Line of Sight Pursuit in Monotone and Scallop Polygons

We study a turn-based game in a simply connected polygonal environment between a pursuer and an adversarial evader . Both players can move in a straight line to any point within unit distance during their turn. The pursuer wins by capturing the evader, meaning that their distance satisfies , while the evader wins by eluding capture forever. Both players have a map of the environment, but they have different sensing capabilities. The evader always knows the location of . Meanwhile, only has line-of-sight visibility: observes the evader’s position only when the line segment connecting them lies entirely within the polygon. Therefore must search for when the evader is hidden from view. We provide a winning strategy for in two families of polygons: monotone polygons and scallop polygons. In both families, a straight line can be moved continuously over so that (1) is a line segment and (2) every …