Kidney transplant is sometimes the best treatment for people who suffer from chronic kidney disease. However, due to medical incompatibility issues, a direct kidney transplant is not always possible even for those patients that are fortunate enough to have a willing donor. This is where Kidney Exchange comes in: It enables two or more donor-patient pairs to swap donors, so that each patient receives a compatible kidney. In recent years, hospitals have enrolled patients into regional or even national kidney exchange programs. However, hospitals may choose not to participate if they can match more of their own patients on their own -- economists would say that the exchange is not individually rational for hospitals. This behavior significantly reduces the social welfare -- the total number of patients that receive a kidney transplant.
In this work, we revisit the problem of designing optimal, individually rational kidney exchange mechanisms. We offer a new perspective on this problem by showing that under mild probabilistic assumptions, any optimal kidney exchange is likely to be individually rational up to lower-order terms. We also show that a simple and practical mechanism is (fully) individually rational, and likely to be optimal up to lower-order terms.
This talk is based on joint work with Avrim Blum, Ioannis Caragiannis, Ariel Procaccia, Eviatar Procaccia, and Rohit Vaish (SODA'17).