Pursuit-evasion games in the presence of a line segment obstacle

This paper studies planar pursuit-evasion games in the presence of line segment obstacles that inhibit the motions of the players. The key achievement of the paper is to provide the dominance regions, where a point in the plane is said to be dominated by one of the players if that player is able to reach the point before the opposing player, regardless of the opposing player´s actions. This paper also presents a study of the effects of introducing line segment obstacles by comparing the dominance regions in the presence of obstacles with the dominance regions in the absence of obstacles.