THE SOLUTION OF GAME PROBLEMS OF DYNAMICS

In this paper we present the results of an investigation of two challe nging problems of the theory of differential games with several player s. To tackle these problems on the basis of well-known methods is rath er complicated. In the first problem we construct the optimal position al strategies for all players in the pursuit-evasion differential game with one pursuer and two evaders. We assume that at some time instant (unknown in advance) one of the evaders quits the game. In the second problem we construct the value function for the simple pursuit-evasio n game with three pursuers and one evader that has an advantage over t he pursuers in the control resource. The value function is constructed for any initial position of the game. We assume that the game is perf ormed on a plane, and the cost functional is the distance between the evader and the nearest pursuer at the termination instant of the game.