In 2012, the Nobel Memorial Prize in Economic Sciences was awarded to Alvin E. Roth and Lloyd Shapley for their work on matching theory.
One category is matching with nontransferrable utility (NTU), where match payoffs are nontransferable and stability requires individual rationality and double coincidence of wants.
This strand of the literature emerged from the Gale and Shapley (1962) introduction of the stable marriage problem.
The latter dates back to work on Monge (1781) and Kantorovich (1942) work on optimal transportation theory, in particular following Koopmans and Beckmann (1957) who studies the problem with pricing.
Matching theory has been applied to study a wide set of applications, including: marriage, housing allocation, kidney exchange, the National Resident Matching Program, and school choice.