Local-game Decomposition for Multiplayer Perimeter-defense Problem

This paper studies a multi-player game between intruders and defenders. The intruder team tries to score by sending as many intruders as possible to the target. The defender team tries to minimize this score by intercepting the intruders. Finding the strategies for both teams and estimating the outcome of the game is challenging due to the high dimensionality of the joint state space. The state-of-the-art method decomposes the game into two-player games and reduces the design of the defense strategy to an assignment problem, whose solution gives an upper bound on the score. We investigate the cooperative aspects of the multi-player game that are not captured in the aforementioned approach and propose a decomposition method that leads to the formation of local sub-teams. We use the method to design a cooperative-intrusion strategy that guarantees a lower bound on the score. The presented results enable a more accurate estimation of the game outcome, and are expected to be useful in the design and evaluation of defender-team strategies.