Stackelberg strategy for two-player game with time delay

In this paper, we mainly study the leader-follower game with time delay appearing in the control of the leader. Although the problem without delay has been well studied in the past decades, there is little progressing for the problem with time delay to the best of our knowledge. Our main contribution is to give a sufficient and necessary condition to ensure the existence and uniqueness of the open-loop Stackelberg strategy for the game with delay. Further, to prevent the coupled and nonsymmetric Riccati equations found in some solutions for the game without delay, we derive the decoupled and symmetric Riccati equations which are easier to be solved by introducing two new co-states.