Exercise 1 There are two players A and B. Player B can be of two types t {0,1} with Pr (t-1) =p [0,1]. The actions and payoffs of the game are given by: L U (ii) D (iv) (v) 4, t 0, (1-t) R where the row player is player A. We will use the following notation: a: probability that player A plays U Obt: probability that player B plays L if she is of type t. Part I (2 marks): Complete information (No explanation needed) (i) 0, 4(1-t) 1, 4t (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: (Oa, Obl) = (...) (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: (Oa, Obo) (.,.) Part II (5 marks): Incomplete information Suppose p = 0.5. Check whether the following strategy profiles constitute a BNE: (i) (Oa, Obl, Obo) = (1,1,1) (ii) (da, Obl, Ob0) = (0,0,0) (iii) (Oa, Obl, Obo) = (1,1,0) (Oa, Obl, Ob0) = (0,0,1) (Oa, 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.