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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

In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose…

Probability · Mathematics 2017-07-31 Saran Ahuja , Weiluo Ren , Tzu-Wei Yang

We study mean-field game (MFG) problems with rough common noise, in which the representative state dynamics are governed by a controlled rough stochastic differential equation driven by an idiosyncratic Brownian motion and a deterministic…

Probability · Mathematics 2026-05-19 Erhan Bayraktar , Xihao He , Xiang Yu , Fengyi Yuan

This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories…

Optimization and Control · Mathematics 2026-05-05 Pierre Lavigne , Quentin Petit , Xavier Warin

In this paper, we prove the existence of classical solutions for second order stationary mean-field game systems. These arise in ergodic (mean-field) optimal control, convex degenerate problems in calculus of variations, and in the study of…

Analysis of PDEs · Mathematics 2015-03-24 Edgard A. Pimentel , Vardan Voskanyan

In this paper, we propose and study an inverse boundary problem for the mean field games (MFGs) governed by the first-order master equation in a bounded domain. We establish the unique identifiability result by showing that the running cost…

Analysis of PDEs · Mathematics 2022-12-21 Hongyu Liu , Shen Zhang

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…

Optimization and Control · Mathematics 2017-11-07 Piermarco Cannarsa , Rossana Capuani

This paper concerns a Mean Field Game (MFG) system related to a Nash type equilibrium for dynamical games associated to large populations. One shows that the MFG system may be viewed as the Euler-Lagrange system for an optimal control…

Optimization and Control · Mathematics 2025-03-21 Stefana-Lucia Anita

This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…

Optimization and Control · Mathematics 2025-11-10 Lijun Bo , Jingfei Wang , Xiang Yu

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 this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…

Optimization and Control · Mathematics 2026-03-27 François Delarue , Pierre Lavigne

We consider variational Mean Field Games endowed with a constraint on the maximal density of the distribution of players. Minimizers of the variational formulation are equilibria for a game where both the running cost and the final cost of…

Analysis of PDEs · Mathematics 2019-06-19 Hugo Lavenant , Filippo Santambrogio

We present a novel framework for mean field games with finite state space and common noise, where the common noise is given through shocks that occur at random times. We first analyze the game for up to $n$ shocks, in which case we are able…

Optimization and Control · Mathematics 2024-04-15 Berenice Anne Neumann , Frank T. Seifried

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a…

Optimization and Control · Mathematics 2024-08-21 Felix Höfer , H. Mete Soner

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…

Optimization and Control · Mathematics 2014-01-09 Pierre Cardaliaguet , Philip Jameson Graber

We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…

Optimization and Control · Mathematics 2018-02-05 Charafeddine Mouzouni

We consider stochastic differential games with $N$ players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is…

Analysis of PDEs · Mathematics 2014-07-10 Martino Bardi , Fabio S. Priuli

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

Analysis of PDEs · Mathematics 2019-09-25 Jose A. Carrillo , Edgard A. Pimentel , Vardan K. Voskanyan

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

Analysis of PDEs · Mathematics 2021-11-04 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou