Linear quadratic leader–follower stochastic differential games for mean-field switching diffusions

Lv，Siyu1; Xiong，Jie2; Zhang，Xin1

2023-08-01

10.1016/j.automatica.2023.111072

Automatica   影响因子和分区

0005-1098

1873-2836

In this paper, we consider a linear quadratic (LQ) leader–follower stochastic differential game for regime switching diffusions with mean-field interactions. One of the salient features of this paper is that conditional mean-field terms are included in the state equation and cost functionals. Based on stochastic maximum principles (SMPs), the follower's problem and the leader's problem are solved sequentially and an open-loop Stackelberg equilibrium is obtained. Further, with the help of the so-called four-step scheme, the corresponding Hamiltonian systems for the two players are decoupled and then the open-loop Stackelberg equilibrium admits a state feedback representation if some new-type Riccati equations are solvable.

Leader–follower game Linear quadratic problem Markov chain Mean-field interaction Riccati equation

SCI ; EI

英语

通讯

National Natural Science Foundation of China[11801072];National Natural Science Foundation of China[11831010];National Natural Science Foundation of China[12171086];National Key Research and Development Program of China[2022YFA1006102];National Key Research and Development Program of China[2022ZD0120001];Fundamental Research Funds for the Central Universities[2242021R41082];Fundamental Research Funds for the Central Universities[2242021R41175];Fundamental Research Funds for the Central Universities[2242023K40012];

Automation & Control Systems ; Engineering

Automation & Control Systems ; Engineering, Electrical & Electronic

WOS:001001732600001

PERGAMON-ELSEVIER SCIENCE LTD

20232014100156

Equations of state ; Game theory ; Hamiltonians ; Markov processes ; State feedback ; Stochastic systems

Control Systems:731.1 ; Calculus:921.2 ; Probability Theory:922.1 ; Systems Science:961

ENGINEERING

2-s2.0-85159224620

Scopus

1.School of Mathematics,Southeast University,Nanjing,211189,China
2.Department of Mathematics and SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

Lv，Siyu,Xiong，Jie,Zhang，Xin. Linear quadratic leader–follower stochastic differential games for mean-field switching diffusions[J]. Automatica,2023,154.

Lv，Siyu,Xiong，Jie,&Zhang，Xin.(2023).Linear quadratic leader–follower stochastic differential games for mean-field switching diffusions.Automatica,154.

Lv，Siyu,et al."Linear quadratic leader–follower stochastic differential games for mean-field switching diffusions".Automatica 154(2023).