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We study mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…

Probability · Mathematics 2018-02-01 Alekos Cecchin , Markus Fischer

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 establishes unique solvability of a class of Graphon Mean Field Game equations. The special case of a constant graphon yields the result for the Mean Field Game equations.

Optimization and Control · Mathematics 2022-03-14 Peter E. Caines , Daniel W. C. HO , Minyi Huang , Jiamin Jian , Qingshuo Song

We study the local stability properties of solutions to ergodic and discounted mean field games systems, as the time horizon $T \to +\infty$, around stationary equilibria, when the Hamiltonian is quadratic. We replace the usual monotonicity…

Analysis of PDEs · Mathematics 2026-04-28 Marco Cirant , Nicolò De Bernardi

Mean field games allow to describe tractable models of dynamic games with a continuum of players, explicit interaction and heterogeneous states. Thus, these models are of great interest for socio-economic applications. A particular class of…

Optimization and Control · Mathematics 2020-10-20 Berenice Anne Neumann

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 investigate the existence and uniqueness of solutions to a stationary mean field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian with possibly singular congestion effects.…

Analysis of PDEs · Mathematics 2014-08-01 Diogo A. Gomes , Hiroyoshi Mitake

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

In a discrete space and time framework, we study the mean field game limit for a class of symmetric $N$-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows to construct…

Optimization and Control · Mathematics 2022-12-06 Ofelia Bonesini , Luciano Campi , Markus Fischer

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

A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential…

Probability · Mathematics 2015-05-21 Rene Carmona , Francois Delarue , Daniel Lacker

We introduce a mean field game for a family of filtering problems related to the classic sequential testing of the drift of a Brownian motion. To the best of our knowledge this work presents the first treatment of mean field filtering games…

Optimization and Control · Mathematics 2024-03-28 Steven Campbell , Yuchong 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 propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

Numerical Analysis · Mathematics 2015-11-23 Simone Cacace , Fabio Camilli , Claudio Marchi

The goal of the paper is to introduce a set of problems which we call mean field games of timing. We motivate the formulation by a dynamic model of bank run in a continuous-time setting. We briefly review the economic and game theoretic…

Probability · Mathematics 2017-01-24 Rene Carmona , Francois Delarue , Daniel Lacker

This paper establishes the existence of equilibria result of a class of mean field games with singular controls. The interaction takes place through both states and controls. A relaxed solution approach is used. To circumvent the tightness…

Optimization and Control · Mathematics 2022-05-10 Guanxing Fu

We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…

Analysis of PDEs · Mathematics 2020-09-28 Pierre Cardaliaguet , Panagiotis Souganidis

This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.

Probability · Mathematics 2026-03-09 Imane Jarni , Ayoub Laayoun , Badr Missaoui

In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…

Analysis of PDEs · Mathematics 2023-08-23 Alpár R. Mészáros , Chenchen Mou

We consider mean field games with discrete state spaces (called discrete mean field games in the following) and we analyze these games in continuous and discrete time, over finite as well as infinite time horizons. We prove the existence of…

Optimization and Control · Mathematics 2019-09-04 Josu Doncel , Nicolas Gast , Bruno Gaujal