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Related papers: Mean Field Games with Singular Controls

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Here, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequalities techniques, we prove…

Analysis of PDEs · Mathematics 2016-01-13 Rita Ferreira , Diogo Gomes

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

In this article, from the viewpoint of control theory, we discuss the relationships among the commonly used monotonicity conditions that ensure the well-posedness of the solutions arising from problems of mean field games (MFGs) and mean…

Optimization and Control · Mathematics 2024-12-09 Alain Bensoussan , Ziyu Huang , Shanjian Tang , Sheung Chi Phillip Yam

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

Probability · Mathematics 2014-08-13 Daniel Lacker

We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…

Analysis of PDEs · Mathematics 2017-09-08 Martino Bardi , Marco Cirant

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 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

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

The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on $\mathbb R^{d}$. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria), as Borel probability…

Optimization and Control · Mathematics 2019-12-11 Piermarco Cannarsa , Cristian Mendico

We consider discounted infinite-horizon potential mean-field games (MFGs) on the $d$-dimensional torus. Without imposing monotonicity assumptions, we prove that every weak limit point of a time-dependent equilibrium, as time tends to…

Analysis of PDEs · Mathematics 2026-04-21 Felix Höfer

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

In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…

Optimization and Control · Mathematics 2021-07-12 Luciano Campi , Markus Fischer

We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized…

Optimization and Control · Mathematics 2026-01-01 Grégoire Lambrecht , Mathieu Laurière

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…

Probability · Mathematics 2015-04-09 Rene Carmona , Daniel Lacker

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized…

Optimization and Control · Mathematics 2026-03-09 Ulrich Horst , Takashi Sato

This paper presents a class of evolutive Mean Field Games with multiple solutions for all time horizons T and convex but non-smooth Hamiltonian H, as well as for smooth H and T large enough. The phenomenon is analyzed in both the PDE and…

Analysis of PDEs · Mathematics 2018-02-12 Martino Bardi , Markus Fischer

We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with…

Optimization and Control · Mathematics 2022-01-21 Jodi Dianetti , Giorgio Ferrari , Markus Fischer , Max Nendel

We consider discrete-time stationary mean field games (MFG) with unknown dynamics and design algorithms for finding the equilibrium with finite-time complexity guarantees. Prior solutions to the problem assume either the contraction of a…

Optimization and Control · Mathematics 2025-02-13 Sihan Zeng , Sujay Bhatt , Alec Koppel , Sumitra Ganesh

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

Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…

Analysis of PDEs · Mathematics 2018-04-25 Marco Cirant , Levon Nurbekyan