Explained by MR:
In honor of the Nobel prizes to Al Roth and Lloyd Shapley, here is a primer on matching theory. Matching is a fundamental property of many markets and social institutions. Jobs are matched to workers, husbands to wives, doctors to hospitals, kidneys to patients.
The field of matching may be said to start with the Gale-Shapley deferred choice algorithm. Here is how it works, applied to men and women and marriage (n.b. the algorithm can also work for gay marriage but it’s a little easier to explain and implement with men and women). Each man proposes to his first ranked choice. Each woman rejects any unacceptable proposals but defers accepting her highest-ranked remaining suitor. Each rejected man proposes to his second ranked choice. Each woman now rejects again any unacceptable proposals, which may include previous suitors who have now become unacceptable. The process repeats until no further proposals are made; each woman then accepts her most preferred suitor and the matches are made.
And here is a good quote:
Roth has applied heavy-duty theory to the very practical problems of matching doctors to residency programs, children to schools, economists to departments and kidneys to patients in a way that is stable, incentive-compatible, and maximizes the gains from exchange. In my view, Roth is the most influential economist working today. Influential among other economists? Yes. But what I really mean is influential in the world.
Not Unreasonable 