Strategic issues with (combined) early and late matching, by Mumcu and Saglam

  Here's a paper on early decision in college admissions. I read it with particular interest because of related discussions going on right now about early and late matching to medical residencies in the U.S. In their model, early matching introduces either or both strategic behavior and instabilities.

Strategic Issues in College Admissions with Early Decision by Ayse Mumcu and Ismail Saglam, Economics Bulletin, Volume 41, Issue 1, 2021

Abstract: In this paper, we consider college admissions with early decision (ED) using a many-to-one matching model with two periods. As in reality, each student commits to only one college in the ED period and agrees to enroll if admitted. Under responsive and consistent preferences for both colleges and students, we show that there exists no stable matching system, consisting of ED and regular decision (RD) matching rules, which is nonmanipulable via ED quotas by colleges or ED preferences by colleges or students. We also show that when colleges or students have common preferences and each student applies early only to the top-ranked college with respect to her RD preference, then no college has a strict incentive to offer a single-choice ED program. On the other hand, if students compromise in the ED market and make early application to colleges that are not top-ranked, then colleges may become better off when they offer ED programs than when they do not.