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The hospitals/residents problem – also known as the college admissions problem – differs from the stable marriage problem in that a hospital can take multiple residents, or a college can take an incoming class of more than one student.
A stable matching always exists, and the algorithmic problem solved by the Gale–Shapley algorithm is to find one. [3] The stable matching problem has also been called the stable marriage problem, using a metaphor of marriage between men and women, and many sources describe the Gale–Shapley algorithm in terms of marriage proposals. However ...
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis is a book on matching markets in economics and game theory, particularly concentrating on the stable marriage problem. It was written by Alvin E. Roth and Marilda Sotomayor , with a preface by Robert Aumann , [ 1 ] [ 2 ] and published in 1990 by the Cambridge University Press ...
1. A matching is called weakly stable unless there is a couple each of whom strictly prefers the other to his/her partner in the matching. Robert W. Irving [1] extended the Gale–Shapley algorithm as shown below to provide such a weakly stable matching in time, where n is the size of the stable marriage problem. Ties in the men and women's ...
In economics, 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 .
The Zegers fell in love after their first date and were engaged four weeks later. Now, 50 years later, they share the secret behind their romance.
Agreements between young friends to marry later in life are a trope of American entertainment, [1] popularized in the film My Best Friend's Wedding, [2] [3] that also occur occasionally in life. [1] The stable marriage problem, and human matching more generally, is a problem of allocation.
The secretary problem demonstrates a scenario involving optimal stopping theory [1] [2] that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.