The NBER working paper series this week is giving me some plane reading for the next few days:
It has been previously shown that for sufficiently large pools of patient-donor pairs, (almost) effcient 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.
I have a vague recollection of reading about kidney chains a few months ago, probably in the NYT, and getting a warm, fuzzy feeling inside about altruistic donors and how long chains helped to reach those who didn’t have an altruistic donor. I love it when economics comes together and puts everything in a neat little package for me. I’m excited to read this later.
Source: The Need for (long) Chains in Kidney Exchange (gated)
by Itai Ashlagi, David Gamarnik, Michael A. Rees, Alvin E. Roth NBER Working Paper 18202 (HC)