It has been previously shown that for sufficiently large pools of patient-donor pairs, (almost) efficient kidney exchange can be achieved by using at most 3-way cycles, i.e. by using cycles among no more than 3 patient-donor pairs. However, as kidney exchange has grown in practice, cycles among...

As multi-hospital kidney exchange clearinghouses have grown, the set of players has grown from patients and surgeons to include hospitals. Hospitals have the option of enrolling only their hard-to-match patient-donor pairs, while conducting easily arranged exchanges internally. This behavior has...