空中防御者与地面入侵者的周界防御博弈
Perimeter-defense Game between Aerial Defender and Ground Intruder
摘要：
我们研究了一个变种的追求-逃避游戏的背景下，周边防御。在这个问题中，入侵者的目标是到达半球的基面而不被防御者捕获，而防御者试图捕获入侵者。周界防御博弈以前是在假设防守者在圆周上移动的情况下研究的。我们将问题推广到防御者在半球上移动的情况。为了解决这个问题，我们分析的基础上的突破点，入侵者试图达到目标的战略和预测的目标位置，定义为最佳突破点，这是由双方球员的最佳策略。我们提供的障碍，将状态空间分为防守者获胜和入侵者获胜的区域，并证明了双方的最佳策略是走向最佳突破点。仿真结果表明，博弈的最优性作为一个纳什均衡。
英文摘要：
We study a variant of pursuit-evasion game in the context of perimeter defense. In this problem, the intruder aims to reach the base plane of a hemisphere without being captured by the defender, while the defender tries to capture the intruder. The perimeter-defense game was previously studied under the assumption that the defender moves on a circle. We extend the problem to the case where the defender moves on a hemisphere. To solve this problem, we analyze the strategies based on the breaching point at which the intruder tries to reach the target and predict the goal position, defined as optimal breaching point, that is achieved by the optimal strategies on both players. We provide the barrier that divides the state space into defender-winning and intruder-winning regions and prove that the optimal strategies for both players are to move towards the optimal breaching point. Simulation results are presented to demonstrate that the optimality of the game is given as a Nash equilibrium.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
