TIME-CONSISTENT SOLUTION OF A COOPERATIVE GROUP PURSUIT GAME

Abstract

In this paper we study a time-optimal model of pursuit in which players move on a plane with bounded velocities. This game is supposed to be a nonzero-sum group pursuit game. The key point of the work is to construct and compare cooperative and non-cooperative solutions of the game and make a conclusion about the cooperation in differential pursuit games. We consider all possible cooperations between the players in the game. For this purpose with every game Γ(x0, y0, z0) we associate a corresponding game in characteristic function form Γv(x0, y0, z0). We show that in the game Γv(x0, y0, z0) there exists the core for any initial positions of the players. The core can take four various forms depending on 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 study how the core is changed when the game is proceeding and prove that the core in this game is time-consistent. Moreover, we point out an allocation from the core which could be accepted as a reasonable one by all players. Finally, we discuss advantages and disadvantages of choosing this or that allocation from the core.