Game Theory In Kidney Exchanges
http://www.coalitiontheory.net/content/kidney-exchange-application-matching-theory-and-mechanism-design
There are hundred of thousands of people who need Kidney’s donated to them, and the wait list could seem endless based on your blood type. It used to work that when someone died, their kidney would be transplanted to someone on the list, however since people only need one kidney to survive, living donors is a possibility.
The idea of kidney exchanges is that if patients p1, p2 and donors d1,d2 are matched (p1,d1) and (p2,d2) but they are incompatible in their blood types, a new matching (p1,d2) and (p2,d1) would occur – otherwise known as a kidney exchange.
One way in which game theory can be applied and how kidney exchanges happen are of the following:
1) Top Trading Cycle (As learned in Networks II) in which each patient will point to their top item (kidney in this situation) and each “round” if there is a complete circle of kidneys being pointed. (I.e: A -> B ; B- > A ; C- > A — A and B would swap because they complete a circle). This happens until there are no more circles. What happens in this situation is that people can game their preferences and their choices in order to acquire kidneys.
2) A second way would be to use a matching algorithm in which we match patients to their rank order preferences of kidneys. However in this situation the game can also be cheated in which patients change their preference – unless there we want a stable matching -> such that no donor and no patient would rather be matched up than their current matching (other wise they have to break their current matchings) and that every matching is happy.
It is interesting to see how we can apply techniques and theories learned in the Networks I and II class in order to apply game theory to a serious topic and that the kidney exchange market can actually have a strategy to it.