Suppose Andy and Brian play a guessing game. There are two slips of paper; one is black and the other is white. Each player has one of the slips of paper pinned to his back. Neither of the players observes which of the two slips is pinned to his own back. (Assume that nature puts the black slip on each player's back with probability 1>2.)
The players are arranged so that Andy can see the slip on Brian's back, but Brian sees neither his own slip nor Andy's slip. After nature's decision, the players interact as follows. First, Andy chooses between Y and N. If he selects Y, then the game ends; in this case, Brian gets a payoff of 0, and Andy obtains 10 if Andy's slip is black and -10 if his slip is white. If Andy selects N, then it becomes Brian's turn to move. Brian chooses between Y and N, ending the game. If Brian says Y and Brian's slip is black, then he obtains 10 and Andy obtains 0. If Brian chooses Y and the white slip is on his back, then he gets -10 and Andy gets 0. If Brian chooses N, then both players obtain 0.
(a) Represent this game in the extensive form.
(b) Draw the Bayesian normal-form matrix of this game.