Question 3 An economics department admissions committee is deciding whether to admit an applicant to their PhD program. Applicants have two possible types: they can be a slacker or an ambitious type. Applicants may choose to get a Master's degree before applying to the PhD program or they can decide not to get a Master's degree. It is mentally costly for the candidate to obtain a Master's degree and we are ignoring the financial costs of getting a degree in this question. An applicant know her type, but this is private information, hence it is unknown to the admissions committee. However, the admissions committee knows whether the candidate has a Master's degree or not. The cost of obtaining a Master's degree depends on the applicant's type. It is more costly for slackers to obtain a Master's degree than the ambitious types. Specifically, candidates' costs are given by,

---------//Applicant does not have a Master's degree /Applicant has a Master's degree

Slacker / 40 / 120

Ambitious/ 35 / 90

The applicant's payoff is the benefit of being admitted minus the cost. The applicant receives a benefit of 120 regardless of her type if the admissions commitee admits her or 60 if the committee does not admit her. For example, if a slacker decides not to have a degree and she is offered admission, she receives a payoff of 120 - 40 = 80 and if an ambitious candidate has a Master's degree and she is not offered admission she receives a payoff of 60 - 90 = -30. Before the admissions committee sees the applicant's application, they believe the probability that the applicant is a slacker is 0.5 and the probability that she is ambitious is 0.5. The admissions commitee will receive a payoff of 90 if they hire an ambitious person, 0 if they hire 2 a slacker, and 50 if they admit no one. a) (12.5 points) Does this game have a pooling equilibrium? Why or why not? Defend your answer carefully and show every step of your calculations. b) (12.5 points) Does this game have a separating equilibrium? Why or why not? Defend your answer carefully and show every step of your calculations.