{"title":"Sign properties and axiomatizations of the weighted division values","authors":"Wenzhong Li , Genjiu Xu , René van den Brink","doi":"10.1016/j.jmateco.2024.102969","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study axiomatic foundations of the class of weighted division values. Firstly, while keeping efficiency, additivity and the nullifying player property from the original axiomatization of the equal division value, we consider relaxations of symmetry in line with Casajus (2019) to characterize the class of (positively) weighted division values. Secondly, we show that the class of weighted division values can also be characterized by replacing linearity in three axiomatizations of Béal et al. (2016) with additivity. Finally, we show how strengthening an axiom regarding null, non-negative, respectively nullified players in these three axiomatizations, provides three axiomatizations of the class of positively weighted division values.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"112 ","pages":"Article 102969"},"PeriodicalIF":1.0000,"publicationDate":"2024-03-16","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/S0304406824000314","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
In this paper, we study axiomatic foundations of the class of weighted division values. Firstly, while keeping efficiency, additivity and the nullifying player property from the original axiomatization of the equal division value, we consider relaxations of symmetry in line with Casajus (2019) to characterize the class of (positively) weighted division values. Secondly, we show that the class of weighted division values can also be characterized by replacing linearity in three axiomatizations of Béal et al. (2016) with additivity. Finally, we show how strengthening an axiom regarding null, non-negative, respectively nullified players in these three axiomatizations, provides three axiomatizations of the class of positively weighted division values.
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