Deterministic dynamic Stackelberg games: Time-consistent open-loop solution

In this paper, the known deterministic linear-quadratic Stackelberg game is revisited, whose open-loop solution actually possesses nature of time inconsistency. To handle inconsistency, a two-tier framework introduced: upper-tier works according to Stackelberg’s scenario between leader and follower, outcomes two lower-tier intertemporal games characterize, respectively, follower’s leader’s response controls that mimic notion time-consistent equilibrium control in existing literature. The obtained shown be weakly sense adopted policies will no longer denied future only if past are consistent with policies. On existence uniqueness such solution, necessary sufficient conditions obtained, which characterized via solutions several Riccati-like equations.