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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

Here, we study radial solutions for first- and second-order stationary Mean-Field Games (MFG) with congestion on $\mathbb{R}^d$. MFGs with congestion model problems where the agents' motion is hampered in high-density regions. The radial…

Analysis of PDEs · Mathematics 2017-03-23 David Evangelista , Diogo A. Gomes , Levon Nurbekyan

We study first order evolutive Mean Field Games where the Hamiltonian is non-coercive. This situation occurs, for instance, when some directions are "forbidden" to the generic player at some points. We establish the existence of a weak…

Analysis of PDEs · Mathematics 2018-12-03 Paola Mannucci , Claudio Marchi , Carlo Mariconda , Nicoletta Tchou

In this paper we provide the existence of classical solutions to stationary mean field game systems in the whole space $\mathbb{R}^N$, with coercive potential, aggregating local coupling, and under general conditions on the Hamiltonian,…

Analysis of PDEs · Mathematics 2018-03-14 Annalisa Cesaroni , Marco Cirant

We study the generalized conditional gradient (GCG) method for time-dependent second-order mean field games (MFG) with local coupling terms. While explicit convergence rates of the GCG method were previously established only for globally…

Numerical Analysis · Mathematics 2026-01-27 Haruka Nakamura , Norikazu Saito

Here, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct…

Analysis of PDEs · Mathematics 2020-01-14 Rita Ferreira , Diogo Gomes , Teruo Tada

The paper is concerned with the deterministic limit of mean field games with the nonlocal coupling. It is assumed that the dynamics of mean field games are given by nonlinear Markov processes. This type of games includes stochastic mean…

Optimization and Control · Mathematics 2018-01-08 Yurii Averboukh

We analyse fully nonlinear second-order mean field games (MFG) with nondifferentiable Hamiltonians, which take the form of a coupled system of a fully nonlinear Hamilton-Jacobi-Bellman equation and a Kolmogorov-Fokker-Planck partial…

Analysis of PDEs · Mathematics 2025-11-18 Thomas Sales , Iain Smears

While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward-forward problem is still poorly understood - even in the one-dimensional setting.…

Analysis of PDEs · Mathematics 2016-06-30 Diogo Gomes , Levon Nurbekyan , Marc Sedjro

We consider the variational approach to prove the existence of solutions of second order stationary Mean Field Games on a bounded domain $\Omega\subseteq \mathbb{R}^{d}$, with Neumann boundary conditions, and with and without density…

Analysis of PDEs · Mathematics 2017-04-19 Alpár Richárd Mészáros , Francisco J. Silva

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

In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games master equations. A rate of dissipation of a bilinear form is…

Analysis of PDEs · Mathematics 2022-04-04 Wilfrid Gangbo , Alpár R. Mészáros , Chenchen Mou , Jianfeng Zhang

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 a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both…

Analysis of PDEs · Mathematics 2017-06-27 Yves Achdou , Alessio Porretta

In this paper we provide the existence of classical solutions to stationary mean field game systems in the whole space $\mathbb{R}^N$, with coercive potential and aggregating local coupling, under general conditions on the Hamiltonian. The…

Analysis of PDEs · Mathematics 2018-10-17 Annalisa Cesaroni , Marco Cirant

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

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

The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…

Optimization and Control · Mathematics 2024-07-29 Piyush Grover , Mandy Huo

In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints,…

Analysis of PDEs · Mathematics 2026-04-10 Jameson Graber , Kyle Rosengartner

In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel unique identifiability results for the intrinsic structure…

Analysis of PDEs · Mathematics 2025-05-14 Hongyu Liu , Catharine W. K. Lo