Consider the following signaling game. Player 1 is of two types, S and T, each with probability

0.5. Type is private information. Player 1 has two signals, x and y.

Player 2 observes player 1's signal and can respond either with action a or action b. Payoffs

are as follows.

Type S plays x. If player 2 plays a, then payoff is (3, 4) and if player 2 plays b, then

payoff is (2, 2).

Type S plays y. If player 2 plays a, then payoff is (5, 7) and if player 2 plays b, then

payoff is (1, 2).

Type T plays x. If player 2 plays a, then payoff is (2, 4) and if player 2 plays b, then

payoff is (0, 5).

Type T plays y. If player 2 plays a, then payoff is (4, 3) and if player 2 plays b, then

payoff is (5, 6).

(a) Draw the extensive form of this game. (4)

(b) Find the separating equilibrium of this game. (8)

(c) Find a pooling equilibrium in which player 2 responds with different actions to different

signals. Does it satisfy the intuitive criterion? (8)