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Undid revision 1219675419 by NT1036 (talk) with respect to you and with respect to your contribution here, what meaning do you think that inserting the phrase "with respect to" clarifies or adds, with respect to the existing wording of the article? |
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In [[mathematics]], [[economics]], and [[computer science]], the '''Gale–Shapley algorithm''' (also known as the '''deferred acceptance algorithm''',{{r|roth}} '''propose-and-reject algorithm''',{{r|carter-price}} or '''Boston Pool algorithm'''{{r|roth}}) is an [[algorithm]] for finding a solution to the [[stable matching problem]]. It is named for [[David Gale]] and [[Lloyd Shapley]], who published it in 1962, although it had been used for the [[National Resident Matching Program]] since the early 1950s. Shapley and [[Alvin E. Roth]] (who pointed out its prior application) won the 2012 [[Nobel Memorial Prize in Economic Sciences|Nobel Prize in Economics]] for work including this algorithm.
The stable matching problem seeks to pair up equal numbers of participants of two types, using preferences from each participant. The pairing must be stable: no pair of participants should prefer each other to their assigned match. In each round of the Gale–Shapley algorithm, unmatched participants of one type propose a match to the next participant on their preference list. Each proposal is accepted if its recipient prefers it to their current match. The resulting procedure is a [[truthful mechanism]] from the point of view of the proposing participants, who receive their most-preferred pairing consistent with stability. In contrast, the recipients of proposals receive their least-preferred pairing. The algorithm can be implemented to run
The stable matching problem, and the Gale–Shapley algorithm solving it, have widespread real-world applications, including matching American medical students to residencies and French university applicants to schools. For more, see {{slink|Stable marriage problem|Applications}}.
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