http://kuznets.fas.harvard.edu/~aroth/papers/LargeScaleKidneyExchange.pdf

Individual rationality and participation in large scale, multi-hospital kidney exchange
Itai Ashlagi and Alvin E. Roth

January 14, 2011

Abstract
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 en-
rolling only their hard-to-match patient-donor pairs, while conducting easily arranged
exchanges internally. This behavior has already started to be observed.
We show that the cost of making it individually rational for hospitals to participate
fully is low in almost every large exchange pool (although the worst-case cost is very
high), while the cost of failing to guarantee individually rational allocations could be
large, in terms of lost transplants. We also identify an incentive compatible mechanism.