Question 1 There are two players called 1 and 2. Player I can be of two types te {0,1} with Pr (t=1) = n E (0,1). [Here, it is a symbol] The actions and payoffs of the game are given by: left right LID 0.4 1, 1 down 1,2 t.4 where the row player is player 1. We will use the following notation: Gi(t): probability that player 1 plays up if she is of type t; 62: probability that player 2 plays left. Part I (2 marks) Suppose It = 0.5. Is (61(0), 61(1), 62) = (0,1,0) a Bayes-Nash equilibrium? [Hint: To prove something is a BNE you have to check no player-type has an incentive to deviate from the proposed strategy profile. To prove something is not a BNE, you need to check just one of the three - type-0 player 1, type-1 player 1, or player 2 has an incentive to deviate]Part ll {3 marks) 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 = i], i.e. oii} E {I}. 1 }. We therefore proceed to construct such an equilibrium and then verify for which values of it this equilibrium exists. At the end of the exercise. you should complete the following \"Proposition" Proposition 1. If n E (. , ...], then there exists a Bayes Nash equilibrium in which player 1 mixes between up and down whenever she is of type t=tl , i.e. mill} E {11,1}. In this equilibrium o1{ll}= ...; 111(1) = ...; or = ... ... ... . l. {I mark} If type{I player 1 is mixing, what condition must be satisfied in this equilibrium? (Hint: if I am mixing then it means that I am ...} 2. {I mark} Using the condition derived in part 1, you should be able to nd player 2 's equilibrium strategy :31. What is it? 3. {2 marks} Using your answers to parts 1 and 2, we can immediately conclude that in this equilibrium typel player 1 must play...'? (Hint: remember to state your answer as a value for m{ 1}} 4. {3 marks} Now you shode be able to nd mm]. What is it? [Hint the answer is a formula containing 1:. Notice that it is easy to mess up signs when calculating add}, so be careful and doublecheck your math. 5. {I mark} You now have a complete profile of strategies given by trim]. o|[l is us. But you can notice that for some values of it it is not true that o|[ll} E {(1.1). Find the values of a: for which will} E {(1.1}