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The lack of stability in some matching problems suggests that alternative solution concepts to the core might be a step towards furthering the understanding of matching market performance. The authors propose absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts other matchings when the core is empty. Furthermore, it satisfies the interesting property of outer stability. They also determine the matchings in absorbing sets and find that in the case of multiple absorbing sets a similar structure is shared by all.
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