Alvin Roth’s Kidney Matching Algorithm: A Practical Matching Market Example
This article describes how Alvin Roth, a 2012 Economic Science Nobel Prize winner, applied his understanding of matching markets to improve New York City’s high school lottery, the assignment of medical residencies, and finding kidney donors. The hardships that come with kidney transplants are that there are not many donors, so it is not easy to find good, compatible matches between donors and recipients. Roth understood the kidney marketplace and saw an opportunity to improve it and ultimately help save people’s lives.
The kidney market can be seen as an example of a kind of matching market, where there are a kidney donors (sellers) and recipients (buyers). Based on this, Roth devised a formula that would match multiple donor-patient pairs where each donor could not give a kidney to their intended recipient because of immunological incompatibility, so recipients could benefit from another pair’s donor in a long chain of exchanges between pairs. In these situations, there is perfect matching among the donors and recipients as the algorithm Roth created found people seeking specific kidney types paired along with people willing to donate their kidneys that would not work for their intended recipient. Roth believes this methodology in matching kidney recipients and donors has saved thousands of lives, makes for a more efficient system, and increases the overall social welfare of kidney transplants.
However, the world is not perfect and there are plenty of people who are still left without compatible kidneys to be transplanted, creating what is known as a constricted set in market matching where not every buyer has a match to another seller (in this case donors and recipients). Roth tried to overcome this obstacle as well by suggesting that if an incompatible donor-recipient pair was willing to give their kidney to someone on the waiting list for a matching cadaver’s kidney, then the recipient of that pair would be put at the top of the list for the next matching cadaver kidney. It is obviously a system in which there will never be true perfect matching, but Roth’s algorithms have ultimately saved more lives than not.
In class, we discussed matching markets in the context of sellers looking to put items on the market and sell them based on how they are valued by a set of buyers until everyone has a price they would pay for their highest valued item. It is interesting to see the concept of matching markets used in practical situations like kidney transplant pairings. It’s amazing that such an economic concept can have such a profound effect in an area like health where real lives can be affected.