Kidney exchange programs utilize both deceased-donor and live-donor kidneys. One of these programs, a two-way kidney paired donation (KPD), involves two patients exchanging their live donors[modifier letter apostrophe] kidneys. Another possibility is a list exchange (LE): a living incompatible donor provides a kidney to a candidate on the deceased-donor waitlist and in return the intended recipient of this donor receives a priority on the waitlist. By taking into consideration the fact that transplants from live donors have a higher chance of success than those from cadavers, we characterize the set of efficient and egalitarian exchanges involving the KPD[modifier letter apostrophe]s and LE[modifier letter apostrophe]s.
