Price of fairness in kidney exchange

Kidney exchange provides a life-saving alternative to long waiting lists for patients in need of a new kidney. Fielded exchanges typically match under utilitarian or near-utilitarian rules; this approach marginalizes certain classes of patients. In this paper, we focus on improving access to kidneys for highly-sensitized, or hard-tomatch, patients. Toward this end, we formally adapt a recently introduced measure of the tradeoff between fairness and efficiency— the price of fairness—to the standard kidney exchange model. We show that the price of fairness in the standard theoretical model is small. We then introduce two natural definitions of fairness and empirically explore the tradeoff between matching more hard-tomatch patients and the overall utility of a utilitarian matching, on real data from the UNOS nationwide kidney exchange and simulated data from each of the standard kidney exchange distributions.