Before revision:  First, we show that the value of the game exists in stationary strategies, which depend solely on the previous action of the player (and not the entire history ), and we provide a full characterization of the value and the optimal strategies.
After revision:  First, we show that the value of the game exists in stationary strategies, which depend solely on the previous action of the minimizing player, not the entire history ), and we provide a full characterization of the value and the optimal strategies.