Volume 26, 2020
|Number of page(s)||38|
|Published online||21 October 2020|
Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information*
School of Mathematics, Shandong University,
250100, PR China
2 School of Control Science and Engineering, Shandong University, Jinan 250061, PR China
3 Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, PR China
** Corresponding author: firstname.lastname@example.org
Accepted: 30 January 2020
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.
Mathematics Subject Classification: 60H10 / 91A23 / 93E20 / 93E11
Key words: Stackelberg differential game / stochastic linear quadratic optimal control / overlapping information / maximum principle / stochastic filtering
This work is financially supported by the National Key R&D Program of China (Grant No. 2018YFB1305400), the National Natural Science Funds of China (Grant No. 11971266, 11831010, 11571205, 61821004, 61873325, 61925306), and the Southern University of Science and Technology Start-Up Fund (Grant No. Y01286220).
© EDP Sciences, SMAI 2020
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