There are two players called 1 and 2. Player I can be of two types t c {0, 1} with Pr (t = 1) =# E (0, 1). The actions and payoffs of the game are given by left right up 0,4 1, 1 down 1,2 t, 4 where the row player is player 1. We will use the following notation: 01 (t) is the probability that player 1 plays up if she is of type t; 02 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 = 0, i.e. 01 (0) e (0, 1). We therefore proceed to construct such an equilibrium and then verify for which values of a this equilibrium exists. At the end of the exercise, you should complete the following "Proposition" Proposition 1. If . .............., then there exists a Bayes Nash equilibrium in which player 1 mires between up and down whenever she is of type t = 0, i.e. 01 (0) E (0, 1). In this equilibrium o1 (0) = . ...........; 01 (1)= .........; and 02 = . . . . . . .... 1.1 If type-0 player 1 is mixing, what condition must be satisfied 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 find player 2's equilibrium strategy 02. What is it?1.3 Using your answers to parts 1.1 and 1.2, we can imme- diately conclude that in this equilibrium type-1 player 1 must play...? (Hint: remember to state your answer as a value for of (1)) 1.4 Now you should be able to find of (0). What is it? Hint: the answer is a formula containing 7. Notice that it is easy to mess up signs when calculating of (0), so be careful and double-check your math) 1.5 You now have a complete profile of strategies given by 01 (0) , 01 (1), 02. But you can notice that for some values of 7 it is not true that of (0) E (0, 1). Find the values of T for which of (0) E (0, 1)