1 There are two players called 1 and 2. Player 1 can be of two types te {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: of (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 T . . .............; 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