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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

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…

Optimization and Control · Mathematics 2023-08-22 Pierre Lavigne , Laurent Pfeiffer

We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the…

Optimization and Control · Mathematics 2026-02-12 Kui Ren , Nathan Soedjak , Shanyin Tong

We provide an approximation scheme for first-order stationary mean field games with a separable Hamiltonian. First, we discretize Hamilton-Jacobi equations by discretizing in time, and then prove the existence of minimizing holonomic…

Analysis of PDEs · Mathematics 2021-11-24 Renato Iturriaga , Kaizhi Wang

This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

Machine Learning · Computer Science 2026-04-16 Anna C. M. Thöni , Yoram Bachrach , Tal Kachman

We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…

Numerical Analysis · Mathematics 2026-02-13 Haruka Nakamura , Norikazu Saito

Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory,…

Machine Learning · Computer Science 2022-06-08 Lars Ruthotto , Stanley Osher , Wuchen Li , Levon Nurbekyan , Samy Wu Fung

In this paper we consider extended stationary mean field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean field…

Analysis of PDEs · Mathematics 2013-05-14 Diogo A. Gomes , Stefania Patrizi , Vardan Voskanyan

Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…

Optimization and Control · Mathematics 2014-12-24 Pierre Degond , Michael Herty , Jian-Guo Liu

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…

Optimization and Control · Mathematics 2020-07-23 Lisang Ding , Wuchen Li , Stanley Osher , Wotao Yin

Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riemannian manifolds. We formulate the mean-field game Nash…

Optimization and Control · Mathematics 2023-04-26 Jiajia Yu , Rongjie Lai , Wuchen Li , Stanley Osher

Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…

Optimization and Control · Mathematics 2019-12-30 Julien Claisse , Zhenjie Ren , Xiaolu Tan

A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…

Optimization and Control · Mathematics 2013-05-08 Arturo Berrones , Jonás Velasco , Juan Banda

In this article, we introduce a method to approximate solutions of some variational mean field game problems with congestion, by finite sets of player trajectories. These trajectories are obtained by solving a minimization problem similar…

Optimization and Control · Mathematics 2022-01-14 Clément Sarrazin

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

In this paper, we present a new development of inspection games in a mean field setting. In our dynamic version of an inspection game, there is one inspector and a large number N interacting inspectees with a finite state space. By applying…

Optimization and Control · Mathematics 2015-07-31 Vassili Kolokoltsov , Wei Yang

We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows…

Optimization and Control · Mathematics 2023-03-07 J. Frédéric Bonnans , Pierre Lavigne , Laurent Pfeiffer

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…

Probability · Mathematics 2022-05-25 Matteo Burzoni , Luciano Campi

We investigate the global numerical approximation of a class of extended mean field control problems (MFC), where the dynamics and costs depend on the joint distribution of the state and the control. We propose a framework to approximate…

Optimization and Control · Mathematics 2026-03-23 Athena Picarelli , Marco Scaratti , Jonathan Tam