Notes for “ Decentralized College Admissions ” Yeon - Koo Che and Youngwoo Koh

Before proceeding, we make the following observations: First, for each student, applying to a college dominates not applying at all. Second, since a student does not know the score and the student’s preference is independent of the score, the student’s application depends solely on the preference. Third, since each student’s preference depends on the state, the mass of students applying to each college varies across states. Let ni(s) be the mass of students who apply to college i = A,B in state s.