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If the stable roommates problem instance has a stable matching, then there is a stable matching contained in any one of the stable tables. Any stable subtable of a stable table, and in particular any stable subtable that specifies a stable matching as in 2, can be obtained by a sequence of rotation eliminations on the stable table.
Hedonic games with preferences based on the worst player behave very similarly to stable roommates problems with respect to the core, [10] but there are hardness results for other solution concepts. [13] Many of the preceding hardness results can be explained through meta-theorems about extending preferences over single players to coalitions. [23]
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.
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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 ...
Image credits: lv_eventing Last year, the National Student Accommodation Survey asked over 1,000 students in the United Kingdom about the most common annoying housemate habits, and the results ...
The resort consists of 22 tiny homes, and in September 2021, I convinced my two roommates to spend two nights in a 212-square-foot house. Before arriving at the property in Lyons, Colorado, we ...
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 .