Centralized school assignment algorithms must distinguish between applicants with the same preferences and priorities. This is done with randomly assigned lottery numbers, nonlottery tie-breakers like test scores, or both. The New York City public high school match illustrates the latter, using...

This note points out that the proof of Theorem 1, the main theorem, in Ergin (2002) needs two corrections. We provide two counterexamples to Ergin's (2002) proof and show that the theorem holds as it is by providing an alternative proof.

We study the effect of different school choice mechanisms on schools' incentives for quality improvement. To do so, we introduce the following criterion: A mechanism respects improvements of school quality if each school becomes weakly better whenever that school improves and thereby becomes...

We consider the many-to-many two-sided matching problem under a stringent domain restriction on preferences called the max-min criterion. We show that, even under this restriction, there is no stable mechanism that is weakly Pareto efficient, strategy-proof, or monotonic (i.e. respects...