On a single-type differential game with a non-convex terminal payoff

In a normed space of finite dimension we consider a single-type differential game. The vectograms of players are described by the same ball with different time–depend radii. The motion is constructed using polygonal lines. A non-convex terminal payoff is specified, which is defined as the modulus of the deviation of the norm of the phase vector at a fixed point in time from a given value. The goal of the first player is to minimize this payoff. The goal of the second player is opposite. For this problem, the price of the game is found and the corresponding optimal controls of the players are constructed.