Linear-Quadratic Time-Inconsistent Mean-Field Type Stackelberg Differential Games: Time-Consistent Open-Loop Solutions

• 成果类型: Article
• 署名作者: Moon, Jun; Yang, Hyun Jong
• 署名单位: Hanyang University; Ulsan National Institute of Science & Technology (UNIST)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2979128
• 发表日期: 2021
• 页码: 375-382
• 关键词: games; optimal control; Differential equations; State feedback; moon; ELECTRONIC MAIL; Stochastic processes; Equilibrium control; Stackelberg differential games; time-inconsistent stochastic control problem

摘要

In this article, we consider the linear-quadratic time-inconsistent mean-field type leader-follower Stackelberg differential game with an adapted open-loop information structure. The objective functionals of the leader and the follower include conditional expectations of state and control (mean field) variables, and the cost parameters could be general nonexponential discounting depending on the initial time. As stated in the existing literature, these two general settings of the objective functionals induce time inconsistency in the optimal solutions. Given an arbitrary control of the leader, we first obtain the follower's (time consistent) equilibrium control and its state feedback representation in terms of the nonsymmetric coupled Riccati differential equations (RDEs) and the backward stochastic differential equation (SDE). This provides the rational behavior of the follower, characterized by the forward-backward SDE (FBSDE). We then obtain the leader's explicit (time consistent) equilibrium control and its state feedback representation in terms of the nonsymmetric coupled RDEs under the FBSDE constraint induced by the follower. With the solvability of the nonsymmetric coupled RDEs, the equilibrium controls of the leader and the follower constitute the time-consistent Stackelberg equilibrium. Finally, the numerical examples are provided to check the solvability of the nonsymmetric coupled RDEs.