A linear-quadratic mean-field stochastic Stackelberg differential game with random exit time

Abstract

This paper is concerned with a new model of linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which only the leader is allowed to stop her strategy at a random time. By employing the backward induction method, the state equation is divided into two-stage equations. Then, the open-loop Stackelberg solution is obtained by using the maximum principle and the verification theorem. In a special case, with the help of Riccati equations, the open-loop Stackelberg solution is expressed as a feedback form of both the state and its mean.

Keywords:

• Stochastic Stackelberg differential game
• mean-field stochastic differential equation
• random exit time
• Stackelberg solution

2020 Mathematics Subject Classifications:

• 49N80
• 60H20
• 60J76
• 93E20

Acknowledgments

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant Numbers 11671282, 12171339].