In this note, the known deterministic linear-quadratic Stackelberg game is revisited, whose open-loop solution actually possesses the nature of time inconsistency. To handle the time inconsistency, a time-consistent open-loop solution is introduced for the deterministic linear-quadratic Stackelberg game. On the existence and uniqueness of such a kind of solution, necessary and sufficient conditions are obtained, which are characterized via several Riccati-like equations.
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