We develop the first Bayesian model of decentralized college admissions, with heterogeneous students, costly portfolio applications, and noisy college evaluations. Students face a nontrivial portfolio choice, and colleges choose admissions standards that act like market-clearing prices.
We derive the two college model equilibrium, deriving a “law of demand”. Surprisingly, the worse college might impose higher standards, and weaker students sometimes apply more aggressively. The lesser college impacts its rival through student portfolio reallocation. Also, the weaker college counters affirmative action at its rival with a discriminatory admissions policy, and may poach students from its rival using early admissions.
