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I study how colleges compete for better students in an admission mechanism with two key frictions: each student can send a limited number of applications, and applications have uncertain outcomes. Departing from existing literature, I allow students’ preferences to depend on costly investments by colleges before applications are made. I find that colleges might mutually benefit from limiting students’ applications, contrary to what earlier analyses predict. The low-ranked college benefits by capturing some cautious applicants whom the high-ranked college could admit. The high-ranked college benefits despite losing such students: this concession mitigates the competitive pressure imposed by its contender and allows it to attract its share of applicants with a preferable level of investment. This finding helps us better understand why these frictions prevail in various college admission systems.
