A Mean-Field Linear-Quadratic Stochastic Stackelberg Differential Game with one Leader and Two Followers

2020 ◽  
Vol 33 (5) ◽  
pp. 1383-1401
Author(s):  
Guangchen Wang ◽  
Susu Zhang
Keyword(s):  
Differential Game ◽  
Mean Field ◽  
Linear Quadratic ◽  
Stackelberg Differential Game

scholarly journals Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Kai Du ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mean Field ◽  
Open Loop ◽  
Stackelberg Equilibrium ◽  
Linear Quadratic ◽  
Stackelberg Differential Game ◽  
Lq Optimal Control

This paper is concerned with a new kind of Stackelberg differential game of mean-field backward stochastic differential equations (MF-BSDEs). By means of four Riccati equations (REs), the follower first solves a backward mean-field stochastic LQ optimal control problem and gets the corresponding open-loop optimal control with the feedback representation. Then the leader turns to solve an optimization problem for a 1×2 mean-field forward-backward stochastic differential system. In virtue of some high-dimensional and complicated REs, we obtain the open-loop Stackelberg equilibrium, and it admits a state feedback representation. Finally, as applications, a class of stochastic pension fund optimization problems which can be viewed as a special case of our formulation is studied and the open-loop Stackelberg strategy is obtained.

scholarly journals Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

2020 ◽  
Vol 26 ◽  
pp. 83
Author(s):  
Jingtao Shi ◽  
Guangchen Wang ◽  
Jie Xiong
Keyword(s):  
Differential Game ◽  
Direct Calculation ◽  
Stackelberg Equilibrium ◽  
Equilibrium Strategy ◽  
Optimal Controls ◽  
State Variables ◽  
Linear Quadratic ◽  
Stochastic Filtering ◽  
Stackelberg Differential Game ◽  
The Cost

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.

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