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In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…

Numerical Analysis · Mathematics 2026-04-08 Yaxin Feng , Yang Xiang , Haomin Zhou

The paper considers a forward-backward system of parabolic PDEs arising in a Mean Field Game (MFG) model where every agent controls the drift of a trajectory subject to Brownian diffusion, trying to escape a given bounded domain $\Omega$ in…

Analysis of PDEs · Mathematics 2022-12-23 Romain Ducasse , Guilherme Mazanti , Filippo Santambrogio

In this paper, we propose and study an inverse boundary problem for the mean field games (MFGs) governed by the first-order master equation in a bounded domain. We establish the unique identifiability result by showing that the running cost…

Analysis of PDEs · Mathematics 2022-12-21 Hongyu Liu , Shen Zhang

This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is…

Optimization and Control · Mathematics 2022-02-21 Guilherme Mazanti , Filippo Santambrogio

In this paper we construct short time classical solutions to a class of master equations in the presence of non-degenerate individual noise arising in the theory of mean field games. The considered Hamiltonians are non-separable and $local$…

Analysis of PDEs · Mathematics 2022-06-16 David M. Ambrose , Alpár R. Mészáros

In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…

Analysis of PDEs · Mathematics 2026-01-14 Mohit Bansil , Alpár R. Mészáros

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

A central question in routing games has been to establish conditions for the uniqueness of the equilibrium, either in terms of network topology or in terms of costs. This question is well understood in two classes of routing games. The…

Computer Science and Game Theory · Computer Science 2016-01-01 Eitan Altman , Corinne Touati

We consider stochastic differential games with $N$ players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is…

Analysis of PDEs · Mathematics 2014-07-10 Martino Bardi , Fabio S. Priuli

We study a nonlinear system of partial differential equations arising in macroeconomics which utilizes a mean field approximation. This system together with the corresponding data, subject to two moment constraints, is a model for debt and…

Analysis of PDEs · Mathematics 2019-04-15 David M. Ambrose

In this paper, the notion of $\mathbb{C}$-simulation function is introduced and the existence and uniqueness of common fixed points of two self-mappings satisfying contractive conditions in the setting of complex valued metric spaces via…

Functional Analysis · Mathematics 2019-05-10 Anuradha Gupta , Manu Rohilla

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

Numerical Analysis · Mathematics 2015-11-23 Simone Cacace , Fabio Camilli , Claudio Marchi

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

We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both…

Optimization and Control · Mathematics 2026-02-27 Eyal Neuman , Sturmius Tuschmann

We consider minimization problems for curves of measure, with kinetic and potential energy and a congestion penalization, as in the functionals that appear in Mean Field Games with a variational structure. We prove L infinity regularity…

Analysis of PDEs · Mathematics 2017-05-17 Hugo Lavenant , Filippo Santambrogio

We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $\alpha^j$ plus a minimum jumping rate $\eta$. Instead of working under…

Probability · Mathematics 2020-03-18 Erhan Bayraktar , Xin Zhang

We study the problem of computing Stackelberg equilibria Stackelberg games whose underlying structure is in congestion games, focusing on the case where each player can choose a single resource (a.k.a. singleton congestion games) and one of…

Computer Science and Game Theory · Computer Science 2018-08-31 Matteo Castiglioni , Alberto Marchesi , Nicola Gatti , Stefano Coniglio

We introduce a class of fully nonlinear mean field games posed in $[0,T]\times\mathbb{R}^d$. We justify that they are related to controlled local or nonlocal diffusions, and more generally in our setting, to a new control interpretation…

Analysis of PDEs · Mathematics 2024-08-30 Indranil Chowdhury , Espen R. Jakobsen , Miłosz Krupski

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens…

Analysis of PDEs · Mathematics 2024-03-25 P. Jameson Graber , Alpár R. Mészáros

We establish the existence and uniqueness of distributed equilibria to possibly nonsymmetric $N$ player differential games with interactions through controls under displacement semimonotonicity assumptions. Surprisingly, the nonseparable…

Analysis of PDEs · Mathematics 2026-04-01 Hei Jie Lam , Alpár R. Mészáros