For question 1.4, I've already written two equations about the utility of player2 which include pie, but when I combined them together, the pie was eliminated. so I'm stuck in the question 1.4. Could you please help me to solve it? Thank you so much

There are two players called 1 and 2. Player 1 can be of two types t 6 {0,1} with Pr (t = 1) = 7r E (0, 1). The actions and payoffs of the game are given by --- -0,4 1,1 -1,2 a4 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, Le. 01 (0) E (0,1). We therefore proceed to construct such an equilibrium and then verify for which values of 7r 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 mixes between up and down whenever she is of type t = 0, i.e. 01 (0) 6 (0,1). In this equilibrium 01 (0) = ............ ; 01 (1) = ......... ,- and 02 =