{"title":"Finding all stable matchings with assignment constraints","authors":"Gregory Z. Gutin , Philip R. Neary , Anders Yeo","doi":"10.1016/j.geb.2024.09.004","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main contribution is an algorithm, based on the iterated deletion of unattractive alternatives (<span><span>Balinski and Ratier, 1997</span></span>; <span><span>Gutin et al., 2023</span></span>), that determines if and when a given list of constraints is compatible with stability. Whenever there is a stable matching that satisfies the constraints, our algorithm outputs all of them (each in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings subject to assignment constraints, and (ii) a tool to implement them when feasible.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"148 ","pages":"Pages 244-263"},"PeriodicalIF":1.0000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Games and Economic Behavior","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0899825624001350","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main contribution is an algorithm, based on the iterated deletion of unattractive alternatives (Balinski and Ratier, 1997; Gutin et al., 2023), that determines if and when a given list of constraints is compatible with stability. Whenever there is a stable matching that satisfies the constraints, our algorithm outputs all of them (each in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings subject to assignment constraints, and (ii) a tool to implement them when feasible.
期刊介绍:
Games and Economic Behavior facilitates cross-fertilization between theories and applications of game theoretic reasoning. It consistently attracts the best quality and most creative papers in interdisciplinary studies within the social, biological, and mathematical sciences. Most readers recognize it as the leading journal in game theory. Research Areas Include: • Game theory • Economics • Political science • Biology • Computer science • Mathematics • Psychology