{"title":"室友问题的等级差距和核心的大小","authors":"Paula Jaramillo, Çagatay Kayi, F. Klijn","doi":"10.2139/ssrn.2974123","DOIUrl":null,"url":null,"abstract":"This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents’ rankings. Finally, we show that most of our bounds are tight.","PeriodicalId":446687,"journal":{"name":"Universidad de los Andes Department of Economics Research Paper Series","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rank Gaps and the Size of the Core for Roommate Problems\",\"authors\":\"Paula Jaramillo, Çagatay Kayi, F. Klijn\",\"doi\":\"10.2139/ssrn.2974123\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents’ rankings. Finally, we show that most of our bounds are tight.\",\"PeriodicalId\":446687,\"journal\":{\"name\":\"Universidad de los Andes Department of Economics Research Paper Series\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Universidad de los Andes Department of Economics Research Paper Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.2974123\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Universidad de los Andes Department of Economics Research Paper Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.2974123","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文处理的是可解的室友问题(Gale and Shapley, 1962)，即具有非空核(稳定匹配集)。利用最大秩差和平均秩差研究了稳定匹配的分类性和核心的大小。我们提供了代理排名中最大分歧和平均分歧的上限。最后，我们证明了大多数边界是紧的。
Rank Gaps and the Size of the Core for Roommate Problems
This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents’ rankings. Finally, we show that most of our bounds are tight.
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