Abstract
We study the college admission problem with entrance criterion. Each student receives a score from a central exam. The students are divided into two groups: those who are eligible to apply to colleges, and those who are not. Eligibility respects the students’ scores. Each college has a strict preference relation over the students and each student has a strict preference relation over the colleges. We extend the model studied by Perach and Rothblum (2010) to a general case where the students may have the same scores from the central exam. We study ways of assigning students to colleges that respect eligibility criteria. We define several notions of stability. We define three new rules based on the McVitie-Wilson algorithm that satisfy different notions of stability.
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