The winners of the Nobel prize in economics this year are Alvin Roth and Lloyd Shapley. As always, Tyler Cowen and Alex Tabarrok has written brief summaries with good links in them (here and here). Also, if you want to know what matching theory is about, I highly recommend Tabarrok’s primer.
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 is also good for gay marriage but it’s a little easier to explain with men and women). Each man proposes to his first ranked choice. Each woman rejects any unacceptable proposals but defers accepting her remaining suitors. 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 suitors and the matches are made.
Although in this first example marriage is used to illustrate the algorithm, it has been usefully deployed to match students to schools, patients to hospitals, and liver donors to recipients. More at the link.
Congratulations to the winners!