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Related papers: First order Mean Field Games on networks

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We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…

Optimization and Control · Mathematics 2014-01-09 Pierre Cardaliaguet , Philip Jameson Graber

We consider a stationary Mean Field Games system defined on a network. In this framework, the transition conditions at the vertices play a crucial role: the ones here considered are based on the optimal control interpretation of the…

Analysis of PDEs · Mathematics 2015-05-20 Fabio Camilli , Claudio Marchi

A general class of mean field games are considered where the governing dynamics are controlled diffusions in $\mathbb{R}^d$. The optimization criterion is the long time average of a running cost function. Under various sets of hypotheses,…

Optimization and Control · Mathematics 2019-08-21 Ari Arapostathis , Anup Biswas , Johnson Carroll

First, we study the existence of solutions for a class of first order mean field games systems \begin{equation*} \left\{\begin{aligned} &H(x,u,Du)=F(x,m(t)),\quad &&x\in M,\ \forall\ t\in[0,T],\\ &\partial_t…

Analysis of PDEs · Mathematics 2025-07-15 Xiaotian Hu

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

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

In this work, we consider a first order mean field games system with non-local couplings. A Lagrange-Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton-Jacobi-Bellman equation, is proposed to…

Analysis of PDEs · Mathematics 2023-03-28 E Carlini , Francisco José Silva , Ahmad Zorkot

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

Analysis of PDEs · Mathematics 2020-06-24 Z Kobeissi

We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…

Analysis of PDEs · Mathematics 2023-01-12 Sebastian Munoz

We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…

Optimization and Control · Mathematics 2020-07-09 Géraldine Bouveret , Roxana Dumitrescu , Peter Tankov

We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…

Analysis of PDEs · Mathematics 2020-03-10 Y Achdou , Z Kobeissi

We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…

Optimization and Control · Mathematics 2025-06-03 Dirk Becherer , Christoph Reisinger , Jonathan Tam

In this paper, we prove the existence of classical solutions for second order stationary mean-field game systems. These arise in ergodic (mean-field) optimal control, convex degenerate problems in calculus of variations, and in the study of…

Analysis of PDEs · Mathematics 2015-03-24 Edgard A. Pimentel , Vardan Voskanyan

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

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 investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…

Systems and Control · Electrical Eng. & Systems 2026-04-10 Uğur Aydın , Naci Saldi

Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…

Probability · Mathematics 2015-04-09 Daniel Lacker

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

Optimization and Control · Mathematics 2022-12-21 Justina Gianatti , Francisco J. Silva

This paper studies a mean field game inspired by crowd motion in which agents evolve in a compact domain and want to reach its boundary minimizing the sum of their travel time and a given boundary cost. Interactions between agents occur…

Optimization and Control · Mathematics 2020-01-31 Samer Dweik , Guilherme Mazanti

In this paper, we examine the stationary relaxed singular control problem within a multi-dimensional framework for a single agent, as well as its mean field game equivalent. We demonstrate that optimal relaxed controls exist for two problem…

Optimization and Control · Mathematics 2025-06-04 Asaf Cohen , Chuhao Sun