Finding Stable Matches
How to bring different players together in the best possible way is a key economic problem. Examples of situations where this problem arises include matching children with different schools, and kidneys or other organs with patients who require transplants. From the 1960s onward, Lloyd Shapley used what is known as Cooperative Game Theory to study different matching methods. Within the framework of this theory, it is especially important that a stable match is found. A stable match entails that there are no two agents who would prefer one another over their current counterparts. In collaboration with other researchers, Shapley has succeeded in identifying methods that achieve this stability.
Beginning in the 1980s, Alvin Roth used Shapley's theoretical results to explain how markets function in practice. Through empirical studies and lab experiments, Roth and his colleagues demonstrated that stability was critical to successful matching methods. Roth has also developed systems for matching doctors with hospitals, school pupils with schools, and organ donors with patients.