Virginia Postrel has an excellent piece in the online Atlantic on the shortage of transplant organs, it includes a very good discussion of both the promise and limitations of kidney swaps and donor chains. Imagine that Mrs. Smith and Mr. Jones each need a kidney transplant. Mr. Smith is willing but due to an incompatible blood type unable to donate a kidney to his wife. Similarly, Mrs Jones is willing but unable to donate a kidney to her husband. In a kidney swap, Mr. Smith donates to Mr. Jones and Mrs. Jones donates to Mrs. Smith. Everyone is happy.
Donor chains extend this idea. We start with an altruistic donor willing to give to anyone – by careful arrangement it's then possible to produce many transplants. Recently, a single donor led to a chain of ten transplants!
Despite the promise of these techniques they are being underutilized. Amazingly, the National Kidney Registry, which coordinates swaps and chains, has donors who are waiting to give. A clear reminder that $500 bills aren't always picked up as quickly as we would like.
Even the maximal use of swaps and chains won't solve the crisis, however. For that we are going to need better incentives to encourage more donors.