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, and introduce an individually rational, Pareto‐efficient, and incentive‐compatible mechanism. Construction of this mechanism requires novel technical tools regarding bilateral exchanges under partial‐order‐induced preferences. Through simulations we show that not only can liver exchange increase the number of transplants by more than 30%, it can also increase the share of the safer left‐lobe transplants.

Over the last 15 years, kidney exchange has become a mainstream paradigm to increase transplants. However, compatible pairs do not participate, and full benefits from exchange can be realized only if they do. We propose incentivizing compatible pairs to participate in exchange by insuring their patients against future renal failure via increased priority in deceased-donor queue. We analyze equity and welfare benefits of this scheme through a new dynamic continuum model. We calibrate the model with US data and quantify substantial gains from adopting incentivized exchange, both in terms of access to living-donor transplants and reduced competition for deceased-donor transplants.