AI Research Solves 2-vs-1 Surveillance Game with Geometric Strategies

A team led by Philipp Braun from multiple institutions has published a paper on arXiv extending a previously solved 1-vs-1 surveillance-evasion differential game to a 2-vs-1 setting. The game models a 'prying pedestrian' (pursuer) trying to stay within surveillance range of a less agile evader for as long as possible, while the evader aims to escape. In this new work, the authors derive semi-explicit solutions for two specific 2-vs-1 scenarios: when both pursuers are static (stationary) and when the evader is at least twice as fast as the pursuers. The key innovation is a geometric reinterpretation of the optimal strategies, avoiding a coordinate transformation that worked for 1-vs-1 but not for the multi-pursuer case.

This geometric approach not only enables progress on the 2-vs-1 game but also yields new insights into the original 1-vs-1 strategies. The findings have practical implications for multi-agent surveillance, drone swarms, and autonomous tracking systems where a team of slower agents must corner a faster evader. The partial solutions provide a foundation for further extensions to more pursuers or dynamic environments, bridging differential game theory with real-world multi-robot coordination.