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Related papers: High-dimensional Mean-Field Games by Particle-base…

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In recent years, point cloud generation has gained significant attention in 3D generative modeling. Among existing approaches, point-based methods directly generate point clouds without relying on other representations such as latent…

Computer Vision and Pattern Recognition · Computer Science 2025-11-26 Petr Molodyk , Jaemoo Choi , David W. Romero , Ming-Yu Liu , Yongxin Chen

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

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…

Computer Science and Game Theory · Computer Science 2023-12-19 Kai Cui , Gökçe Dayanıklı , Mathieu Laurière , Matthieu Geist , Olivier Pietquin , Heinz Koeppl

In this article, we propose two numerical methods, the Gaussian Process (GP) method and the Fourier Features (FF) algorithm, to solve mean field games (MFGs). The GP algorithm approximates the solution of a MFG with maximum a posteriori…

Numerical Analysis · Mathematics 2022-05-10 Chenchen Mou , Xianjin Yang , Chao Zhou

Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality…

Machine Learning · Computer Science 2025-08-07 Justin Lee , Behnaz Moradijamei , Heman Shakeri

Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…

We address scaling up equilibrium computation in Mean Field Games (MFGs) using Online Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash equilibrium under a natural and well-motivated set of monotonicity…

Artificial Intelligence · Computer Science 2021-03-02 Julien Perolat , Sarah Perrin , Romuald Elie , Mathieu Laurière , Georgios Piliouras , Matthieu Geist , Karl Tuyls , Olivier Pietquin

This paper presents a Mean Field Game (MFG) model for maritime traffic flow, treating the navigation of ships between seaports as a large-scale stochastic control problem. The MFG framework enables the modeling of agents at a microscopic…

Optimization and Control · Mathematics 2025-12-02 Charles-Albert Lehalle , Giulia Livieri

Modern robotic systems frequently engage in complex multi-agent interactions, many of which are inherently multi-modal, i.e., they can lead to multiple distinct outcomes. To interact effectively, robots must recognize the possible…

Robotics · Computer Science 2025-08-12 Maulik Bhatt , Iman Askari , Yue Yu , Ufuk Topcu , Huazhen Fang , Negar Mehr

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses…

Numerical Analysis · Mathematics 2015-11-23 Noha Almulla , Rita Ferreira , Diogo Gomes

We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value…

Analysis of PDEs · Mathematics 2020-10-27 Jameson Graber , Alan Mullenix , Laurent Pfeiffer

Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…

Analysis of PDEs · Mathematics 2017-10-05 David Evangelista , Rita Ferreira , Diogo A. Gomes , Levon Nurbekyan , Vardan Voskanyan

We study Mean Field Games (MFGs) driven by a large class of nonlocal, fractional and anomalous diffusions in the whole space. These non-Gaussian diffusions are pure jump L\'evy processes with some $\sigma$-stable like behaviour. Included…

Analysis of PDEs · Mathematics 2021-03-10 Olav Ersland , Espen Robstad Jakobsen

Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…

Analysis of PDEs · Mathematics 2024-07-31 Vincenzo Ignazio , Michele Ricciardi

The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…

Optimization and Control · Mathematics 2024-07-29 Piyush Grover , Mandy Huo

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

Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs…

Analysis of PDEs · Mathematics 2016-11-28 David Evangelista , Diogo A. Gomes

Learning by experience in Multi-Agent Systems (MAS) is a difficult and exciting task, due to the lack of stationarity of the environment, whose dynamics evolves as the population learns. In order to design scalable algorithms for systems…

Optimization and Control · Mathematics 2020-02-24 Romuald Elie , Julien Pérolat , Mathieu Laurière , Matthieu Geist , Olivier Pietquin

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…

Optimization and Control · Mathematics 2023-04-26 Daisuke Inoue , Yuji Ito , Takahito Kashiwabara , Norikazu Saito , Hiroaki Yoshida