grounds, it is carried out. If the transplant from the willing donor is not feasible, the patient typically enters (or remains on) the queue for a cadaver kidney, while the donor returns home. Recently, however, in a small number of cases, additional possibilities have been utilized when a transplant from a live donor and the intended recipient is infeasible. One of these, called a paired exchange, involves two patient-donor couples, for each of whom a transplant from donor to intended recipient is infeasible, but such that the patient in each couple could feasibly receive a transplant from the donor in the other couple [Rapaport 1986; Ross et al. 1997]. This pair of couples can then exchange donated kidneys. Compared with receiving cadaver kidneys at an unknown future time, this improves the welfare of the patients. In addition, it relieves the demand on the supply of cadaver kidneys, and thus potentially improves the welfare of those patients on the cadaver queue. A small number of these two-couple operations have been done, and the transplantation community has issued a consensus statement declaring them to be ethically acceptable [Abecassis et al. 2000].2 Another possibility is an indirect exchange (or list exchange) involving an exchange between one incompatible patient-donor couple, and the cadaver queue [Ross and Woodle 2000]. In this kind of exchange, the patient in the couple receives high priority on the cadaver queue, in return for the donation of his donor’s kidney to someone on the queue.3 This improves the welfare of the patient in the couple, compared with having a long wait for a suitable cadaver kidney, and it benefits the recipient of the live 2. UNOS also published a legal opinion that such exchanges do not violate the NOTA (http://www.asts.org/ezefiles/UNOSSection_301_NOTA_pdf). 3. Priority on the cadaver queue is actually a bit complex, as queues are organized regionally, and consist of multiple queues, on which priority is determined by a scoring rule that gives points for how well matched the available kidney is to each patient, how long the patient has been waiting, etc. Giving high priority on the queue could be implemented by giving an appropriate number of points in the scoring rule. KIDNEY EXCHANGE 459 kidney, and others on the queue who benefit from the increase in kidney supply due to an additional living donor. However, Ross and Woodle note that this may have a negative impact on type O patients already on the cadaver queue, an issue studied by Zenios, Woodle, and Ross [2001], to which we shall return. In contrast to the system for cadaveric organs, and despite the growing interest in at least small-scale exchanges involving living donors, there is no national system, or even an organized registry at any level, for managing exchanges of kidneys from live donors. However, individual hospitals are beginning to think about larger scale living donor exchanges. As this paper was being written, the first three-couple kidney transplant exchange in the United States was reported at Johns Hopkins Comprehensive Transplant Center in Baltimore, among three couples for whom no two-couple transfer was feasible [Olson, August 2, 2003]. In the present paper we will consider how such a system of exchanges might be organized, from the point of view of achieving efficiency, and providing consistent incentives to patients, donors, and doctors, and what its welfare implications might be. We will see that the benefits of wider exchange accrue not only to the parties to the exchange. The resulting increase in live organ donation also benefits patients waiting for cadaver kidneys, including type O patients. The design we propose is partly inspired by the mechanism design literature on “house allocation,” and is intended to build on and complement the existing practices in kidney transplantation. In this respect and others it is in the modern tradition of engineering economics (see Roth [2002]) as applied to other problems of allocation, such as labor market clearinghouses (see Roth and Peranson [1999]), or auctions (see Milgrom [2004]), in which practical implementation often involves incremental change in existing practices. II. BACKGROUND II.A. Kidney Transplantation End Stage Renal Disease (ESRD) is a fatal disease unless treated with dialysis or kidney transplantation. Transplantation is the preferred treatment. Two genetic characteristics play key roles in the feasibility and success of a kidney transplant. The first is the ABO blood-type: There are four blood types: A, B, AB, and O. Absent other complications, type O kidneys can be trans460 QUARTERLY JOURNAL OF ECONOMICS planted into any patient; type A or type B kidneys can be transplanted into same type or type AB patients; and type AB kidneys can only be transplanted into type AB patients. (So type O patients can only receive type O kidneys.) The second genetic characteristic is tissue type, also known as HLA type: HLA type is a combination of six proteins. As the HLA mismatch between the donor and the recipient increases, the likelihood of graft (i.e., transplanted organ) survival decreases [Opelz 1997]. HLA plays another key role in transplantation through the pretransplant “crossmatch” test. Prior to transplantation, the potential recipient is tested for the presence of preformed antibodies against HLA in the donor kidney. The presence of antibodies, called a positive