Two players A and B play the following sequential game by using a black box. Round 1. A puts 0 or 1 matches in the box. Round 2. B puts 0 or 1 matches in the box. Round 3. A puts 0 or 1 matches in the box. After these three rounds a referee opens the box and counts the matches in it. If the total number of matches in the box is an odd number, A wins and the resulting payoff profile is (1, 1). If the total number of matches in the box is an even number however, B wins and the resulting payoff profile is (1, 1). This would have been an easy game for A if he did not have such a terrible memory. At the beginning of round 3, he can not remember how many matches he put in the box in round 1 (he can, however, remember how many matches player B put in the box in round 2). (a) Draw the game tree for this interaction. (b) Write down the players strategy sets. (c) How many subgames does this game have?