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The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on $\mathbb R^{d}$. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria), as Borel probability…

Optimization and Control · Mathematics 2019-12-11 Piermarco Cannarsa , Cristian Mendico

In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the…

Probability · Mathematics 2023-08-29 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

Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…

Analysis of PDEs · Mathematics 2024-07-31 Vincenzo Ignazio , Michele Ricciardi

We consider stochastic differential games with $N$ players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is…

Analysis of PDEs · Mathematics 2014-07-10 Martino Bardi , Fabio S. Priuli

This paper investigates a class of general linear-quadratic mean field games with common noise, where the diffusion terms of the system contain the state variables, control variables, and the average state terms. We solve the problem using…

Optimization and Control · Mathematics 2025-08-29 Yu Si , Jingtao Shi

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of…

Optimization and Control · Mathematics 2022-06-14 Bing-Chang Wang , Huanshui Zhang , Minyue Fu , Yong Liang

We consider a controlled linear-quadratic (LQ) large-population system with mixture of three types agents: major leader, minor leaders and minor followers. The Stackelberg-Nash-Cournot (SNC) approximate equilibrium is studied by a…

Optimization and Control · Mathematics 2019-05-28 Kehan Si , James Huang , Zhen Wu

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…

Optimization and Control · Mathematics 2019-10-17 Zuyue Fu , Zhuoran Yang , Yongxin Chen , Zhaoran Wang

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 provide a thorough study of a general class of linear-quadratic extended mean field games and control problems in any dimensions where the mean field terms are allowed to be unbounded and there are also presence of cross terms in the…

Optimization and Control · Mathematics 2023-11-10 Alain Bensoussan , Bohan Li , Sheung Chi Phillip Yam

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

A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always…

Optimization and Control · Mathematics 2025-07-15 Jiajia Yu , Xiuyuan Cheng , Jian-Guo Liu , Hongkai Zhao

This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…

Optimization and Control · Mathematics 2025-08-05 Idriss Boutaayamou , Fouad Et-Tahri , Lahcen Maniar

This paper is concerned with a class of linear-quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each…

Optimization and Control · Mathematics 2024-08-20 Min Li , Na Li , Zhen Wu

We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…

Systems and Control · Computer Science 2014-01-21 Abhishek Gupta , Ashutosh Nayyar , Cedric Langbort , Tamer Basar

We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…

Optimization and Control · Mathematics 2024-01-15 Marco Cirant , Davide Francesco Redaelli

In this paper, we study a large population game with heterogeneous dynamics and cost functions solving a consensus problem. Moreover, the agents have communication constraints which appear as: (1) an Additive-White Gaussian Noise (AWGN)…

Systems and Control · Electrical Eng. & Systems 2022-08-26 Shubham Aggarwal , Muhammad Aneeq uz Zaman , Tamer Başar

The finite horizon $H_2/H_\infty$ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, we derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the…

Optimization and Control · Mathematics 2016-07-05 Zhang Weihai , Ma Limin

Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash…

Computer Science and Game Theory · Computer Science 2026-03-17 Mahdis Rabbani , Navid Mojahed , Shima Nazari