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We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…

Optimization and Control · Mathematics 2017-10-10 Ying Hu , Jianhui Huang , Tianyang Nie

We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents…

Analysis of PDEs · Mathematics 2016-02-16 Marco Cirant

This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon…

Systems and Control · Electrical Eng. & Systems 2021-10-22 Shuang Gao , Peter E. Caines , Minyi Huang

Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…

Analysis of PDEs · Mathematics 2017-03-30 Diogo Gomes , Marc Sedjro

We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a…

Optimization and Control · Mathematics 2014-07-28 Pierre Cardaliaguet , J. Graber , Alessio Porretta , Daniela Tonon

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

Machine Learning · Computer Science 2023-01-05 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang

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

In this paper, we present a new generalized Hughes model designed to intelligently depict pedestrian congestion dynamics, allowing pedestrian groups to either navigate through or circumvent high-density regions. First, we describe the…

Analysis of PDEs · Mathematics 2023-10-18 Mohamed Ghattassi , Nader Masmoudi

We propose a fully-corrective generalized conditional gradient method (FC-GCG) for the minimization of the sum of a smooth, convex loss function and a convex one-homogeneous regularizer over a Banach space. The algorithm relies on the…

Optimization and Control · Mathematics 2023-07-17 Kristian Bredies , Marcello Carioni , Silvio Fanzon , Daniel Walter

We study a particle approximation for one-dimensional first-order Mean-Field-Games (MFGs) with local interactions with planning conditions. Our problem comprises a system of a Hamilton-Jacobi equation coupled with a transport equation. As…

Optimization and Control · Mathematics 2021-09-07 Marco Di Francesco , Serikbolsyn Duisembay , Diogo Aguiar Gomes , Ricardo Ribeiro

This paper introduces a framework of Constrained Mean-Field Games (CMFGs), where each agent solves a constrained Markov decision process (CMDP). This formulation captures scenarios in which agents' strategies are subject to feasibility,…

Optimization and Control · Mathematics 2025-10-15 Anran Hu , Zijiu Lyu

We study a Mean Field Games (MFG) system in a real, separable infinite dimensional Hilbert space. The system consists of a second order parabolic type equation, called Hamilton-Jacobi-Bellman (HJB) equation in the paper, coupled with a…

Analysis of PDEs · Mathematics 2025-09-05 Salvatore Federico , Fausto Gozzi , Andrzej Święch

We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekyan, Osher "Computational methods for nonlocal mean field…

Optimization and Control · Mathematics 2020-07-02 Siting Liu , Levon Nurbekyan

In this paper we establish quantitative convergence results for both open and closed-loop Nash equilibria of N-player stochastic differential games in the setting of Mean Field Games of Controls (MFGC), a class of models where interactions…

Probability · Mathematics 2025-07-24 Joe Jackson , Alpár R. Mészáros

We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions and feature-space expansions in the spirit of kernel…

Optimization and Control · Mathematics 2020-04-29 Siting Liu , Matthew Jacobs , Wuchen Li , Levon Nurbekyan , Stanley J. Osher

In the present work, we study deterministic mean field games (MFGs) with finite time horizon in which the dynamics of a generic agent is controlled by the acceleration. They are described by a system of PDEs coupling a continuity equation…

Analysis of PDEs · Mathematics 2020-07-29 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard…

Numerical Analysis · Mathematics 2017-05-02 Diogo Gomes , Joao Saude

We study the mean field games equations, consisting of the coupled Kolmogorov-Fokker-Planck and Hamilton-Jacobi-Bellman equations. The equations are complemented by initial and terminal conditions. It is shown that with some specific choice…

Analysis of PDEs · Mathematics 2019-11-22 Sergey I. Nikulin , Olga S. Rozanova

The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized…

Optimization and Control · Mathematics 2016-02-15 Zhaosong Lu , Xiaojun Chen

The goal of this paper is to study the long time behavior of solutions of the first-order mean field game (MFG) systems with a control on the acceleration. The main issue for this is the lack of small time controllability of the problem,…

Optimization and Control · Mathematics 2020-07-07 Pierre Cardaliaguet , Cristian Mendico