Immediate Acceptance Mechanism with Imperfectly Observed Student Ability

A central objective of school choice mechanisms is to match higher-ability students with higher-quality schools, thereby enhancing social efficiency. In practice, however, information regarding student ability is typically limited to imperfect signals such as standardized exam scores. Using the welfare-maximizing allocation under imperfectly observed ability as a benchmark, this paper investigates the welfare implications of the widely adopted Immediate Acceptance (IA) mechanism in settings where student ability is imperfectly observed. We demonstrate that the IA mechanism implements a monotonic cutoff rule, which is a necessary condition for attaining an optimal allocation. In equilibrium, if the lowest-ability students are indifferent between the aggressive and conservative strategies, the IA mechanism generates higher welfare than the Deferred Acceptance (DA) mechanism. Moreover, when this indifference condition holds and the admission process ends in a single round, the IA mechanism achieves the social optimum. Finally, we show that the welfare-maximizing equilibrium of the IA mechanism is generically strictly stable, a refined equilibrium concept that is robust to small strategic deviations.