economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...

, stable matching theory or simply matching theory, is the study of matching markets. Matching markets are distinguished from Walrasian markets in the focus of who matches with whom. Matching theory typically examines matching in the absence of search frictions, differentiating it from

search and matching theory In economics, search and matching theory, is a mathematical framework attempting to describe the formation of mutually beneficial relationships over time. It is closely related to stable matching theory. Search and matching theory has been es ...

. In 2012, the

Nobel Memorial Prize in Economic Sciences The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel ( sv, Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award administered ...

was awarded to

Alvin E. Roth Alvin Eliot Roth (born December 18, 1951) is an American academic. He is the Craig and Susan McCaw professor of economics at Stanford University and the George Gund (philanthropist), Gund professor of economics and business administration emeritu ...

and

Lloyd Shapley Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of ...

for their work on matching theory.

Overview

Matching has two main categories. One category is matching with nontransferrable utility (NTU), where match payoffs are nontransferable and stability requires individual rationality and double

coincidence of wants The coincidence of wants (often known as double coincidence of wants) is an economic phenomenon where two parties each hold an item that the other wants, so they exchange these items directly without any monetary medium. Within economics, this h ...

. This strand of the literature emerged from the

Gale A gale is a strong wind; the word is typically used as a descriptor in nautical contexts. The U.S. National Weather Service defines a gale as sustained surface winds moving at a speed of between 34 and 47 knots (, or ).Shapley Shapley is a surname that might refer to one of the following: * Lieutenant General Alan Shapley (1903–1973), of the U.S. Marine Corps, was a survivor the sinking of the USS Arizona in the attack on Pearl Harbor * Harlow Shapley (1885–1972), Am ...

(1962) introduction of the

stable marriage problem In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each elem ...

. The second category is matching with transferable utility (TU). The latter dates back to work on

Monge Gaspard Monge, Comte de Péluse (9 May 1746 – 28 July 1818) was a French mathematician, commonly presented as the inventor of descriptive geometry, (the mathematical basis of) technical drawing, and the father of differential geometry. Duri ...

(1781) and

Kantorovich Leonid Vitalyevich Kantorovich ( rus, Леони́д Вита́льевич Канторо́вич, , p=lʲɪɐˈnʲit vʲɪˈtalʲjɪvʲɪtɕ kəntɐˈrovʲɪtɕ, a=Ru-Leonid_Vitaliyevich_Kantorovich.ogg; 19 January 19127 April 1986) was a Soviet ...

(1942) work on optimal transportation theory, in particular following

Koopmans Koopmans is a Dutch occupational surname meaning " merchant's".Beckmann Beckmann is a German surname. Notable people with the surname include: *Astrid Beckmann (born 1957), German physicist *Ernst Otto Beckmann (1853–1923), German chemist and discoverer of the Beckmann rearrangement *Johann Beckmann (1739&ndash ...

(1957) who studies the problem with pricing. Modern TU matching follows work by

Shapley Shapley is a surname that might refer to one of the following: * Lieutenant General Alan Shapley (1903–1973), of the U.S. Marine Corps, was a survivor the sinking of the USS Arizona in the attack on Pearl Harbor * Harlow Shapley (1885–1972), Am ...

and Shubik (1971), who provided a TU equivalent of Gale and Shapley (1962), as well as

Becker Becker () is one of the German-language surnames, along with Bäcker and Baecker, that derive from the root, which refers to baking. The surname began as a name for a baker (and thus his family). In northern Germany it can also derive from the ...

(1973) who applied TU matching to the marriage market. Matching theory is typically focuses on two-sided matching, where two types of workers are considered (e.g. men and women in the marriage market, firms and workers in the labor market, and students matching with colleges). A smaller literature considers other types of matching, such as one-sided matching (e.g. the

stable roommates problem In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separati ...

) and many-sided matching (e.g. man-woman-child matching). Within two sided matching, three types of matches are considered: one-to-one, many-to-one, and many-to-many. Matching theory has been applied to study positive questions, such as who matches with who, as well as normative questions regarding how to best

design A design is a plan or specification for the construction of an object or system or for the implementation of an activity or process or the result of that plan or specification in the form of a prototype, product, or process. The verb ''to design'' ...

matching markets.

Applications

Matching theory has been applied to study a wide set of applications, including: marriage, housing allocation, kidney exchange, the

National Resident Matching Program The National Resident Matching Program (NRMP), also called The Match, is a United States-based private non-profit non-governmental organization created in 1952 to place U.S. medical school students into residency training programs located in Unite ...

, and school choice.

Relationship with search and matching theory

Matching theory typically examines matching in the absence of search frictions in a centralized environment, differentiating it from

. Under certain contexts, the search and matching equilibrium converges to a stable matching when search frictions disappear

References

{{reflist Market (economics)

Overview

Applications

Relationship with search and matching theory

See also

References