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Related papers: Singular mean-filed games

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This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

Optimization and Control · Mathematics 2023-11-21 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

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

This paper addresses the crucial question of solution uniqueness in stationary first-order Mean-Field Games (MFGs). Despite well-established existence results, establishing uniqueness, particularly for weaker solutions in the sense of…

Analysis of PDEs · Mathematics 2025-02-28 Rita Ferreira , Diogo Gomes , Vardan Voskanyan

We study the intermediate asymptotic behavior of solutions to the first-order mean field games system with a local coupling, when the initial density is a compactly supported function on the real line, and the coupling is of power type.…

Analysis of PDEs · Mathematics 2024-04-04 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

We study a degenerate second order mean field game (MFG) system in a Hilbert space $H$ which couples a Fokker--Planck equation describing the evolution of probability measures on $H$ with a Hamilton--Jacobi--Bellman (HJB) equation for the…

Analysis of PDEs · Mathematics 2026-05-14 Andrzej Święch , Lukas Wessels

The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many…

Numerical Analysis · Mathematics 2024-04-03 Yohance A. P. Osborne , Iain Smears

We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui's representation problem. Under certain continuity assumptions, where the common noise is generated by…

Optimization and Control · Mathematics 2025-07-28 Giorgio Ferrari , Anna Pajola

We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…

Optimization and Control · Mathematics 2019-07-26 Jodi Dianetti , Giorgio Ferrari , Markus Fischer , Max Nendel

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

This paper investigates stationary mean-field games (MFGs) on the torus with Lipschitz non-homogeneous diffusion and logarithmic-like couplings. The primary objective is to understand the existence of $C^{1,\alpha}$ solutions to address the…

Analysis of PDEs · Mathematics 2023-10-27 Tigran Bakaryan , Giuseppe Di Fazio , Diogo A. Gomes

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

In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the…

Analysis of PDEs · Mathematics 2013-11-26 Diogo A. Gomes , Edgard Pimentel , Héctor Sánchez-Morgado

Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence…

Analysis of PDEs · Mathematics 2019-08-20 Diogo A. Gomes , Hiroyoshi Mitake , Kengo Terai

In this paper we examine fully nonlinear mean-field games associated with a minimization problem. The variational setting is driven by a functional depending on its argument through its Hessian matrix. We work under fairly natural…

Analysis of PDEs · Mathematics 2020-10-30 Pêdra D. S. Andrade , Edgard A. Pimentel

We study a class of local, first-order, stationary mean-field games (MFGs) on bounded domains with nonstandard mixed boundary conditions: prescribed inflow on $\Gamma_N$ and a relaxed Signorini-type exit condition on $\Gamma_D$…

Analysis of PDEs · Mathematics 2026-03-03 AbdulRahman M. Alharbi , Diogo Gomes

We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon $T$ goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations with state constraints from the viewpoint of weak KAM theory,…

Analysis of PDEs · Mathematics 2023-04-04 Piermarco Cannarsa , Wei Cheng , Cristian Mendico , Kaizhi Wang

We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such…

Analysis of PDEs · Mathematics 2024-03-18 Martino Bardi , Hicham Kouhkouh

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

This paper introduces a notion of weak solution for the coupled system of master equations in mean field games with a major player. It extends the previously introduced notion of Lipschitz solutions in mean field games. By relying on a…

Analysis of PDEs · Mathematics 2026-03-17 Charles Meynard