On Reasonable Stability and Deferred Acceptance

Abstract

For school choice problems, an assignment is called reasonably stable if it is not blocked by any stable assignment. We show that the deferred acceptance mechanism is the only mechanism that is strategyproof and reasonably stable. This result strengthens Alcalde and Barberà (1994)'s classical characterization of the deferred acceptance mechanism by relaxing its requirement on stability. In doing so, we also provide detailed structural results on reasonably stable assignments. Our key intermediate result extends Roth (1986)'s rural hospital theorem for stable assignments to reasonably stable assignments.

Keywords: School Choice, Deferred Acceptance Algorithm, Stability

JEL Classification: C78, D61