Matching students to colleges in an optimal way is a very difficult task. This has been extensively studied, for example for medical interns where a mechanism was sought to prevent hospitals to grab the best students when they have barely started their studies. College admissions in the United States is a much larger market and universities, especially elite ones, have been playing strategic games by offering early admission programs with various conditions. The most current one is to have students apply early and get an early response against a binding commitment to attend if accepted. This leads potential students to act strategically in their applications, and it is widely believed that this is particularly detrimental to lower income students.
Ayse Mumcu and Ismail Saglam study this early admission market in the tradition of Gale and Shapley. In the first phase, it is a many-to-one early matching, where students apply to at most one college, and colleges accept students of their choice within a quota, or defer them to general admission or reject them. In the second phase, it is a many-to-one regular matching as students apply to many colleges and may accept only one positive college decision. The schools can then choose which strategy to adopt in terms of admission policy.
It turns out that early decision is the preferred policy for colleges: students can apply at most to one college in the Fall, before general admission, and have to commit to attend if admitted. Colleges want to attract their preferred students, presumably the best students who themselves want to go to the best colleges. To avoid admitting inferior students, they seek commitment from applicants. This, however, benefits colleges more than students, as colleges have a first mover advantage by selecting the admission procedure. Interestingly, Harvard has decided recently to scrap its early admission program, officially to give a better chance ot lower income students. But the real reason is probably that Harvard believes it is a first choice among applicants anyway, so it does not need to coax them into a commitment, as long as other alite colleges follow suit, which seems to be happening despite the fact that it is against their interest.