Consider the following game, which we will call the "truth game": There are two players, called 1 and 2, and a game-master. The game-master has a coin that is bent in such a way that, flipped randomly, the coin will come up "heads" 80% of the time. (The bias of the coin is known to both players.) The game-master flips this coin, and the 2 outcome of the coin flip is shown to player 1. Player 1 then makes an announcement to player 2 about the results of the coin flip; player 1 is allowed to say either "heads" or "tails" (and nothing else). Player 2, having heard what player 1 says but not having seen the results of the coin flip then must guess what the result of the coin flip was - either "heads" or "tails". That end the game. Payoffs are made as follows. For player 2 things are quite simple; player 2 gets $1 if his guess matches the actual results of the coin flip, and he gets $0 otherwise. For player 1 things are more complex. She gets $2 if player 2's guess is that the coin came up "heads", and $0 if player 2 guesses "tails", regardless of how the coin came up. In addition to this, player 1 gets $1 (more) if what she (player 1) says to player 2 matches the results of the coin flip, while she gets $0 more if her message to layer 2 is different from the results of the coin flip.

(a) Draw an extensive form representation of this game.

(b) Convert your extensive form representation to a normal form representation.