2015/05/02 by Andrew Beveridge, Beveridge, Andrew, Yiqing Cai +1
Engineering · Physics and Astronomy · #49N75 #91A24 #Computational Fluid Dynamics and Aerodynamics #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Guidance and Control Systems #Metric Geometry (math.MG) #Optimization and Control (math.OC) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1505.00297
openalex publication_date 2015/05/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restictive capture condition: a pursuer must become colocated with the evader to win the game. We prove two general results about pursuit-evasion games in topological spaces. First, we show that one pursuer has a winning strategy in any CAT(0) space under this restrictive capture criterion. This complements a result of Alexander, Bishop and Ghrist, who provide a winning strategy for a game with positive capture radius. Second, we consider the game played in a compact domain in Euclidean two-space with piecewise analytic boundary and arbitrary Euler characteristic. We show that three pursuers always have a winning strategy by extending recent work of Bhadauria, Klein, Isler and Suri from polygonal environments to our more general setting.