AI 中文总结
研究将行人监视-逃避微分博弈从1v1扩展到2v1，通过推导利用1v1结果的半显式或几何解释，得出2v1博弈部分解，避免无效坐标变换，还产生新几何解释并开启扩展。
AI 中文摘要
在[1]中，作者最近提出并解决了一个监视-逃避微分博弈，其中敏捷的追捕者（窥探行人）试图在给定监视范围内尽可能长时间地跟踪不太敏捷的逃避者，而逃避者则试图尽快逃脱。本文提供了将此博弈从1对1（1v1）设置扩展到有两个追捕者和一个逃避者的2对1（2v1）设置的初步结果。通过推导和利用现有1v1结果的半显式或几何重新解释，我们得出了静态追捕者情况以及逃避者速度至少是追捕者两倍情况下2v1博弈的部分解。本文的2v1结果基于[1]的1v1结果，但开发了一种不同的求解方法，以避免将1v1博弈简化为二维的坐标变换，因为该变换在简化2v1博弈时无效。除了推动2v1博弈取得进展外，我们的新方法还对1v1博弈中最优追捕者和逃避者策略产生了新的几何解释，并开启了进一步可能的扩展。
英文摘要
In [1], the authors recently proposed and solved a surveillance-evasion differential game in which an agile pursuer (the prying pedestrian) seeks to remain within a given surveillance range of a less agile evader for as long as possible while the evader seeks to escape as quickly as possible. In this paper, we provide initial results that extend this game from the 1 versus 1 (1v1) setting to a 2 versus 1 (2v1) setting with two pursuers and one evader. By deriving and exploiting semi-explicit or geometric reinterpretations of the existing 1v1 results, we derive partial solutions to the 2v1 game for the case of static pursuers and for the case of an evader that is at least twice as fast as the pursuers. While the 2v1 results of this paper build on the 1v1 results of [1], a different solution approach is developed to avoid a coordinate transformation that reduces the 1v1 game to two dimensions but which is ineffective at simplifying the 2v1 game. Beyond enabling progress on the 2v1 game, our new approach yields new geometric interpretations of the optimal pursuer and evader strategies in the 1v1 game, and opens further possible extensions.
