Dorm augmented college assignments

Abstract

In college assignments, a common practice is that students receive their dorm allocation after the realization of college placements. This causes wasted resources and unfair allocation. To fix this, we consider a college assignment problem where students simultaneously receive their college and dorm assignments. We first introduce the so-called “Dorm Augmented Deferred Acceptance” (DDA) and show that it is stable and efficient. However, it is not student-optimal stable. We then introduce our next mechanism, “Student-Improving Dorm Augmented Deferred Acceptance” (SDDA). It is mainly built on DDA, but with some extra steps to neutralize the student-harming rejection cycles. We show that SDDA is student-optimal stable, efficient, and unanimously preferred to DDA by students. Stability and strategy-proofness are incompatible, implying that neither of these mechanisms is strategy-proof. None of these mechanisms is more manipulable than the other; hence SDDA improves the students’ welfare without an extra strategic cost.