{"title":"Ekici’s reclaim-proof allocations revisited","authors":"Qianfeng Tang , Zhan Zhu","doi":"10.1016/j.jmateco.2025.103170","DOIUrl":null,"url":null,"abstract":"<div><div>We revisit the concept of reclaim-proof allocations proposed by <span><span>Ekici (2013)</span></span> for house allocation problems with existing tenants. As a concept of core, the definition of reclaim-proof allocations assumes that when a coalition blocks an allocation, an agent in the coalition is allowed to bring her allocated object into the coalition, even when it is privately owned by an outsider. We propose a new notion of core called the effectual core by restoring the feasibility of coalitional blocking in Ekici’s definition. Our main result shows that the effectual core, while by definition weaker than reclaim-proofness, is actually equivalent to it. Together with Ekici’s results, it is then immediate that an allocation is in the effectual core if and only if it is produced by the <em>You request my house-I get your turn</em> (YRMH-IGYT) mechanism (<span><span>Abdulkadiroğlu and Sönmez, 1999</span></span>) and if and only if it is a competitive allocation.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"121 ","pages":"Article 103170"},"PeriodicalIF":0.7000,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304406825000874","RegionNum":4,"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 revisit the concept of reclaim-proof allocations proposed by Ekici (2013) for house allocation problems with existing tenants. As a concept of core, the definition of reclaim-proof allocations assumes that when a coalition blocks an allocation, an agent in the coalition is allowed to bring her allocated object into the coalition, even when it is privately owned by an outsider. We propose a new notion of core called the effectual core by restoring the feasibility of coalitional blocking in Ekici’s definition. Our main result shows that the effectual core, while by definition weaker than reclaim-proofness, is actually equivalent to it. Together with Ekici’s results, it is then immediate that an allocation is in the effectual core if and only if it is produced by the You request my house-I get your turn (YRMH-IGYT) mechanism (Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.
期刊介绍:
The primary objective of the Journal is to provide a forum for work in economic theory which expresses economic ideas using formal mathematical reasoning. For work to add to this primary objective, it is not sufficient that the mathematical reasoning be new and correct. The work must have real economic content. The economic ideas must be interesting and important. These ideas may pertain to any field of economics or any school of economic thought.