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The objective of this work is to study the existence, uniqueness, and stability of equilibria in mean field games involving a major player and a continuum of minor players over finite intervals of arbitrary length. Following earlier…

Optimization and Control · Mathematics 2025-01-07 Francois Delarue , Chenchen Mou

Learning in multi-agent systems is highly challenging due to several factors including the non-stationarity introduced by agents' interactions and the combinatorial nature of their state and action spaces. In particular, we consider the…

Machine Learning · Statistics 2023-05-10 Barna Pásztor , Ilija Bogunovic , Andreas Krause

Mean Field Games (MFGs) provide a principled framework for modelling interactions in large population systems. However, algorithmic progress has been limited since model-free methods are high variance and exact methods scale poorly. Recent…

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 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 propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

Probability · Mathematics 2014-09-26 Rene Carmona , Xiuneng Zhu

In this paper, we consider a discrete-time Stackelberg mean field game with a leader and an infinite number of followers. The leader and the followers each observe types privately that evolve as conditionally independent controlled Markov…

Systems and Control · Electrical Eng. & Systems 2022-09-21 Deepanshu Vasal , Randall Berry

In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations are the complex computations necessary to…

Optimization and Control · Mathematics 2020-09-01 Berenice Anne Neumann

In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a…

Analysis of PDEs · Mathematics 2019-01-21 Levon Nurbekyan , Joao Saude

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

The paper is concerned with distributed learning in large-scale games. The well-known fictitious play (FP) algorithm is addressed, which, despite theoretical convergence results, might be impractical to implement in large-scale settings due…

Optimization and Control · Mathematics 2016-11-17 Brian Swenson , Soummya Kar , Joao Xavier

We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the optimization over the probability measures, and by adding an…

Optimization and Control · Mathematics 2023-08-17 Fan Chen , Zhenjie Ren , Songbo Wang

Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously, the state of every agent moves to the next state, and each agent…

Machine Learning · Computer Science 2019-10-10 Mridul Agarwal , Vaneet Aggarwal , Arnob Ghosh , Nilay Tiwari

We investigate multi-agent imitation learning (IL) within the framework of mean field games (MFGs), considering the presence of time-varying correlated signals. Existing MFG IL algorithms assume demonstrations are sampled from Mean Field…

Multiagent Systems · Computer Science 2024-10-04 Zhiyu Zhao , Qirui Mi , Ning Yang , Xue Yan , Haifeng Zhang , Jun Wang , Yaodong Yang

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

The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of…

Optimization and Control · Mathematics 2023-11-03 François Delarue , Athanasios Vasileiadis

We design and analyze reinforcement learning algorithms for Graphon Mean-Field Games (GMFGs). In contrast to previous works that require the precise values of the graphons, we aim to learn the Nash Equilibrium (NE) of the regularized GMFGs…

Computer Science and Game Theory · Computer Science 2023-10-27 Fengzhuo Zhang , Vincent Y. F. Tan , Zhaoran Wang , Zhuoran Yang

We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step…

Analysis of PDEs · Mathematics 2021-09-14 J Frédéric Bonnans , Pierre Lavigne , Laurent Pfeiffer

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

Mean field games (MFG) and mean field control (MFC) problems have been introduced to study large populations of strategic players. They correspond respectively to non-cooperative or cooperative scenarios, where the aim is to find the Nash…

Computer Science and Game Theory · Computer Science 2023-12-19 Rene Carmona , Gokce Dayanikli , Francois Delarue , Mathieu Lauriere