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In a paper with David Gale in 1962, Mr. Shapley explained how individuals could be paired together in a stable match even when they disagreed about what qualities made the right match.
An example of a stable match for this situation is represented as three pairs $(a ,e $ $(b,f $, $(c,d)$.
The stable marriage problem is the problem of finding a stable match between two sets of elements given a set of preferences for each element.
Moreover, we use the college admission framework (CAF) to find a stable match between two sets of elements (MSs and RSs).
In spite of this, subjects are remarkably good at reaching a stable match, even when the payoffs of others are not publicly observed.
Virtual arrays are formed by finding a stable match between two sets of single antenna devices such as mobile stations (MSs) and relay stations (RSs) based on a game theoretic approach derived from the concept of the college admissions problem.
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But imagine a scenario with thousands of men and an equal number of women all longing for a stable match-making outcome, that is, one where no man and woman who are not partners actually prefer each other to their respective partner.
For a roommate matching problem instance, there might not exist a stable matching.
The stable roommate problem is to find a stable matching [17].
There does not exist a stable matching procedure to make a dominate strategy for colleges to reveal their preferences.
When regional quotas are imposed, a stable matching may no longer exist since fairness and nonwastefulness, which compose stability, are incompatible.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com