Pursuit Strategies for Capture-the-Flag Games With Half-Plane Flag and Return Region

This article studies a multiplayer capture-the-flag (CTF) differential game, where multiple pursuers try to intercept evaders whose objectives are to first reach a flag and then reach a return region. The critical point is that the flag and the return region are half-planes. Our goal is to address the problem of determining the game winner and computing the pursuit winning strategies. By decomposing the complex multiplayer game into many manageable subgames involving multiple pursuers and one evader, we present the strategies under which the pursuers guarantee to win against the evader, regardless of the evader's strategy, with the necessary and sufficient conditions to determine the game winner. We then extend the results to the cases of the flag-staying time and the minimum safe flag position. To reduce the computational burdens, we prove that if multiple pursuers can ensure the pursuit winning against an evader, then at most two pursuers in this coalition are required. Finally, we solve the multiplayer game by evaluating pairwise subgame outcomes for pursuer-evader matchings. Numerical and experimental results are presented to illustrate the theoretical conclusions.