The stability of the roommate problem revisited
نویسندگان
چکیده
The lack of stability in some matching problems suggests that alternative solution concepts to the core might be a step towards furthering our understanding of matching market performance. We 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. We also determine the matchings in absorbing sets and find that in the case of multiple absorbing sets a similar structure is shared by all.
منابع مشابه
Credible Stability in the Roommate Problem
In the roommate problem, it is known that a stable matching may not exist. In this paper, we propose a new deviation-proof concept, called credible stability, and show that the concept resolves the problem. At a credibly stable matching, any coalition which deviates from the matching is punishable; a deviating coalition is punishable if there exists a further deviation that makes some agent in ...
متن کاملStable marriage and roommate problems with individual-based stability
Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each deviation is by a group of players. There has been little focus in matching theory on stability concepts such as Nash stability and individual stability in w...
متن کاملThe roommates problem revisited
One of the oldest but least understood matching problems is Gale and Shapley’s (1962) “roommates problem”: is there a stable way to assign 2N students into N roommate pairs? Unlike the classic marriage problem or college admissions problem, there need not exist a stable solution to the roommates problem. However, the traditional notion of stability ignores the key physical constraint that roomm...
متن کاملSOLVING FUZZY LINEAR PROGRAMMING PROBLEMS WITH LINEAR MEMBERSHIP FUNCTIONS-REVISITED
Recently, Gasimov and Yenilmez proposed an approach for solving two kinds of fuzzy linear programming (FLP) problems. Through the approach, each FLP problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. Then, the crisp problem is solved by the use of the modified subgradient method. In this paper we will have another look at the earlier defuzzifi...
متن کاملNP-Complete Stable Matching Problems
This paper concerns the complexity analysis of the roommate problem and intern assignment problem with couples. These are two special cases of the matching problems known as stable matching. The roommate problem is that of assigning a set of people to rooms of exactly two occupants in accordance with the preferences of the members of the set. The intern assignment problem with couples is that o...
متن کامل