Theory Behind Matching Markets Sparks Kidney Donor Revolution
In the United States, over 100,000 people are patiently waiting for a kidney transplant. If possible, a friend or family members would come forth, willing to donate a kidney to their loved one. Unfortunately, in most of these cases, the donor-patient pairs are incompatible and the patient is added to a waiting list for a deceased donor. In fact, of the 17,000 transplants taking place each year, only 6,000 will be from living donors.
In 2012, Harvard University economist Alvin Roth and UCLA professor emeritus Lloyd S. Shapley were awarded the Nobel Prize in Economics for their work in matching markets. In the past, donors and patients worked through a single transplant center. However, the system Roth built accumulates kidney donors and patients across transplant centers and, using an algorithm resembling the market-clearing algorithm studied in our Networks, computes matches, allowing compatible donors to swap and take the place of originally incompatible donor-patient pairs. The algorithm matches donors with unknown patients but promises both pairs of patients will receive a transplant. Roth’s work revolutionized the kidney donor process, resulting in 2,000 matches through the system as of 2012.
In order to apply the classroom concept of matching markets, we must identify the buyers, sellers, and values. The buyers will be the patients and sellers are the donors. Organizations such as the Scientific Operations Committee have determined a scoring rubric in order to place values on each donor-patient pair which includes DR-locus mismatches, pediatric recipient (age), travel distance, etc. However, as there are not as many donors as there are patients, “ghost” donors may be added to fill in to apply the algorithm. Once donor-pairs are identified by slowly incrementing the price to minimize patients contending for each donor, matches are made and market-clearing prices or rubric scores for each donor is identified. As one might expect, Roth’s system contains many more complicated features to identify matches; Nonetheless, the underlying theorem we learned in class is partially responsible for the revolution of kidney transplants.
http://www.reuters.com/article/nobel-prize-roth-kidney-idUSL1E8LFFW320121015
http://paireddonation.org/about-us/algorithm/