Efficient Kidney Exchange: Coincidence of Wants in a Structured Market∗

Patients needing kidney transplants may have willing donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other such pairs. The situation facing such pairs resembles models of the “double coincidence of wants,” and relatively few exchanges have been consummated by decentralized means. As the population of available patient-donor pairs grows, the frequency with which exchanges can be arranged will depend in part on how exchanges are organized. We study the potential frequency of exchanges as a function of the number of patient-donor pairs, and the size of the largest feasible exchange. Developing infrastructure to identify and perform 3-way as well as 2-way exchanges will have a substantial effect on the number of transplants, and will help the most vulnerable patients. Larger than 3-way exchanges have much smaller impact. Larger populations of patient-donor pairs increase the percentage of patients of all kinds who can Þnd exchanges. ∗We thank Audrey Bohnengel, Kevin Cheung, Francis Delmonico, Michael Goemans, Selçuk Karabatõ, Jonathan Kopke, Michael Rees, Susan Saidman, Jun Wako and Steve Woodle for discussions and comments, Rui Dong for her research assistance, Hüseyin Çankaya for his assistance on drawing the Þgures. Sönmez acknowledges the research support of KoçBank via the KoçBank scholar program and Turkish Academy of Sciences in the framework of the Young Scientist Award Program via grant TS/TÜBA-GEBú IP/2002-1-19, and Roth and Ünver acknowledge support from the NSF via grant no: 0338619. Any errors are our own. †E-mail: [email protected]; address: Department of Economics, Harvard University, Cambridge, MA 02138 and Harvard Business School, Boston, MA 02163. ‡E-mail: [email protected]; address: Koç University, Department of Economics, College of Administrative Sciences and Economics, Rumeli Feneri Yolu, Sarõyer, ú Istanbul, 34450, Turkey and Harvard Business School, Mellon Hall D2-4, Boston, MA 02163. §E-mail: [email protected]; address: Koç University, Department of Economics, College of Administrative Sciences and Economics, Rumeli Feneri Yolu, Sarõyer, ú Istanbul, 34450, Turkey.