Sufficient and Necessary Open-Loop Stackelberg Strategy for Two-Player Game With Time Delay
研究了带时间延迟的领导者-追随者博弈，通过引入新共态变量克服策略设计的非因果性，给出了开环Stackelberg策略存在的充要条件及显式解。
This paper is concerned with both difference and differential leader-follower games with time delay. The problem remains challenging although the leader-follower game for delay-free system has been well studied in the past decades. The main obstacle encountered is the noncausality of strategy design caused by the delay. The key technique developed to overcome the difficulty is the introduction of the new co-states which capture the future information of the control and the new state which contains the past effects. The novel contributions of this paper are as follows. First, the sufficient and necessary solvability condition is given to ensure the existence of a unique open-loop Stackelberg strategy for the difference game. Second, the open-loop strategy is explicitly obtained in terms of decoupled and symmetric Riccati equations. Last but not least, a unique strategy for continuous time systems is also given by applying the techniques developed in this paper.