Question 8 Consider the two-sided matching model where n = 4 (i.e., we have 4 applicants and 4 hospitals), and let P be the given preference prole. Suppose that (according to P) each applicant has exactly the same preference list. You are not given any more information. Let M be the output of the applicant-proposing GS algorithm. Select the correct answer among the choices below. (A) An applicant A and a hospital H are matched under M such that each is the other's first choice. (B) An applicant A and a hospital H are matched under M such that H is A's first choice and A is H's second choice. (C) An applicant A and a hospital H are matched under M such that H is A's rst choice and A is H's third choice. (D) An applicant A and a hospital H are matched under M such that H is A's rst choice and A is H's fourth choice. Answer: A Explanation: Suppose that applicants7 preferences are and suppose further that H1 's rst Choice is A2. Note that there is no loss of generality here: if you choose another preference prole (as long as each applicant has exactly the same preference list), and another rstchoice applicant for H1, the analysis is as follows. Now, A2 and H1 will be matched to each other under M (the output of the applicant proposing GS algorithm). Verify this yourself: Run the applicanteproposing GS algorithm and convince yourself that the output matching M will contain the pair (A2: H1)' Furthermore, because A; is matched to H1 under M, no other applicant is matched to H1 under M. Thus, only applicant A2 is matched to their topchoice hospital (i.e., H1), and, indeed, each of A: and H1 is the other's rst choice