Discrete game on a line with information delays

An antagonistic multistep game with time lag is considered on a straight line; in it the gunner maximizes the probability of hitting the target with “projectiles” before the latter reaches the “bunker”. The hitting probability depends on the distance between the point at which the “projectile bursts” and the target. A recursion relation is obtained for the payoff of the game, and optimal strategies are constructed for the players.