Patients needing kidney transplants may have donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other pairs only when there is a "double coincidence of wants." Developing infrastructure to perform three-way as well as two-way exchanges will have a substantial effect on the number of transplants that can be arranged. Larger than three-way exchanges have less impact on efficiency. In a general model of type-compatible exchanges, the size of the largest exchanges required to achieve efficiency equals the number of types. (JEL C78, I12)

In connection with an earlier paper on the exchange of live donor kidneys (Roth, Sönmez, and Ünver 2004) the authors entered into discussions with New England transplant surgeons and their colleagues in the transplant community, aimed at implementing a Kidney Exchange program. In the course of those discussions it became clear that a likely Þrst step will be to implement pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than exchanges involving more than two pairs. Furthermore, the experience of these surgeons suggests to them that patient and surgeon preferences over kidneys should be 0-1, i.e. that patients and surgeons should be indifferent among kidneys from healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival probabilities, regardless of the closeness of tissue types between patient and donor (unless there is a rare perfect match). In the present paper we show that, although the pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patientdonor pairs and surgeons have 0-1 preferences. This class of mechanisms includes deterministic mechanisms that would accomodate the kinds of priority setting that organ banks currently use for the allocation of cadaver organs, as well as stochastic mechanisms that allow considerations of distributive justice to be addressed. * We would like to thank

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A computerized matching protocol can be used to identify donor/recipient pairs from a registry of incompatible pairs who can potentially enter into donor exchanges that otherwise would not readily occur.

In a list exchange (LE), the intended recipient in an incompatible pair receives priority on the deceased donor waitlist (DD-waitlist) after the paired incompatible donor donates a kidney to a DD-waitlist candidate. A nondirected donor's (ND-D) kidney is usually transplanted directly to a DD-waitlist candidate. These two established practices would help even more transplant candidates if they were integrated with kidney paired donation (KPD). We consider a scenario in which the donor of an LE intended recipient (LE-IR) donates to a compatible KPD intended recipient (KPD-IR), and the KPD donor (KPD-D) donates to the waitlist (an LE-chain). We consider a similar scenario in which an ND-D donates to a KPD-IR and the KPD-D donates to the DD-waitlist (an NDchain).Using data derived from the New England Program for Kidney Exchange (NEPKE) and from OPTN/SRTR recipient-donor distributions, simulations are presented to evaluate the potential impact of chain exchanges coordinated with KPD. LE donors (LE-D) and ND-D who are ABO-O result in the highest number of additional transplants, while results for ABO-A and B donors are similar to each other. We recommend that both LE and ND donations be utilized through chain exchanges.