There are two players called 1 and 2. Player 1 can be of two types f e (0, 1} with Pr( = 1) =we (0, 1). The actions and payoffs of the game are given by right 0.4 1, 1 down 1, 2 t, 4 where the row player is player 1. We will use the following notation: on (t) is the probability that player 1 plays up if she is of type f; oy 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. o (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. I/7................ then there exists a Bayes Nash equilibrium in which player 1 mixes between up and down whenever she is of type t = 0. i.e. of (0) e (0, 1). In this equilibrium g1(0) = ...... ;01(]]=.........; and = .... ...... 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 of. What is it