Intuitive Criterion In The Far West

2. [Applying the Intuitive Criterion in the Far West (Beer-Quiche game)] Con-sider the following sequential game with incomplete information. It represents a Saloonin the FarWest. Player 1 just moved into town, and nobody else but himknows whetherhe is .Wimpy.or .Surely.(i.e., Weak or Strong). At that moment in the morningthe Saloon is a quite place, and he is deciding whether to have Quiche for breakfast(something that he really enjoys if he is aWimpy type) or a Beer (something he prefersto Quiche when he is of the Surely type). Then, player 2 (the typical character lookingfor trouble in this kind of .lms) enters into the Saloon and observes the newcomerhaving breakfast, but does not know whether he is Surely or Wimpy.(a) Check if the pooling equilibrium in which both types of player 1 have Beer forbreakfast survives the Cho and Kreps.(1987) Intuitive Criterion.Answer:Suppose player 2 believes that player1 chooses ‘Quiche’ given that he is of type ‘weak’ with probability ‘p’ whereas chooses ‘Quiche’ given that he is of type ‘strong’ with probability ‘1-p’ .Also suppose that player 2 believes that player 1 chooses ‘Beer’ given that he is of type ‘Weak’ with probability ‘q’ whereas chooses ‘Beer’ given that he