Journal of the
Korean Mathematical Society JKMS

In this paper we study a time-optimal model of pursuit in which the players move on a plane with bounded velocities. This game is supposed to be a nonzero-sum group pursuit game. The main point of the work is to construct and compare cooperative and non-cooperative solutions in the game and make a conclusion about cooperation possibility in differential pursuit games. We consider all possible cooperations of the players in the game. For that purpose for every game $\Gamma(\bf x_0,\bf y_0,\bf z_0)$ we construct the corresponding game in characteristic function form $\Gamma_v(\bf x_0,\bf y_0,\bf z_0)$. We show that in this game there exists the nonempty core for any initial positions of the players. The core can take four various forms depending on initial positions of the players. We study how the core changes when the game is proceeding. For the original agreement (an imputation from the original core) to remain in force at each current instant $t$ it is necessary for the core to be time-consistent. Nonemptiness of the core in any current subgame constructing along a cooperative trajectory and its time-consistency are shown. Finally, we discuss advantages and disadvantages of choosing this or that imputation from the core.

Keywords: differential game, time-optimal solution, cooperative trajectory, Nash equilibrium, core, time-consistency

MSC numbers: Primary 49N70, 49N75, 49N90; Secondary 91A23, 91A24