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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]
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 ...
The comparator circuit value problem (CCVP) is CC-complete. In the stable marriage problem, there is an equal number of men and women. Each person ranks all members of the opposite sex. A matching between men and women is stable if there are no unpaired man and woman who prefer each other over their current partners. A stable matching always ...
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 ...
Download QR code; Print/export Download as PDF; Printable version; In other projects ... Stable marriage problem; Stable marriage with indifference;
By applying linear programming to the stable matching polytope, one can find the minimum or maximum weight stable matching. [1] Alternative methods for the same problem include applying the closure problem to a partially ordered set derived from the lattice of stable matchings, [6] or applying linear programming to the order polytope of this ...
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 .