-12-23 Saeed Sadeghi Arjmand , Guilherme Mazanti

In this paper, we study a large population game with heterogeneous dynamics and cost functions solving a consensus problem. Moreover, the agents have communication constraints which appear as: (1) an Additive-White Gaussian Noise (AWGN)…

Systems and Control · Electrical Eng. & Systems 2022-08-26 Shubham Aggarwal , Muhammad Aneeq uz Zaman , Tamer Başar

We introduce a nonconvex Mean Field Games system by studying a model with a large number of identical pairs of players who are all rational, and each pair plays an identical zero-sum differential game. We study existence and uniqueness of…

Analysis of PDEs · Mathematics 2016-12-15 Hung Vinh Tran

In this paper, a novel decentralized intelligent adaptive optimal strategy has been developed to solve the pursuit-evasion game for massive Multi-Agent Systems (MAS) under uncertain environment. Existing strategies for pursuit-evasion games…

Systems and Control · Electrical Eng. & Systems 2020-08-10 Zejian Zhou , Hao Xu