Policymakers have adopted centralized matching for public school assignments in various set- tings. However, the mechanisms requiring such policy interventions have been little studied. We theoretically show that similarity in level of school quality and coverage of applicants can lead to voluntary adoption of centralized matching, which is welfare-improving and particularly beneficial to students with limited resources to cover application costs. Our predictions are con- sistent with empirical findings based on college admissions data from Chile. Colleges of similar quality and size agreed to run centralized matching, which reduced the number of vacancies and decreased the disadvantages for students from poor families.