The Need for (Long) Chains in Kidney Exchange

33 Pages Posted: 7 Jul 2012

See all articles by Itai Ashlagi

Itai Ashlagi

Stanford University - Management Science & Engineering

David Gamarnik

Massachusetts Institute of Technology (MIT)

Michael Rees

affiliation not provided to SSRN

Alvin E. Roth

Dept. of Economics, Stanford University; National Bureau of Economic Research (NBER)

Date Written: July 2012

Abstract

It has been previously shown that for sufficiently large pools of patient-donor pairs, (almost) efficient kidney exchange can be achieved by using at most 3-way cycles, i.e. by using cycles among no more than 3 patient-donor pairs. However, as kidney exchange has grown in practice, cycles among n>3 pairs have proved useful, and long chains initiated by non-directed, altruistic donors have proven to be very effective. We explore why this is the case, both empirically and theoretically.We provide an analytical model of exchange when there are many highly sensitized patients, and show that large cycles of exchange or long chains can significantly increase efficiency when the opportunities for exchange are sparse. As very large cycles of exchange cannot be used in practice, long non-simultaneous chains initiated by non-directed donors significantly increase efficiency in patient pools of the size and composition that presently exist. Most importantly, long chains benefit highly sensitized patients without harming low-sensitized patients.

Suggested Citation

Ashlagi, Itai and Gamarnik, David and Rees, Michael and Roth, Alvin E., The Need for (Long) Chains in Kidney Exchange (July 2012). NBER Working Paper No. w18202. Available at SSRN: https://ssrn.com/abstract=2101930

Itai Ashlagi (Contact Author)

Stanford University - Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

David Gamarnik

Massachusetts Institute of Technology (MIT) ( email )

Cambridge, MA 02139
United States

Michael Rees

affiliation not provided to SSRN ( email )

Alvin E. Roth

Dept. of Economics, Stanford University ( email )

Landau Economics Building
579 Serra Mall
STANFORD, CA 94305-6072
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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