An algorithm for solving S-games and differential S-games

We present an algorithm for solving S-Games. Our algorithm can be used to compute approximately the value of the game as well as ??-optimal strategies of the two players. For games with similar structure to S-games which do not necessarily possess a value, the algorithm can sometimes be used as a heuristic procedure for determining the existence of a minimax solution. Further, it is shown that a certain simple class of differential games (we call them "differential S-games") can be viewed as static games and solved by the above procedure.