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We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the…

Optimization and Control · Mathematics 2024-02-16 Eduardo Abi Jaber , Eyal Neuman , Moritz Voß

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

This paper investigates an indefinite linear-quadratic partially observed mean-field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual…

Optimization and Control · Mathematics 2025-08-05 Tian Chen , Tianyang Nie , Zhen Wu

The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the mean field type. These equations occur in the study of mean field games and the…

Probability · Mathematics 2012-11-20 Rene Carmona , Francois Delarue

Motivated by mean-field games (MFG) with common noise on the one hand and pathwise stochastic control theory on the other, we formulate here a linear-quadratic (LQ) MFG with rough common noise, along with a satisfactory well-posedness…

Probability · Mathematics 2026-04-14 Peter K. Friz , Ioannis Gasteratos , Ulrich Horst , Stefanos Theodorakopoulos

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

This paper is concerned with a class of mean-field type coupled forward-backward stochastic differential equations (MF-FBSDEs, for short), in which the coupling appears in integral terms, terminal terms, and initial terms. Inspired by…

Optimization and Control · Mathematics 2022-03-29 Ran Tian , Zhiyong Yu

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

In this paper, we consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way. We assume that the cost function satisfies a convexity and a weak monotonicity…

Optimization and Control · Mathematics 2021-05-26 Ziyu Huang , Shanjian Tang

We study a class of linear-quadratic mean-field games with incomplete information. For each agent, the state is given by a linear forward stochastic differential equation with common noise. Moreover, both the state and control variables can…

Optimization and Control · Mathematics 2023-07-04 Min Li , Tianyang Nie , Shunjun Wang , Ke Yan

The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

Optimization and Control · Mathematics 2020-03-11 Yves Achdou , Mathieu Laurière

We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the…

Optimization and Control · Mathematics 2026-05-28 Hanchao Liu , Dena Firoozi

This paper investigates the so-called asymptotic solvability problem in linear quadratic (LQ) mean field games. The model has asymptotic solvability if for all sufficiently large population sizes, the corresponding game has a set of…

Optimization and Control · Mathematics 2018-11-02 Minyi Huang , Mengjie Zhou

This paper is concerned with a kind of linear-quadratic (LQ, for short) two-person zero-sum stochastic differential game problems with partial observation. We propose the notions of explicit and implicit feedback laws under partial…

Optimization and Control · Mathematics 2025-10-29 Zhiyong Yu , Wanying Yue

We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…

Optimization and Control · Mathematics 2025-01-23 Alain Bensoussan , Ho Man Tai , Tak Kwong Wong , Sheung Chi Phillip Yam

This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium…

Optimization and Control · Mathematics 2021-04-09 Xun Li , Jingtao Shi , Jiongmin Yong

This paper delves into studying the differences and connections between open-loop and closed-loop strategies for the linear quadratic (LQ) mean field games (MFGs) by the direct approach. The investigation begins with the finite-population…

Optimization and Control · Mathematics 2025-04-21 Yong Liang , Bing-Chang Wang , Huanshui Zhang

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

This paper is concerned with a linear-quadratic partially observed mean field Stackelberg stochastic differential game, which contains a leader and a large number of followers. Specifically, the followers confront a large-population Nash…

Optimization and Control · Mathematics 2025-12-09 Yu Si , Yueyang Zheng , Jingtao Shi

In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique…

Optimization and Control · Mathematics 2025-03-04 Jie Xiong , Wen Xu , Ying Yang