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Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer (2018) and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting…

Probability · Mathematics 2021-11-05 Luciano Campi , Maddalena Ghio , Giulia Livieri

This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…

Optimization and Control · Mathematics 2025-08-12 Wenyu Cong , Jingtao Shi , Bingchang Wang

We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…

Optimization and Control · Mathematics 2019-02-08 L. M. Briceño-Arias , D. Kalise , F. J. Silva

We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that…

Analysis of PDEs · Mathematics 2025-01-14 Pierre Cardaliaguet , Benjamin Seeger , Panagiotis Souganidis

This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward - forward systems of equations of mean field games. We present local well-posedness, global existence and some…

Probability · Mathematics 2013-03-25 Vassili Koloklotsov , Wei Yang

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of…

Optimization and Control · Mathematics 2016-07-08 P. Jameson Graber

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 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

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

We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent's dynamics can spend finite time both in the interior of the edges and at the vertices. The…

Analysis of PDEs · Mathematics 2025-01-17 Jules Berry , Fabio Camilli

We propose a control-theoretic framework for evolutionary clustering based on Mean Field Games (MFG). Moving beyond static or heuristic approaches, we formulate the problem as a population dynamics game governed by a coupled…

Numerical Analysis · Mathematics 2026-03-31 Alessio Basti , Fabio Camilli , Adriano Festa

We show the existence of "mild solutions" for a first-order mean field game of controls under the state constraint that trajectories be confined in a closed and bounded set in euclidean space. This extends the results of Cannarsa and…

Optimization and Control · Mathematics 2023-01-24 Jameson Graber , Sergio Mayorga

In this paper, the existence of non-trivial time periodic solutions of first order mean field games is proved. It is assumed that there is a non-trivial periodic orbit contained in the Mather set. The whole system is autonomous with a…

Analysis of PDEs · Mathematics 2024-01-17 Panrui Ni

Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we…

General Relativity and Quantum Cosmology · Physics 2017-09-06 R. Di Criscienzo , L. Vanzo , S. Zerbini

We analyze the Poisson structure of the time-dependent mean-field equations for bosons and construct the Lie-Poisson bracket associated to these equations. The latter follow from the time-dependent variational principle of Balian and…

High Energy Physics - Theory · Physics 2009-10-30 Mohamed Benarous

We present a linear--quadratic Stackelberg game with a large number of followers and we also derive the mean field limit of infinitely many followers. The relation between optimization and mean-field limit is studied and conditions for…

Optimization and Control · Mathematics 2020-11-09 Michael Herty , Sonja Steffensen , Anna Thünen

In this paper, we study first-order stationary monotone mean-field games (MFGs) with Dirichlet boundary conditions. While for Hamilton--Jacobi equations Dirichlet conditions may not be satisfied, here, we establish the existence of…

Analysis of PDEs · Mathematics 2018-04-20 Rita Ferreira , Diogo Gomes , Teruo Tada

This paper studies the optimal investment behavior of renewable electricity producers in a competitive market, where both prices and installation costs are influenced by aggregate industry activity. We model the resulting crowding effects…

Optimization and Control · Mathematics 2025-07-16 Emma Hubert , Dimitrios Lolas , Ronnie Sircar

We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…

Probability · Mathematics 2008-06-06 Joan-Andreu Lázaro-Camí , Juan-Pablo Ortega

This paper studies the existence and uniqueness of a solution to linear quadratic (LQ) mean field social optimization problems with uniform agents. We exploit a Hamiltonian matrix structure of the associated ordinary differential equation…

Optimization and Control · Mathematics 2018-11-02 Xiang Chen , Minyi Huang