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Related papers: LQG Graphon Mean Field Games: Analysis via Graphon…

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This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

Optimization and Control · Mathematics 2021-10-12 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang

This paper investigates the linear-quadratic-Gaussian (LQG) mean-field game (MFG) for a class of stochastic delay systems. We consider a large population system in which the dynamics of each player satisfies some forward stochastic…

Optimization and Control · Mathematics 2015-10-05 Na Li , Shujun Wang

Graphon games are a class of games with a continuum of agents, introduced to approximate the strategic interactions in large network games. The first result of this study is an equilibrium existence theorem in graphon games, under the same…

Theoretical Economics · Economics 2025-04-03 Motoki Otsuka

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

We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition…

Optimization and Control · Mathematics 2021-06-16 Alexander Aurell , Rene Carmona , Gokce Dayanikli , Mathieu Lauriere

We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…

Probability · Mathematics 2018-12-04 Enzo Miller , Huyen Pham

We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and…

Optimization and Control · Mathematics 2024-06-07 Fuzhong Zhou , Chenyu Zhang , Xu Chen , Xuan Di

An analysis of infinite horizon linear quadratic Gaussian (LQG) Mean Field Games is given within the general framework of Graphon Mean Field Games (GMFG) on dense infinite graphs (or networks) introduced in Caines and Huang (2018). For a…

Systems and Control · Electrical Eng. & Systems 2022-07-26 Rinel Foguen Tchuendom , Shuang Gao , Peter E. Caines

Motivated by recent interest in graphon mean field games and their applications, this paper provides a comprehensive probabilistic analysis of graphon mean field control (GMFC) problems, where the controlled dynamics are governed by a…

Optimization and Control · Mathematics 2025-12-19 Zhongyuan Cao , Mathieu Laurière

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…

Optimization and Control · Mathematics 2017-10-10 Ying Hu , Jianhui Huang , Tianyang Nie

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

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

In this paper, we study graphon mean field games using a system of forward-backward stochastic differential equations. We establish the existence and uniqueness of solutions under two different assumptions and prove the stability with…

Probability · Mathematics 2022-02-17 Erhan Bayraktar , Ruoyu Wu , Xin Zhang

We study mean field games for large non--exchangeable populations with moderate local interactions and common noise. The finite--player system is driven by two complementary interaction mechanisms : a graphon--type structure, which encodes…

Optimization and Control · Mathematics 2026-05-15 Mao Fabrice Djete

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

Machine Learning · Computer Science 2023-01-05 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang

In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…

Numerical Analysis · Mathematics 2026-04-08 Yaxin Feng , Yang Xiang , Haomin Zhou

Graphon games have been introduced to study games with many players who interact through a weighted graph of interaction. By passing to the limit, a game with a continuum of players is obtained, in which the interactions are through a…

Optimization and Control · Mathematics 2024-04-02 Mathieu Laurière , Ludovic Tangpi , Xuchen Zhou

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the…

Optimization and Control · Mathematics 2022-06-13 Min Li , Chenchen Mou , Zhen Wu , Chao Zhou

Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric $n$-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian…

Optimization and Control · Mathematics 2025-03-25 Asaf Cohen , Ethan Zell

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