Conflicting Objectives in Kidney Exchange

There is no conflict between maximizing the number of transplants and giving priority to, e.g., highly HLA-sensitized recipients in kidney exchange programs that only permit pairwise exchanges. In some programs that feature cyclic exchanges or chains, however, giving priority to some recipients may reduce the number of transplants that can be carried out. This paper identifies the conditions under which there is a trade-off between prioritization and transplant maximization objectives. The results show that kidney exchange programs can permit some cyclic exchanges and chains without introducing such tradeoffs. Whether or not a kidney exchange program has conflicting objectives and regardless of how recipients are prioritized, it can ensure a Pareto efficient outcome by selecting from a new class of matchings. These generalize several classes of matchings used in practice and studied in the literature.