On some excess-based solution concepts of a cooperative game of pursuit

We study a group pursuit game with players - an evader and m pursuers - moving on a plane with bounded velocities. The game is nonzero-sum. The Nash equilibrium is proposed as a solution of the game. We construct a cooperative version of this game and show that its core is not empty. In addition, we consider a particular case when the evader is symmetrically surrounded by the pursuers. The analytical formulas for calculating the nucleolus and the SM-nucleolus are verified. Finally, we give an example that illustrates the results.