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Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation…

Optimization and Control · Mathematics 2026-02-16 William Hofgard , Asaf Cohen , Mathieu Laurière

In this article, we focus on the global stabilizability problem for a class of second order uncertain stochastic control systems, where both the drift term and the diffusion term are nonlinear functions of the state variables and the…

Systems and Control · Electrical Eng. & Systems 2022-05-11 Cheng Zhao , Yanbin Zhang

We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift,…

Probability · Mathematics 2020-07-14 Chiara Benazzoli , Luciano Campi , Luca Di Persio

We consider the variational approach to prove the existence of solutions of second order stationary Mean Field Games on a bounded domain $\Omega\subseteq \mathbb{R}^{d}$, with Neumann boundary conditions, and with and without density…

Analysis of PDEs · Mathematics 2017-04-19 Alpár Richárd Mészáros , Francisco J. Silva

In recent years, mean field games (MFGs) have garnered considerable attention and emerged as a dynamic and actively researched field across various domains, including economics, social sciences, finance, and transportation. The inverse…

Analysis of PDEs · Mathematics 2024-10-02 Hongyu Liu , Catharine W. K. Lo , Shen Zhang

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

We establish the existence and uniqueness of distributed equilibria to possibly nonsymmetric $N$ player differential games with interactions through controls under displacement semimonotonicity assumptions. Surprisingly, the nonseparable…

Analysis of PDEs · Mathematics 2026-04-01 Hei Jie Lam , Alpár R. Mészáros

In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…

Optimization and Control · Mathematics 2023-01-24 Tianliang Zhang , Feiqi Deng , Peng Shi

We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…

Numerical Analysis · Mathematics 2026-02-13 Haruka Nakamura , Norikazu Saito

Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players. Considering the limit when the number of players is infinite, Nash equilibria are studied by considering the interaction of a typical…

Optimization and Control · Mathematics 2021-06-14 Mathieu Lauriere

Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory,…

Machine Learning · Computer Science 2022-06-08 Lars Ruthotto , Stanley Osher , Wuchen Li , Levon Nurbekyan , Samy Wu Fung

Mean field games (MFGs) describe the collective behavior of large populations of interacting agents. In this work, we tackle ill-posed inverse problems in potential MFGs, aiming to recover the agents' population, momentum, and environmental…

Machine Learning · Computer Science 2025-02-18 Jingguo Zhang , Xianjin Yang , Chenchen Mou , Chao Zhou

We propose two numerical methods for the optimal control of McKean-Vlasov dynamics in finite time horizon. Both methods are based on the introduction of a suitable loss function defined over the parameters of a neural network. This allows…

Optimization and Control · Mathematics 2021-03-31 René Carmona , Mathieu Laurière

A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…

Statistical Mechanics · Physics 2017-10-13 Erik Aurell , Stefano Bo

A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…

Analysis of PDEs · Mathematics 2023-11-29 Ansgar Jüngel , Martin Vetter

Mean field games (MFGs) model the limit of large populations of strategically interacting agents, yet both forward and inverse problems remain challenging. For the forward problem, a difficulty is to design numerical methods with global…

Optimization and Control · Mathematics 2026-03-12 Hanwei Yan , Xianjin Yang , Jingguo Zhang

This paper investigates the stabilization and control problems for linear continuous-time mean-field systems (MFS). Under standard assumptions, necessary and sufficient conditions to stabilize the mean-field systems in the mean square sense…

Optimization and Control · Mathematics 2017-05-26 Qingyuan Qi , Huanshui Zhang

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

In this paper, we propose a second-order extension of the continuous-time game-theoretic mirror descent (MD) dynamics, referred to as MD2, which provably converges to mere (but not necessarily strict) variationally stable states (VSS)…

Optimization and Control · Mathematics 2024-10-28 Bolin Gao , Lacra Pavel

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens…

Analysis of PDEs · Mathematics 2024-03-25 P. Jameson Graber , Alpár R. Mészáros