When Colleges Compete: Signals, Noise, and Equilibrium Outcomes

Abstract

We model college admissions with incomplete information and interdependent values. Colleges face a winner's curse in selecting applicants. We establish conditions under which a unique equilibrium in threshold strategies exists. We study three applications of this framework. First, we evaluate how correlation in colleges' signals affects matching and welfare: although each applicant favors independent draws, greater correlation allows more applicants to secure a higher-ranked choice. Weaker applicants gain unambiguously while stronger ones face tradeoffs. This finding speaks to the debate on standardized testing. Second, we show that lowering application costs intensifies competition, making applicants worse off. Third, we provide an informational rationale for why colleges favor early-decision applicants.