Consider the following signaling game. The players are 1 and 2. Nature chooses p
ID: 3267972 • Letter: C
Question
Consider the following signaling game. The players are 1 and 2. Nature chooses player 1’s type. Then player 1 chooses Left or Right. Then player 2 observes player 1’s move (but not type) and chooses Up or Down.
(a) What is the type space and set of pure strategies for player 1?
(b) What is the type space and set of pure strategies for player 2?
(c) What are the possible separating pure strategies for player 1? What are the possible pooling pure strategies for player 1?
(d) Is there a separating perfect Bayesian equilibrium? (e) Is there a pooling perfect Bayesian equilibrium?
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(2,2) (3,A) P1.1, t = A (3,0) prob. = 0.5 Pl.2 Pl.2 prob. = 0.5 P1.1, t = B 1.2 (2,2)Explanation / Answer
(a) Type space is {Type A, Type B} for player 1 and pure strategy is to go Right. This is because Player 2 will always choose to go up for his own maximum benefit. Knowing this, Player 1 should go right, irrespective of his type.
(b) Pure strategy for Player 2 is to go up irrespective of whether player 1 goes right or left.
When Player 1 goes right, the average payoff for going up by player 2 is (4+1)/2 = 2.5, while the average payoff for going down is (1+2)/2 = 1.5. Hence, player 2 would choose going up when player 1 goes right.
When Player 1 goes left, the average payoff for going up by player 2 is (2+1)/2 = 1.5, while the average payoff for going down is (0+2)/2 = 1. Hence, player 2 would choose going up when player 1 goes left.
(c)