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In this paper, we consider a class of linear quadratic extended mean field games (MFGs) with common noises where the state coefficients and the cost functional vary with the mean field term in a nonlinear way. Based on stochastic maximum…

Optimization and Control · Mathematics 2023-11-08 Tianjiao Hua , Peng Luo

This paper focuses on exploring the convergence properties of a generic player's trajectory and empirical measures in an N-player Linear-Quadratic-Gaussian Nash game, where Brownian motion serves as the common noise. The study establishes…

Probability · Mathematics 2023-07-04 Jiamin Jian , Qingshuo Song , Jiaxuan Ye

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

Optimization and Control · Mathematics 2022-12-21 Justina Gianatti , Francisco J. Silva

The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…

Optimization and Control · Mathematics 2024-01-23 Daniel Hernández-Hernández , Joshué Helí Ricalde-Guerrero

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

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

We study an ergodic mean field game problem with state constraints. In our model the agents are affected by idiosyncratic noise and use a (singular) feedback control to prevent the Brownian motion from exiting the domain. We characterize…

Analysis of PDEs · Mathematics 2023-10-05 Alessio Porretta , Michele Ricciardi

Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…

Analysis of PDEs · Mathematics 2016-10-04 Diogo A. Gomes , Stefania Patrizi

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…

Probability · Mathematics 2022-04-21 Vassili Kolokoltsov , Marianna Troeva

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 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

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 extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…

Analysis of PDEs · Mathematics 2026-04-02 Rita Ferreira , Diogo Gomes , Bashayer Majrashi

In this paper, we consider a system of forward-backward stochastic differential equations (FBSDEs) with monotone functionals. We show the existence and uniqueness of such a system by the method of continuation similarly to Peng and Wu…

Probability · Mathematics 2018-08-07 Saran Ahuja , Weiluo Ren , Tzu-Wei Yang

Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…

Analysis of PDEs · Mathematics 2017-03-30 Diogo Gomes , Marc Sedjro

We study the singular perturbation problem for mean field game systems with control of acceleration. For such a problem we analyze the behavior of solutions as the acceleration costs vanishes. In this setting the Hamiltonian fails to be…

Optimization and Control · Mathematics 2023-04-04 Cristian Mendico

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

Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…

Computer Science and Game Theory · Computer Science 2026-02-27 Yannick Eich , Christian Fabian , Kai Cui , Heinz Koeppl

This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a…

Optimization and Control · Mathematics 2017-01-03 Jianhui Huang , Minyi Huang

In this paper, we consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way. We assume that the cost function satisfies a convexity and a weak monotonicity…

Optimization and Control · Mathematics 2021-05-26 Ziyu Huang , Shanjian Tang