1 . There are two players called 1 and 2. Player 1 can be of two types t E {I}, 1} with Pr (t = 1) = 1r E {I}, 1}. The actions and payoffs of the game are given by --- where the row player is player 1. We will use the following notation: in (t) is the probability that player 1 plays up if she is of type t; a2 is the probability that player 2 plays left. We want to know whether and when it is possible that in a Bayes Nash equilibrium player 1 mixes between up and down whenever she is of type t = , i.e. e1 (0) E (D, 1). We therefore proceed to construct such an equilibrium and then verify for which values of 11' this equilibrium exists. At the end of the exercise1 you should complete the following \"Proposition\" Proposition 1. I f 1r ............... , then there exists a Bayes Nash equilibrium in which player 1 mixes between up and down whenever she is of type t = I], i.e. 0'1 (0) E (0,1)- In this equilibrium 51(0) 2 ............ ; ol (1) = ......... ; and a2 = .......... 1.1 If type0 player 1 is mixing, what condition must be satised in this equilibrium? (Hint: if I am mixing then it means that I am...) 1.2 Using the condition you derived in part 1.1, you should be able to nd player 2's equilibrium strategy 02. What is it? 1.3 1.4 1.5 Using your answers to parts 1.1 and 1.2, we can imme- diately conclude that in this equilibrium type1 player 1 must play...? (Hint: remember to state your answer as a value for J1(1)) Now you should be able to nd 01(0) What is it? (Hint: the answer is a formula containing arr. Notice that it is easy to mess up signs when calculating 01 (D), so be careful and double-check your math) You now have a complete prole of strategies given by :71 (0),:71 (1),:12. But you can notice that for some values of 11' it is not true that 01(0) E (D, 1). Find the values of 11' for which 0'1 (0) E (0,1)