Mechanisms : Student - optimality vs

1. Abstract The college admissions problem is an example of a two-sided matching market. Even though it is closely-related to the stable marriage problem, it is in fact not equivalent. However, the problems are similar enough that the mechanisms used to solve them share some properties—the mechanisms are only guaranteed to produce an optimal stable outcome for one of the parties, but not both. In this paper, we will try to answer which of the two mechanisms is more preferable in the college admissions problem, at least in practice. While a men-optimal stable mechanism and a women-optimal stable mechanism in the marriage problem are symmetric of each other, a student-optimal stable mechanism and a college-optimal stable mechanism in the college admissions problem are not. Due to this asymmetry, it has been shown that a college-optimal stable mechanism has more undesirable properties than its counterpart. Moreover, the results from experiments that ran a student-optimal stable mechanism and a college-optimal stable mechanism over real data from the National Resident Matching Program that matches hospitals and medical interns (including medical specialties) in the US revealed that participating programs (colleges) would not have been much worse-off under a student-optimal stable matching (approximately 2% of the programs would have been worse off).