Cooperative Team Strategies for Multi-player Perimeter-Defense Games

This paper studies a variant of the multi-player reach-avoid game played between intruders and defenders with applications to perimeter defense. The intruder team tries to score by sending as many intruders as possible to the target area, while the defender team tries to minimize this score by intercepting them. Finding the optimal strategies of the game is challenging due to the high dimensionality of the joint state space, and the existing works have proposed approximation methods to reduce the design of the defense strategy into assignment problems. However they suffer from either suboptimal defender performance or computational complexity. Based on a novel decomposition method, this paper proposes a scalable (polynomial-time) assignment algorithm that accommodates cooperative behaviors and outperforms the existing defense strategies. For a certain class of initial configurations, we derive the exact score by showing that the lower bound provided by the intruder team matches the upper bound provided by the defender team, which also proves the optimality of the team strategies.