Two Approaches for Solving a Group Pursuit Game

In this paper we study a game of group pursuit in which players move on a plane with bounded velocities. The game is supposed to be a nonzero-sum simple pursuit game between a pursuer and $m$ evaders acting independently of each other. The case of complete information is considered. Here we assume that the evaders are discriminated. Two different approaches to formalize this pursuit problem are considered: noncooperative and cooperative. In a noncooperative case we construct a Nash equilibrium, and in a cooperative case we construct the core. We proved that the core is not empty for any initial positions of the players.