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 ?2. What is it?

1.3 Using your answers to parts 1.1 and 1.2, we can immediately conclude that in this equilibrium type-1 player 1 must play...? (Hint: remember to state your answer as a value for ?1 (1))

1.4 Now you should be able to find ?1 (0). What is it? (Hint: the answer is a formula containing ?. Notice that it is easy to mess up signs when calculating ?1 (0), so be careful and double-check your math)

1.5 You now have a complete profile of strategies given by ?1 (0), ?1 (1), ?2. But you can notice that for some values of ? it is not true that ?1 (0) ? (0, 1). Find the values of ? for which ?1 (0) ? (0, 1).

1 There are two players called 1 and 2. Player 1 can be of two types tE {0.1} with Pr = 1): if E (0,1). The actions and payoffs of the game are given by --- mil- Izm- where the row player is player 1. We will use the following notation: 01(12)- is the probability that player 1 plays up if she is of type t; or; 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 = U. i.e. 61(0) E (0,1). We therefore proceed to construct such an equilibrium and then verify for which values of 17 this equilibrium exists. At the end of the exercise: you should complete the following \"Proposition\" Proposition 1. Ifir ............... , then there ecists n Bayes Nash equilibrium in which player 1 mixes between up and down whenever she is of type t = O, i.e. 51(0) E (0,1). In this equilibrium 5101]) = ............ ; 01(1) 2 ......... ; and 5.2 = .......... 1.1 If type-l) player 1 is mixing, what condition must be satised in this equilibrium? (Hint: \"'1 am mixing then it means that I am...) 1.2 Using the condition you derived in part 1.1, you should be able to nd player 2's equilibrium strategy 02. What is it