Question 1 There are two players called 1 and 2. Player I can be of two types te {0,1} with Pr (t=1) = E (0,1). [Here, It is a symbol] 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: G1(t): probability that player 1 plays up if she is of type t; . 62: probability that player 2 plays left.1. (1 mark) 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 ...) 2. (1 mark) Using the condition derived in part 1, you should be able to find player 2's equilibrium strategy 62. What is it? 3. (2 marks) Using your answers to parts 1 and 2, we can immediately conclude that in this equilibrium type-1 player 1 must play...? (Hint: remember to state your answer as a value for ci(1)) 4. (3 marks) Now you should be able to find o(0). What is it? [Hint: the answer is a formula containing at. Notice that it is easy to mess up signs when calculating o(0), so be careful and double-check your math. 5. (1 mark) You now have a complete profile of strategies given by Gi (0), G1(1), 62. But you can notice that for some values of it it is not true that 1 (0) E (0, 1). Find the values of it for which of (0) E (0,1).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. G(0) E (0,1). We therefore proceed to construct such an equilibrium and then verify for which values of n this equilibrium exists. At the end of the exercise, you should complete the following "Proposition" Proposition 1. If I E (.., ...), 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. G1(0) E (0,1). In this equilibrium of (0) = ...; 61(1) = ...; 61 =