Consider the following signaling game, in which player 1 is type 1, type 2, or type 3 with equal probability. Each type chooses A or B, and then player 2 observes what player 1 chose (but not player 1's type) and chooses C or D.

2. (24 points) Consider the following signaling game, in which player 1 is type 1, type 2, or type 3 with equal probability. Each type chooses A or B, and then player 2 observes what player 1 chose (but not player 1's type) and chooses C or D. (3, 0) C A B E (2. 1) t1 (4, 1) D IF (2. 0) (5, 2) (4, 2) t 2 (6, 1) 13 (4, 0) (7, 2) (a) Are any strategies strictly dominated or weakly dominated for player 1? If there are any strictly/weakly dominated strategies, find them. (b) Are there any pooling equilibria in pure strategies (weak sequential equilibrium with all types of player 1 playing the same strategy) in this game? Verify your answer and if there are any pooling equilibria, find them. (c) Find all separating equilibrium in pure strategies of this game. Ex- plain your answer clearly. (d) Find any weak sequential equilibria with 1) player 1 of types 1 and 2 playing A and type 3 mixing A and B and 2) player 2 playing a mixed action at only one of its information sets