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Related papers: Linear-Quadratic Graphon Mean Field Games with Com…

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In this paper, we address an instance of uniquely solvable mean-field game with a common noise whose corresponding counterpart without common noise has several equilibria. We study the selection problem for this mean-field game without…

Probability · Mathematics 2018-08-29 François Delarue , Rinel Foguen Tchuendom

Graphon control has been proposed and developed in [1]-[3] to approximately solve control problems for very large-scale networks (VLSNs) of linear dynamical systems based on graphon limits. This paper provides a solution method based on…

Systems and Control · Electrical Eng. & Systems 2021-06-24 Shuang Gao , Peter E. Caines

Linear-quadratic Gaussian games provide a framework for modeling strategic interactions in multi-agent systems, where agents must estimate system states from noisy observations while also making decisions to optimize a quadratic cost.…

Systems and Control · Electrical Eng. & Systems 2026-03-19 Tianyu Qiu , Filippos Fotiadis , Xinjie Liu , Christian Ellis , Jesse Milzman , Wesley Suttle , Ufuk Topcu , David Fridovich-Keil

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

Mean field game (MFG) systems consisting of a major agent and a large number of minor agents were introduced in (Huang, 2010) in an LQG setup. The Nash certainty equivalence was used to obtain a Markovian closed-loop Nash equilibrium for…

Optimization and Control · Mathematics 2022-10-19 Dena Firoozi

Forcing finite state mean field games by a relevant form of common noise is a subtle issue, which has been addressed only recently. Among others, one possible way is to subject the simplex valued dynamics of an equilibrium by a so-called…

Probability · Mathematics 2021-11-03 Erhan Bayraktar , Alekos Cecchin , Asaf Cohen , François Delarue

This paper studies open-loop and feedback solutions to leader-follower mean field linear-quadratic-Gaussian games with multiplicative noise by the direct approach. The leader-follower game involves a leader and many followers, where the…

Optimization and Control · Mathematics 2025-12-04 Bing-Chang Wang , Huanshui Zhang , Ji-Feng Zhang

We present a Reinforcement Learning (RL) algorithm to solve infinite horizon asymptotic Mean Field Game (MFG) and Mean Field Control (MFC) problems. Our approach can be described as a unified two-timescale Mean Field Q-learning: The…

Optimization and Control · Mathematics 2021-06-01 Andrea Angiuli , Jean-Pierre Fouque , Mathieu Laurière

The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of…

Optimization and Control · Mathematics 2014-03-25 Jianhui Huang , Shujun Wang

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 is concerned with an indefinite linear-quadratic mean field games of stochastic large-population system, where the individual diffusion coefficients can depend on both the state and the control of the agents. Moreover, the…

Optimization and Control · Mathematics 2024-07-01 Wenyu Cong , Jingtao Shi

We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be…

Systems and Control · Computer Science 2017-08-21 Rabih Salhab , Roland P. Malhamé , Jerome Le Ny

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 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

In this paper, we analyze linear-quadratic stochastic differential games with a continuum of players interacting through graphon aggregates, each state being subject to idiosyncratic Brownian shocks. The major technical issue is the joint…

Probability · Mathematics 2021-05-27 Alexander Aurell , Rene Carmona , Mathieu Lauriere

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

This paper is concerned with a linear-quadratic mean field Stackelberg stochastic differential game with partial information and common noise, which contains a leader and a large number of followers. To be specific, the followers face a…

Optimization and Control · Mathematics 2025-03-25 Yu Si , Jingtao Shi

In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to…

Optimization and Control · Mathematics 2025-11-19 Ruimeng Hu , Jihao Long , Haosheng Zhou

In this paper, we study two kinds of inverse problems for Mean Field Games (MFGs) with common noise. Our focus is on MFGs described by a coupled system of stochastic Hamilton-Jacobi-Bellman and Fokker-Planck equations. Firstly, we establish…

Analysis of PDEs · Mathematics 2024-12-12 Qi Lü , Zhonghua Liao

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…

Optimization and Control · Mathematics 2017-12-01 Marcel Nutz