Efficient and incentive-compatible liver exchange

Abstract

Liver exchange has been practiced in small numbers, mainly to overcome blood-type incompatibility between patients and their living donors. A donor can donate either his smaller left lobe or the larger right lobe, although the former option is safer. Despite its elevated risk, right-lobe transplantation is often utilized due to size-compatibility requirement with the patient. We model liver exchange as a market-design problem, focusing on logistically simpler two-way exchanges. First, with two patient-donor sizes, we introduce an algorithm when only the safer left-lobe transplantation is feasible. We then introduce an individually rational, Pareto-efficient, and incentive-compatible mechanism that truthfully elicits the right- lobe-donation willingness of donors, and finally extend these results to a general model with any number of patient/donor sizes. The generalization requires new technical tools regarding bilateral exchanges under partial-order-induced preferences. Through simulations we show that not only liver exchange can increase the number of transplants by more than 30%, it can also increase the share of the safer left-lobe transplants.