Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

Shi，Jingtao1; Wang，Guangchen2; Xiong，Jie3

2020

10.1051/cocv/2020006

ESAIM - Control, Optimisation and Calculus of Variations   影响因子和分区

1292-8119

1262-3377

This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term "overlapping"means that there are common part between the follower's and the leader's information, while they have no inclusion relation. Optimal controls of the follower and the leader are obtained by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to give the state estimate feedback representation of the Stackelberg equilibrium strategy, while its solvability is a rather difficult open problem. A special case is then studied and is applied to the continuous-time principal-agent problem.

Maximum principle Overlapping information Stackelberg differential game Stochastic filtering Stochastic linear quadratic optimal control

SCI ; EI

英语

其他

National Key R&D Program of China[2018YFB1305400] ; National Natural Science Funds of China[11971266][11831010][11571205][61821004][61873325][61925306] ; Southern University of Science and Technology Start-Up Fund[Y01286220]

Automation & Control Systems ; Mathematics

Automation & Control Systems ; Mathematics, Applied

WOS:000586380900002

EDP SCIENCES S A

20204509450613

Information filtering ; Quadratic programming ; Game theory ; Continuous time systems ; Stochastic systems ; Maximum principle ; Stochastic control systems

Control Systems:731.1 ; Information Sources and Analysis:903.1 ; Calculus:921.2 ; Probability Theory:922.1 ; Systems Science:961

MATHEMATICS

2-s2.0-85094681829

Scopus

1.School of Mathematics,Shandong University,Jinan,250100,China
2.School of Control Science and Engineering,Shandong University,Jinan,250061,China
3.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

Shi，Jingtao,Wang，Guangchen,Xiong，Jie. Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information[J]. ESAIM - Control, Optimisation and Calculus of Variations,2020,26.

Shi，Jingtao,Wang，Guangchen,&Xiong，Jie.(2020).Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information.ESAIM - Control, Optimisation and Calculus of Variations,26.

Shi，Jingtao,et al."Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information".ESAIM - Control, Optimisation and Calculus of Variations 26(2020).