It is known that in two-sided many-to-many matching problems, pairwise-stable matchings may not be immune to group deviations, unlike in many-to-one matching problems (Blair 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has...

We introduce a two-sided, many-to-one matching with contracts model in which agents with unit demand match to branches that may have multiple slots available to accept contracts. Each slot has its own linear priority order over contracts; a branch chooses contracts by filling its slots...

Within the last decade kidney exchange has become a mainstream paradigm to increase the number of kidney transplants. However, compatible pairs do not participate, and the full benefit from exchange can be realized only if they do. In this paper, we propose a new incentive scheme that relies on...

The Pennsylvania Adoption Exchange (PAE) helps case workers representing children in state custody by recommending prospective families for adoption. We describe PAE's operational challenges using case worker surveys and a regression analysis of data on child outcomes over multiple years. Using...

We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchange, in which each firm has to avoid being a net-exporter of workers. These exchanges use decentralized markets, making it difficult to achieve a balance between exports and imports. We show...

To encourage diversity, branches may vary contracts' priorities across slots. The agents who match to branches, however, have preferences only over match partners and contractual terms. Ad hoc approaches to resolving agents' indifferences across slots in the Chicago and Boston school choice...

We show that an ambiguity in setting the primitives of the matching with contracts model by Hatfield and Milgrom (2005) has serious implications for the model. Of the two ways to clear the ambiguity, the first (and what we consider more "clean") remedy renders several of the results of the paper...

We show that Hatfield and Kojima (2010) inherits a critical ambiguity from its predecessor Hatfield and Milgrom (2005), and clearing this ambiguity has strong implications for the paper. Of the two potential remedies, the first one results in the failure of all theorems except one in the absence...

Patients needing kidney transplants may have willing donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other such pairs. The situation facing such pairs resem- bles models of the double coincidence of...

Many school districts in the U.S. use a student assignment mechanism that we refer to as the Boston mechanism. Under this mechanism a student loses his priority at a school unless his parents rank it as their first choice. Therefore parents are given incentives to rank high on their list the...