TY  - JOUR
AU  - Ashlagi,Itai
AU  - Gamarnik,David
AU  - Rees,Michael A.
AU  - Roth,Alvin E.
TI  - The Need for (long) Chains in Kidney Exchange
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 18202
PY  - 2012
Y2  - July 2012
UR  - http://www.nber.org/papers/w18202
L1  - http://www.nber.org/papers/w18202.pdf
N1  - Author contact info:
Itai Ashlagi
Massachusetts Institute of Technology
Sloan School of Management, E62-577
Cambridge, MA 02142
E-Mail: iashlagi@mit.edu

David Gamarnik
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139
E-Mail: gamarnik@mit.edu

Michael A. Rees
University of Toledo 
Department of Urology
3000 Arlington Avenue
Mail Stop 1091 
Toledo, OH 43614
E-Mail: michael.rees2@utoledo.edu

Alvin E. Roth
Department of Economics
Stanford University
579 Serra Mall
Stanford, CA 94305
Tel: 650/725-9147
E-Mail: alroth@stanford.edu
AB  - 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.
ER  -