Decentralized College Admissions

We study decentralized college admissions with uncertain student preferences. Colleges strategically admit students likely to be overlooked by competitors. Highly ranked students may receive fewer admissions or have a higher chance of receiving no admissions than those ranked below. When students' attributes are multidimensional, colleges avoid head-on competition by placing excessive weight on school-specific attributes such as essays. Restricting the number of applications or wait-listing alleviates enrollment uncertainty, but the outcomes are inefficient and unfair. A centralized matching via Gale and Shapley's deferred acceptance algorithm attains efficiency and fairness but may make some colleges worse off than under decentralized matching.