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

Jun Moon, Hyun Jong Yang

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number9026927
Pages (from-to)375-382
Number of pages8
JournalIEEE Transactions on Automatic Control
Volume66
Issue number1
DOIs
StatePublished - 2021 Jan

Keywords

  • Equilibrium control
  • Stackelberg differential games
  • time-inconsistent stochastic control problem

Fingerprint Dive into the research topics of 'Linear-Quadratic Time-Inconsistent Mean-Field Type Stackelberg Differential Games: Time-Consistent Open-Loop Solutions'. Together they form a unique fingerprint.

Cite this