Matching function

In economics, matching theory, also known as search and matching theory, is a mathematical framework attempting to describe the formation of mutually beneficial relationships over time.

Matching theory has been especially influential in labor economics, where it has been used to describe the formation of new jobs, as well as to describe other human relationships like marriage. Matching theory evolved from an earlier framework called 'search theory'. Where search theory studies the microeconomic decision of an individual searcher, matching theory studies the macroeconomic outcome when one or more types of searchers interact. It offers a way of modeling markets in which frictions prevent instantaneous adjustment of the level of economic activity. Among other applications, it has been used as a framework for studying frictional unemployment.

One of the founders of matching theory is Dale T. Mortensen of Northwestern University. A textbook treatment of the matching approach to labor markets is Christopher A. Pissarides' book Equilibrium Unemployment Theory. Mortensen and Pissarides, together with Peter A. Diamond, were awarded the 2010 Nobel Prize in Economics for 'fundamental contributions to search and matching theory'. The 2012 Economic Prize Committee of the Royal Swedish Academy of Sciences was awarded to Alvin E. Roth and Lloyd Shapley for their work on matching theory.

A matching function is a mathematical relationship that describes the formation of new relationships (also called 'matches') from unmatched agents of the appropriate types. For example, in the context of job formation, matching functions are sometimes assumed to have the following 'Cobb–Douglas' form:

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