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We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common…

Optimization and Control · Mathematics 2025-06-16 De-xuan Xu , Zhun Gou , Nan-jing Huang

This paper is concerned with zero-sum stochastic linear-quadratic differential games in a regime switching model. The coefficients of the games depend on the underlying noises, so it is a non-Markovian regime switching model. Based on the…

Optimization and Control · Mathematics 2024-09-10 Panpan Zhang , Zuo Quan Xu

This paper presents a pioneering investigation into discrete-time two-person non-zero-sum linear quadratic (LQ) stochastic games with random coefficients. We derive necessary and sufficient conditions for the existence of open-loop Nash…

Optimization and Control · Mathematics 2025-06-24 Yiwei Wu , Xun Li , Qingxin Meng

In this paper we study a class of HJB equations which solve for equilibria for general time-inconsistent deterministic linear quadratic control problems within the intra-personal game theoretic framework, where the inconsistency arises from…

Optimization and Control · Mathematics 2025-05-21 Yunfei Peng , Wei Wei

We consider stochastic differential games with $N$ nearly identical players, linear-Gaussian dynamics, and infinite horizon discounted quadratic cost. Admissible controls are feedbacks for which the system is ergodic. We first study the…

Analysis of PDEs · Mathematics 2014-03-18 Fabio S. Priuli

This paper investigates an inhomogeneous non-zero-sum linear-quadratic (LQ, for short) differential game problem whose state process and cost functional are regulated by a Markov chain. Under the $L^2$ stabilizability framework, we first…

Optimization and Control · Mathematics 2024-05-17 Fan Wu , Xun Li , Xin Zhang

This paper is concerned with a linear-quadratic (LQ) leader-follower differential game with mixed deterministic and stochastic controls. In the game, the follower is a random controller which means that the follower can choose adapted…

Optimization and Control · Mathematics 2025-09-26 Jingtao Shi , Guangchen Wang

This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. We employ a rescaling approach to derive a low…

Optimization and Control · Mathematics 2021-09-20 Minyi Huang , Xuwei Yang

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 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

In this article, we provide a comprehensive study of the linear-quadratic mean field games via the adjoint equation approach; although the problem has been considered in the literature by Huang, Caines and Malhame (HCM, 2007a), their method…

Optimization and Control · Mathematics 2014-04-24 Alain Bensoussan , Joseph Sung , Phillip Yam , Siu Pang Yung

Leveraging tools from the study of linear fractional transformations and algebraic Riccati equations, a local characterization of consistent conjectural variations equilibrium is given for two player games on continuous action spaces with…

Computer Science and Game Theory · Computer Science 2023-06-07 Daniel J. Calderone , Benjamin J. Chasnov , Samuel A. Burden , Lillian J. Ratliff

This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population's state distribution through its quantile function. Such a…

Optimization and Control · Mathematics 2024-11-05 Shuang Gao , Roland P. Malhamé

The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the…

Dynamical Systems · Mathematics 2013-05-24 Augusto Ferrante , Lorenzo Ntogramatzidis

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 zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…

Optimization and Control · Mathematics 2013-01-15 Erhan Bayraktar , Yu-Jui Huang

This paper is concerned with a Stackelberg stochastic differential game on a finite horizon in feedback information pattern. A system of parabolic partial differential equations is obtained at the level of Hamiltonian to give the…

Optimization and Control · Mathematics 2021-08-17 Qi Huang. Jingtao Shi

This paper is devoted to a Stackelberg stochastic differential game for a linear mean-field type stochastic differential system with a mean-field type quadratic cost functional in finite horizon. The coefficients in the state equation and…

Optimization and Control · Mathematics 2023-08-22 Zixuan Li , Jingtao Shi

We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…

Optimization and Control · Mathematics 2020-11-19 Beniamin Goldys , Gianmario Tessitore , James Yang , Zhou Zhou

One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the deterministic case is to provide the desired feedback controls for linear quadratic…

Optimization and Control · Mathematics 2016-11-28 Qi Lu , Tianxiao Wang , Xu Zhang