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.
Mots-clés : Stackelberg differential game, stochastic linear quadratic optimal control, overlapping information, maximum principle, stochastic filtering
@article{COCV_2020__26_1_A83_0,
author = {Shi, Jingtao and Wang, Guangchen and Xiong, Jie},
title = {Stochastic {Linear} {Quadratic} {Stackelberg} {Differential} {Game} with {Overlapping} {Information}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2020006},
mrnumber = {4165919},
zbl = {1461.91032},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2020006/}
}
TY - JOUR AU - Shi, Jingtao AU - Wang, Guangchen AU - Xiong, Jie TI - Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2020006/ DO - 10.1051/cocv/2020006 LA - en ID - COCV_2020__26_1_A83_0 ER -
%0 Journal Article %A Shi, Jingtao %A Wang, Guangchen %A Xiong, Jie %T Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2020006/ %R 10.1051/cocv/2020006 %G en %F COCV_2020__26_1_A83_0
Shi, Jingtao; Wang, Guangchen; Xiong, Jie. Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 83. doi : 10.1051/cocv/2020006. http://www.numdam.org/articles/10.1051/cocv/2020006/
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Cité par Sources :
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).
