Game Theory and the Kidney Exchange
We all know game theory is very applicable in the real world. We do these types of negotiations all the time but who would have thought that you could apply the theory of matching markets to kidney transplants? Nobel Prize winner Alvin Roth did just that. This economist applied his understanding of matching markets to make practical improvements in finding kidney donors. The system models patients as having preferences for specific kidneys through blood work and health data. Exchanges were allowed among any number of patient-donor pairs in this “marketplace”. The marketplace was a database of all the people that were willing to participate in the New England area and 14 transplant centers. There were also times in which list exchanges (the deceased donor list) were combined with live exchanges. This system of matching markets has been successful in saving peoples’ lives that would otherwise be deemed incompatible with the kidney that was received.
This kidney exchange model is a real life application of game theory. Although it is not the purest form of market clearing, it is very close and still applicable. This bipartite map has patients that need kidneys on one side and donors on the other. Donors can be either alive or deceased (in donor list form). Every patient has a valuation of each donor or, in this case, their preference due to compatibility. With just these valuations, we would not get a perfect matching. The way that Alvin Roth went about this was instead of setting a price for each donor, he made systematic exchanges that would in turn bring the market to clearance. This was done by first looking about just basic first preference exchanges. Then, when there was not a perfect matching, there was an allowance of making plans between live kidney exchanges and list exchanges. For example, a patient and donor may not match so the donor would donate their kidney to the list so that their patient pair would get higher priority on the list for a kidney that would actually match. There is also the possibility of the pair donating the kidney to another live pair that would in turn donate their kidney to them. This model has resulted in about 4,000 kidney transplants that might have never happened if not for the system Alvin Roth created.
http://www.npr.org/sections/health-shots/2015/06/11/412224854/how-an-economist-helped-patients-find-the-right-kidney-donor