| 来源类型 | FEEM working papers "Note di lavoro" series
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| 规范类型 | 论文
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| Stable Matchings for the Room-mates Problem |
| Somdeb Lahiri
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| 发表日期 | 2003
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| 出处 | Climate Change and Sustainable Development
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| 出版年 | 2003
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| 语种 | 英语
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| 摘要 | We show that, given two matchings for a room-mates problem of which say the second is stable, and given a non-empty subset of agents S if (a) no agent in S prefers the first matching to the second, and (b) no agent in S and his room-mate in S under the second matching prefer each other to their respective room-mates in the first matching, then no room-mate of an agent in S prefers the second matching to the first. This result is a strengthening of a result originally due to Knuth (1976). In a paper by Sasaki and Toda (1992) it is shown that if a marriage problem has more than one stable matchings, then given any one stable matching, it is possible to add agents and thereby obtain exactly one stable matching, whose restriction over the original set of agents, coincides with the given stable matching. We are able to extend this result here to the domain of room-mates problems. We also extend a result due to Roth and Sotomayor (1990) originally established for two-sided matching problems in the following manner: If in a room-mates problem, the number of agents increases, then given any stable matching for the old problem and any stable matching for the new one, there is at least one agent who is acceptable to this new agent who prefers the new matching to the old one and his room-mate under the new matching prefers the old matching to the new one. Sasaki and Toda (1992) shows that the solution correspondence which selects the set of all stable matchings, satisfies Pareto Optimality, Anonymity, Consistency and Converse Consistency on the domain of marriage problems. We show here that if a solution correspondence satisfying Consistency and Converse Consistency agrees with the solution correspondence comprising stable matchings for all room-mates problems involving four or fewer agents, then it must agree with the solution correspondence comprising stable matchings for all room-mates problems. |
| 特色分类 | C71,C78
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| 关键词 | Stable matchings,Room-mate problem
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| URL | https://www.feem.it/en/publications/feem-working-papers-note-di-lavoro-series/stable-matchings-for-the-room-mates-problem/
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| 来源智库 | Fondazione Eni Enrico Mattei (Italy)
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| 资源类型 | 智库出版物
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| 条目标识符 | http://119.78.100.153/handle/2XGU8XDN/116945
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推荐引用方式
GB/T 7714 |
Somdeb Lahiri. Stable Matchings for the Room-mates Problem. 2003.
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