College Admissions Problem with Ties and Flexible Quotas

We study an extension of the classical college admission problem where applicants have strict preferences but careers may include ties in their preference lists. We present an algorithm which enables us to find stable assignments without breaking ties rules, but considering flexible quotas. We investigate the properties of this algorithm -- stability, optimality -- and we show that the resulting algorithm is neither monotone nor strategy-proof. The mechanism is used to solve real instances of the Chilean college admission problem. Among our results, we show that the welfare of students is increased if flexible quotas and a student-optimal assignment are combined. Finally, we argue why such assignment may be desirable in the Chilean context.