Some Cases of Cooperation in Differential Pursuit Games

In this paper we study a time-optimal model of pursuit in which players move on a plane with bounded velocities. The game is supposed to be a nonzero-sum simple pursuit game between an evader and m pursuers acting irrespective of each other. The key point of the work is to construct some cooperative solutions of the game and compare them with non-cooperative solutions such as Nash equilibria. It is important to give a reasonable answer to the question if cooperation is profitable in differential pursuit games or not. We consider all possible coalitions of the players in the game. For example, the pursuers promise some amount of the total payoff to the evader for cooperation with him. In that way, a cooperative game in characteristic function form is constructed, and its various cooperative solutions are found. We prove that in the game $\Gamma_v(x_1^0,\dots,z_m^0,z^0)$ there exists the nonempty core for any initial positions of the players. In a dynamic game existence of the core at the initial moment of time is not sufficient for being accepted as a solution in it. We prove that the core in this game is time-consistent.