Exercise 1 There are two players A and B. Player B can be of two types te {0,1} with Pr (t=1) = pe [0, 1]. The actions and payoffs of the game are given by: L R U 4, t 0, 4(1-t) D 0, (1-t) 1, 4t where the row player is player A. We will use the following notation: Ga: probability that player A plays U Out: probability that player B plays L if she is of type t. Part I (2 marks): Complete information (No explanation needed) (i) (1 mark) Suppose p = 1. That is, player B's type is t = 1 for sure. State all Nash equilibria in pure and mixed strategies in the following format: (Ga, Obl) = ( . , . ) (ii) (1 mark) Suppose p = 0. That is, player B's type is t = 0 for sure. State all Nash equilibria in pure and mixed strategies in the following format: (Ga, bo) = ( . , . ) Part II (5 marks): Incomplete information Suppose p =0.5. Check whether the following strategy profiles constitute a BNE: (i) (Ga, Obl, 560) = (1,1,1) (ii) (Ga, Obl, Gb0) = (0,0,0) (iii) (Ga, Obl, Gb0) = (1,1,0) (iv) (Ga, Obl, "bo) = (0,0,1) (v) (Ga, Obl, Obo) = (0.8,0.2,0.2) . To prove something is not a BNE, you need to show that just one of the three - type-0 player B, type-1 player B, or player A has an incentive to deviate. . To prove something is a BNE you have to check that no player-type has an incentive to deviate from the proposed strategy profile