TY - JOUR
T1 - Mixed Linear Quadratic Stochastic Differential Leader-Follower Game with Input Constraint
AU - Xie, Tinghan
AU - Feng, Xinwei
AU - Huang, Jianhui
N1 - Funding Information:
The authors would like to thank the editors and two anonymous referees for their very extensive and constructive suggestions that helped to improve this paper considerably. Xinwei Feng’s work is supported by National Natural Science Foundation of China (No. 12001317), Shandong Provincial Natural Science Foundation (No. ZR2020QA019) and QILU Young Scholars Program of Shandong University; Tinghan Xie and Jianhui Huang’s work are supported by RGC 153005/14P, 153275/16P, P0030808, P0008686, P0031044; the authors also acknowledge the support from The PolyU-SDU Joint Research Centre on Financial Mathematics.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - This paper investigates a mixed leader-follower differential games problem, where the model involves two players with the same hierarchy in decision making and each player has two controls which act as a leader and a follower, respectively. Specifically, we solve a follower problem with unconstrained controls and obtain the corresponding Nash equilibrium. Then a leader problem with constrained controls is tackled and a pair of optimal constrained controls are presented by a projection mapping. Furthermore, the control weights are allowed to be singular. In this case, we first investigate the uniform convexity of the cost functional whose corresponding states are fully-coupled forward-backward stochastic differential equation. After that, the minimizing sequence of solutions with non-degenerate control weights are constructed to study the weak convergence of the corresponding cost functionals. Finally, two examples are addressed for non-singular and singular cases, respectively.
AB - This paper investigates a mixed leader-follower differential games problem, where the model involves two players with the same hierarchy in decision making and each player has two controls which act as a leader and a follower, respectively. Specifically, we solve a follower problem with unconstrained controls and obtain the corresponding Nash equilibrium. Then a leader problem with constrained controls is tackled and a pair of optimal constrained controls are presented by a projection mapping. Furthermore, the control weights are allowed to be singular. In this case, we first investigate the uniform convexity of the cost functional whose corresponding states are fully-coupled forward-backward stochastic differential equation. After that, the minimizing sequence of solutions with non-degenerate control weights are constructed to study the weak convergence of the corresponding cost functionals. Finally, two examples are addressed for non-singular and singular cases, respectively.
KW - Forward-backward stochastic differential equation
KW - Input constraint
KW - Mixed leader-follower problem
KW - Singular control weight
KW - Stochastic differential game
UR - http://www.scopus.com/inward/record.url?scp=85104801080&partnerID=8YFLogxK
U2 - 10.1007/s00245-021-09767-7
DO - 10.1007/s00245-021-09767-7
M3 - Journal article
AN - SCOPUS:85104801080
SN - 0095-4616
VL - 84
SP - 215
EP - 251
JO - Applied Mathematics and Optimization
JF - Applied Mathematics and Optimization
IS - 1
ER -