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In a uniformly-random instance of the stable marriage problem with n men and n women, the average number of stable matchings is asymptotically . [6] In a stable marriage instance chosen to maximize the number of different stable matchings, this number is an exponential function of n. [7]
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.
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 ...
Graphs of probabilities of getting the best candidate (red circles) from n applications, and k/n (blue crosses) where k is the sample size. 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.
WATCH: Sarah Michelle Gellar blames America's marriage woes on ‘disposable’ society. The actress said that "hard work" is the secret behind her 22-year union with Freddie Prinze Jr.
Boston held citywide discussions and hearings on the school selection system and finally in 2005 narrowed the choice to one of two mechanisms: the top trading cycles mechanism for schools and the student-optimal stable mechanism based on the stable marriage problem. Eventually, Boston adopted the student-optimal stable mechanism.