Consider the following game. There are two players, 1 and 2. Player 1 moves first, and names "Head", "Tail", or "Middle". If he chooses either "Head" or "Tail", the game ends with probability 0.5. If it ends and player 1 has said "Head", payoffs are (3,2) (the convention here is that player 1's payoff is listed first, and player 2's payoff is listed second). If it ends and player 1 has said "Tail", payoffs are (4,3). If the game does not end, then player 2 gets to make a choice. The game necessarily terminates after this choice. If player 1 has named "Head", player 2 can choose either "Up" yielding payoffs (9,6), "Down" yielding payoffs (3,1), or "Sideway" yielding payoffs (1,5). Player 2 cannot tell the difference between player 1 choosing "Tail" and player 1 choosing "Middle." In either case, his alternatives are to choose either "Up" or "Backward". If player 1 has chosen "Tail", then "Up" yields (1,1), and "Backward" yields (2,6). If player 1 has chosen "Middle", then "Up" yields (1,1), and "Backward" yields (6,2).

(a) Draw the extensive form of this game. (b) Determine the strategy sets for each player in this game. (c) Draw the normal form of this game.