Many real matching markets are subject to distributional constraints. These constraints often take the form of restrictions on the numbers of agents on one side of the market matched to certain subsets on the other side. Real-life examples include restrictions on regions in medical matching,...

Real matching markets are subject to constraints. For example, the Japanese government introduced a new medical matching system in 2009 that imposes a "regional cap" in each of its 47 prefectures, which regulates the total number of medical residents who can be employed in each region. Based on...

In costly voting models, voters abstain when a stochastic cost of voting exceeds the benefit from voting. In probabilistic voting models, they always vote for a candidate who generates the highest utility, which is subject to random shocks. We prove an equivalence result: In two-candidate...

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...

Accommodating couples has been a longstanding issue in the design of centralized labor market clearinghouses for doctors and psychologists, because couples view pairs of jobs as complements. A stable matching may not exist when couples are present. This paper's main result is that a stable...

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...

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...

This paper considers a decentralized process in many-to-many matching problems. We show that if agents on one side of the market have substitutable preferences and those on the other side have responsive preferences, then, from an arbitrary matching, there exists a finite path of matchings such...