Competing for Priorities in School Choice

Abstract

We present a model in which students can influence their priority in a school choice mechanism through a first-stage costly effort game. We show that efficiency improvements to the mechanism can lead to net efficiency losses if they come at the price of increased allocative inequalities, which in turn increase competition in the effort stage. We apply these results to the deferred and immediate acceptance mechanisms (DA and IA) and show that, even when DA is more allocatively efficient than IA, IA may remain more efficient overall because it features less inequalities between students with high and low priorities.