We define the median stable matching for two-sided matching markets with side payments and prove constructively that it exists.

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 resembles models of the "double coincidence of...

In connection with an earlier paper on the exchange of live donor kidneys (Roth, Sonmez, and Unver 2004) the authors entered into discussions with New England transplant surgeons and their colleagues in the transplant community, aimed at implementing a Kidney Exchange program. In the course of...

Most transplanted kidneys are from cadavers, but there are also substantial numbers of transplants from live donors. Recently, there have started to be kidney exchanges involving two donor-patient pairs such that each donor cannot give a kidney to the intended recipient because of immunological...

In July 2005 the Boston School Committee voted to replace the existing Boston school choice mechanism with a deferred acceptance mechanism that simplifies the strategic choices facing parents. This paper presents the empirical case against the previous Boston mechanism, a priority matching...

School choice plans in many cities grant students higher priority for some (but not all) seats at their neighborhood schools. This paper demonstrates how the precedence order, i.e. the order in which different types of seats are filled by applicants, has quantitative effects on distributional...

In Fall 2009, officials from Chicago Public Schools changed their assignment mechanism for coveted spots at selective college preparatory high schools midstream. After asking about 14,000 applicants to submit their preferences for schools under one mechanism, the district asked them re-submit...