Optimal Strategies in Multiplayer Reach–Avoid Games With Different Speed Ratios

This article investigates reach-avoid games involving defenders equipped with capture radii, where both defenders and attackers have different speeds. The main challenge lies in using geometric methods to analyze different speed ratios, construct barriers, or defensive advantage angles, and divide the state space into defensive and offensive advantage regions. This article proposes optimal analytical strategies for players based on the corresponding payoff functions, depending on the attacker's position within different winning regions under various speed ratios. In addition, we demonstrate the existence of a unique optimal target point within the offensive advantage region. Unlike numerical methods, which are limited by computational complexity and real-time application capabilities, the proposed method allows for the precise calculation of barriers and real-time updates in nonpoint capture scenarios. Finally, simulation results validate the effectiveness of the constructed barriers in multiplayer reach-avoid games.