The approximation error in a differential game

The paper is concerned with a positional differential game of two players, one of whom strives to move the game to a desired objective set at a specified time. The goal of the other player is the opposite. The solution is a set of all initial positions wherefrom the movement is possible. An approximating differential game is introduced in addition to the initial game. An estimate is obtained of proximity of solutions of the initial and approximating games in the case where the objective set is not necessarily convex. If it is, a more accurate estimate is obtained.