We study how barter exchanges should be conducted through a centralized mechanism in a dynamically evolving agent pool with time- and compatibility-based preferences. We derive the dynamically efficient two-way and multi-way exchange mechanisms that maximize total discounted exchange surplus. Recently several live-donor kidney exchange programmes were established to swap incompatible donors of end-stage kidney disease patients. Since kidney exchange can be modelled as a special instance of our more general model, dynamically efficient kidney exchange mechanisms are derived as corollaries. We make policy recommendations using simulations.

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.

Owing to the worldwide shortage of deceased‐donor organs for transplantation, living donations have become a significant source of transplant organs. However, not all willing donors can donate to their intended recipients because of medical incompatibilities. These incompatibilities can be overcome by an exchange of donors between patients. For kidneys, such exchanges have become widespread in the last decade with the introduction of optimization and market design techniques to kidney exchange. A small but growing number of liver exchanges have also been conducted. Over the last two decades, a number of transplantation procedures emerged where organs from two living donors are transplanted to a single patient. Prominent examples include dual‐graft liver transplantation, lobar lung transplantation, and simultaneous liver‐kidney transplantation. Exchange, however, has been neither practiced nor introduced in this context. We introduce dual‐donor organ exchange as a novel transplantation modality, and through simulations show that living‐donor transplants can be significantly increased through such exchanges. We also provide a simple theoretical model for dual‐donor organ exchange and introduce optimal exchange mechanisms under various logistical constraints.

We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchanges, in which export-import balances are required for longevity of programs. These exchanges use decentralized markets, making it difficult to achieve this goal. We introduce the two-sided top trading cycles, the unique mechanism that is balanced-efficient, worker-strategy-proof, acceptable, individually rational, and respecting priority bylaws regarding worker eligibility. Moreover, it encourages exchange, because full participation induces a dominant-strategy equilibrium for firms. We extend it to dynamic settings permitting tolerable yearly imbalances and demonstrate that its regular and tolerable versions perform considerably better than models of current practice.

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.

Patients needing kidney transplants may have donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other pairs only when there is a "double coincidence of wants." Developing infrastructure to perform three-way as well as two-way exchanges will have a substantial effect on the number of transplants that can be arranged. Larger than three-way exchanges have less impact on efficiency. In a general model of type-compatible exchanges, the size of the largest exchanges required to achieve efficiency equals the number of types.

In 2003 there were 8,665 transplants of deceased donor kidneys for the approximately 60,000 patients waiting for such transplants in the United States. While waiting, 3,436 patients died. There were also 6,464 kidney transplants from living donors (Scientific Registry of Transplant Recipients web site). Live donation is an option for kidneys, since healthy people have two and can remain healthy with one. While it is illegal to buy or sell organs, there have started to be kidney exchanges involving two donor–patient pairs such that each (living) donor cannot give a kidney to the intended recipient because of blood type or immunological incompatibility, but each patient can receive a kidney from the other donor. So far these have been rare: as of December 2004, only five exchanges had been performed in the 14 transplant centers in New England. One reason there have been so few kidney exchanges is that there have not been databases of incompatible patient–donor pairs. Incompatible donors were simply sent home. (Databases are now being assembled not only in New England, but also in Ohio and Baltimore.) Lainie Friedman Ross et al. (1997) discussed the possibility of exchange between incompatible patient–donor pairs. Not only have a few such two-way exchanges been performed, but two three-way exchanges (in which the donor kidney from one pair is transplanted into the patient in a second pair, whose donor kidney goes to a third pair, whose donor kidney goes to the first pair) have been performed at Johns Hopkins. There have also been a number of “list exchanges” in which an incompatible patient– donor pair makes a donation to someone on the waiting list for a cadaver kidney, in return for the patient in the pair receiving high priority for a cadaver kidney when one becomes available.