Review of Direct Matching Markets and the Deferred Acceptance Algorithm

Abstract

Alvin E. Roth and Lloyd S. Shapley were awarded the 2012 Nobel Prize in Economic Science "for the theory of stable allocations and the practice of market design;" (Royal Swedish Academy of Sciences, 2012).

This paper, motivated by a desire to understand their accomplishments, reviews successful matching processes adopted in particular market institutions.

In some situations, the standard market mechanism – which adjusts prices and allocates resources by allowing supply to equal demand – cannot be utilized to directly match two sets of agents in markets with prices often unavailable. The deferred acceptance matching algorithm – originally designed by Gale and Shapley (1962) for the college admissions problem – was imbued with several optimum properties, including Pareto optimality for the students, and was subsequently adapted for specific market institutions by Roth; (Roth, 1985).

Designing optimal matching algorithms has been heavily influenced by the practice of adopting and implementing market-specific designs which recognize characteristics of specific markets and sets of agents, rather than directly applying the theory of simple markets; (Roth, 2010). The deferred acceptance matching algorithm and its adaptations and extensions serve as the most highly-preferred stable mechanism to assign matchings in several two-sided markets, such as the medical residency and school choice problems. The deferred acceptance procedure has been successfully linked to other direct-matching market designs.

Keywords: direct matching markets, theory of stable allocations, deferred acceptance matching algorithm, Pareto optimality, strategy-proof, market design, college admissions, medical residency and school choice problems, auctions

JEL Classification: C78, D61, D78, J44, B41