ECON3012 Strategic behaviour

Q2 (33 points) Each year, the School of Economics invites a list of qualified students to com- plete an honours year in Economics. Suppose that the probability that a student is qualified is 0.1. Normally, a qualified student needs to pay a cost of c = 10 in order to get an honours degree (c represents the time and effort spent to complete the advanced coursework and write a thesis). Let's say that a student of this type is a "real" honours student. Imagine that, due to the lack of income, the School of Economics decides to sell honours degrees for money: anyone, qualified or not, can get an honours degree in Economics without any advanced coursework or thesis, as long as they pay a fee of x > 0. Let's say that a student of this type is a "fake" honours student. (Disclaimer: this is purely fictional.) There are two firms, a low-salary firm and a high-salary firm, who seek to hire fresh graduates. The firms know whether a student has an honours degree or not, but they cannot tell if the honours degree is real or fake. The low-salary firm gives job offers to all students. The high-salary firm prefers real honours students. Its offer decision is determined by the payoff table below. In case of a tie, the high-salary firm gives an offer when it is indifferent between giving and not giving. A student's payoff is 90 if he/she accepts an offer from the low-salary firm and 120 if he/she accepts an offer from the high-salary firm. Is the student a real honours student? Yes No Offer High-salary firm's offer decision 20 0 No offer 5 10 High-salary firm's payoff (a) (5 points) Let p denote the probability that a student is a real honours student. Complete the high-salary firm's decision rule below. Show your work. high-salary firm gives an offer if p . does not give an offer if p (b) (28 points) In each of the following cases, please answer: Is there a perfect Bayesian equilibrium in which the expected income received by the School of Economics from selling fake honours degrees is positive? If your answer is "yes", please fully describe the students' equilibrium strategies. If your answer is "no", please explain. 1. x = 5 (6 points) 2. x = 20 (16 points) 3. x = 50 (6 points)