Target defense against a sequentially arriving cooperative intruder team

We consider a variant of the target defense problem where a single defender is tasked to guard a target region from a sequence of incoming intruders. Each intruder's objective is to breach the target boundary without being captured and the defender's objective is to capture as many intruders as possible. The intruders appear sequentially on a fixed circle surrounding the target, resulting in a sequence of 1-vs-1 games between the defender and the intruders. Each 1-vs-1 game is terminated when the target is breached or the intruder is captured. The defender has to start the next game as soon as the current game ends. Each intruder knows the entry point of the last intruder and this information is used to find an optimal entry point. Each game is analyzed by dividing it into two phases: partial information and full information phase. We utilize the notions of engagement surface and capture circle to analyze the strategies for the defender as well as the intruders. Furthermore, we analytically compute the capture percentage for both finite and infinite sequences of intruder arrivals. Finally, the theoretical results are verified through numerical examples using Monte-Carlo type random trials of experiments.