Kidney exchange, where candidates with organ failure trade incompatible but willing donors, is a life-saving alternative to the deceased donor waitlist, which has inadequate supply to meet demand. While fielded kidney exchanges see huge benefit from altruistic kidney donors (who give an organ without a paired needy candidate), a significantly higher medical risk to the donor deters similar altruism with livers. In this paper, we begin by exploring the idea of large-scale liver exchange, and show on demographically accurate data that vetted kidney exchange algorithms can be adapted to clear such an exchange at the nationwide level. We then propose cross-organ donation where kidneys and livers can be bartered for each other. We show theoretically that this multi-organ exchange provides linearly more transplants than running separate kidney and liver exchanges. This linear gain is a product of altruistic kidney donors creating chains that thread through the liver pool; it exists even when only a small but constant portion of the donors on the kidney side of the pool are willing to donate a liver lobe. We support this result experimentally on demographically accurate multi-organ exchanges. We conclude with thoughts regarding the fielding of a nationwide liver or joint liver-kidney exchange from a legal and computational point of view.

Kidney exchange, where candidates with organ failure trade incompatible but willing donors, is a life-saving alternative to the deceased donor waitlist, which has inadequate supply to meet demand. While fielded kidney exchanges see huge benefit from altruistic kidney donors (who give an organ without a paired needy candidate), a significantly higher medical risk to the donor deters similar altruism with livers. In this paper, we begin by proposing the idea of liver exchange, and show on demographically accurate data that vetted kidney exchange algorithms can be adapted to clear such an exchange at the nationwide level. We then explore cross-organ donation where kidneys and livers can be bartered for each other. We show theoretically that this multi-organ exchange provides linearly more transplants than running separate kidney and liver exchanges; this linear gain is a product of altruistic kidney donors creating chains that thread through the liver pool. We support this result experimentally on demographically accurate multi-organ exchanges. We conclude with thoughts regarding the fielding of a nationwide liver or joint liver-kidney exchange from a legal and computational point of view.