compatibly, within existing constraints. The problem resembles some of the “housing” problems studied in the mechanism design literature for indivisible goods, with the novel feature that while live donor kidneys can be assigned simultaneously, cadaver kidneys cannot. In addition to studying the theoretical properties of the proposed kidney exchange, we present simulation results suggesting that the welfare gains from larger scale exchange would be substantial, both in increased number of feasible live donation transplants, and in improved match quality of transplanted kidneys. I. INTRODUCTION Transplantation is the preferred treatment for the most serious forms of kidney disease. There are over 55,000 patients on the waiting list for cadaver kidneys in the United States, of whom almost 15,000 have been waiting more than three years. By way of comparison, in 2002 there were over 8,000 transplants of cadaver kidneys performed in the United States. In the same year, * We thank Muriel Niederle, Erhan So¨nmez, Stefanos Zenios, and the participants of the SITE 2003 Workshop on Matching Markets for their insightful comments and Hu¨seyin C¸ ankaya for his help with the figures. After a first draft of this paper was completed, we also benefited from many helpful conversations with Dr. Frank Delmonico of the New England Organ Bank. So¨nmez gratefully acknowledges the research support of Koc¸Bank via the Koc¸Bank scholar program and Turkish Academy of Sciences in the framework of the Young Scientist Award Program via grant TS/TU¨ BA-GEBI˙P/2002-1-19. We also received support from a National Science Foundation grant through the National Bureau of Economic Research. All errors are our own responsibility. Email: aroth@hbs.edu; address: Harvard University, Department of Economics, Cambridge, MA 02138 and Harvard Business School, Boston, MA 02163. Email: tsonmez@ku.edu.tr; address: Koc¸ University, Department of Economics, College of Administrative Sciences and Economics, Rumeli Feneri Yolu, Sarıyer, I˙stanbul, 34450, Turkey. Email: uunver@ku.edu.tr; address: Koc¸ University, Department of Economics, College of Administrative Sciences and Economics, Rumeli Feneri Yolu, Sarıyer, I˙stanbul, 34450, Turkey. © 2004 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics, May 2004 457 about 3,400 patients died while on the waiting list, and another 900 became too ill to be eligible for transplantation. In addition to transplants of cadaver kidneys, in 2002 there were also somewhat over 6,000 transplants of kidneys from living donors, a number that has been increasing steadily from year to year. See Table I. There is thus a considerable shortage of kidneys, compared with the demand. However, the substantial consensus in the medical community remains firmly opposed to allowing organs— even cadaveric organs—to be bought and sold, and this is a felony under the National Organ Transplant Act (NOTA) of 1984, and the Uniform Anatomical Gift Act of 1987.1 The present paper considers ways to alleviate this shortage, and improve patient welfare, within the constraints of the current social and legal environment. The National Organ Transplant Act of 1984 established the Organ Procurement and Transplantation Network (OPTN). Run 1. There is, however, a steady stream of literature both by doctors and by economists, considering how the shortage of organs might be alleviated by allowing their purchase and sale, and what effects this might have. See, e.g., Nelson et al. [1993] for an argument in favor of the status quo, and, e.g., Becker and Elias [2002] for an argument in favor of a market. Recent Congressional testimony endorsing the status quo but suggesting that empirical investigation of financial incentives might be in order can be found in Sade [2003]. TABLE I U. S. The data for years 1992–2001 are constructed from the annual report of UNOS/OPTN, the data for 2002 are constructed from the national database of UNOS/OPTN. National database numbers are slightly higher than the annual report numbers due to continuous updating regarding previous years. Number of registrations may have multiple counts of patients since one patient may have registered in multiple centers for the wait-list. 458 QUARTERLY JOURNAL OF ECONOMICS by the United Network for Organ Sharing (UNOS), it has developed a centralized priority mechanism for the allocation of cadaveric kidneys. Transplants from live donors generally have a higher chance of success than those from cadavers. The way such transplants are typically arranged is that a patient identifies a healthy willing donor (a spouse, for example) and, if the transplant is feasible on medical