{"title":"Stable allocations in discrete exchange economies","authors":"","doi":"10.1016/j.jet.2024.105921","DOIUrl":null,"url":null,"abstract":"<div><div>We study stable allocations in an exchange economy with indivisible goods. The problem is well-known to be challenging, and rich enough to express fundamentally unstable economies, such as the roommate problem. Our approach stems from generalizing the original study of an exchange economy with unit demand and unit endowments, the <em>housing model</em>. Our first approach uses Scarf's theorem, and proposes sufficient conditions under which a “convexify then round” technique ensures that the core is nonempty. The upshot is that a core allocation exists in categorical economies with dichotomous preferences. Our second approach uses a generalization of the TTC: it works under general conditions, and finds a solution that is a version of the stable set.</div></div>","PeriodicalId":48393,"journal":{"name":"Journal of Economic Theory","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Economic Theory","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022053124001273","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
We study stable allocations in an exchange economy with indivisible goods. The problem is well-known to be challenging, and rich enough to express fundamentally unstable economies, such as the roommate problem. Our approach stems from generalizing the original study of an exchange economy with unit demand and unit endowments, the housing model. Our first approach uses Scarf's theorem, and proposes sufficient conditions under which a “convexify then round” technique ensures that the core is nonempty. The upshot is that a core allocation exists in categorical economies with dichotomous preferences. Our second approach uses a generalization of the TTC: it works under general conditions, and finds a solution that is a version of the stable set.
期刊介绍:
The Journal of Economic Theory publishes original research on economic theory and emphasizes the theoretical analysis of economic models, including the study of related mathematical techniques. JET is the leading journal in economic theory. It is also one of nine core journals in all of economics. Among these journals, the Journal of Economic Theory ranks fourth in impact-adjusted citations.