Two-player LQ Stackelberg difference game with open-loop strategy under stochastic discrete-time dynamics in finite horizon

Abstract

This paper investigates the LQ open-loop Stackelberg game for the discrete-time stochastic systems in finite horizon. A necessary and sufficient condition for the existence and uniqueness of the open-loop Stackelberg strategy is put forward in terms of the positive definiteness of some matrices. By introducing new state and costate variables, it is shown that the open-loop Stackelberg equilibrium admits a feedback representation based on the solutions of three decoupled and symmetric Riccati equations. Finally, two examples are discussed to highlight the effectiveness of the proposed results.