{"title":"拟阵秩估值的加权公平划分：单调性和策略性","authors":"Warut Suksompong , Nicholas Teh","doi":"10.1016/j.mathsocsci.2023.09.004","DOIUrl":null,"url":null,"abstract":"<div><p>We study the problem of fairly allocating indivisible goods to agents with weights corresponding to their entitlements. Previous work has shown that, when agents have binary additive valuations, the maximum weighted Nash welfare rule is resource-, population-, and weight-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time. We generalize these results to the class of weighted additive welfarist rules with concave functions and agents with matroid-rank (also known as binary submodular) valuations.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"126 ","pages":"Pages 48-59"},"PeriodicalIF":0.5000,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Weighted fair division with matroid-rank valuations: Monotonicity and strategyproofness\",\"authors\":\"Warut Suksompong , Nicholas Teh\",\"doi\":\"10.1016/j.mathsocsci.2023.09.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the problem of fairly allocating indivisible goods to agents with weights corresponding to their entitlements. Previous work has shown that, when agents have binary additive valuations, the maximum weighted Nash welfare rule is resource-, population-, and weight-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time. We generalize these results to the class of weighted additive welfarist rules with concave functions and agents with matroid-rank (also known as binary submodular) valuations.</p></div>\",\"PeriodicalId\":51118,\"journal\":{\"name\":\"Mathematical Social Sciences\",\"volume\":\"126 \",\"pages\":\"Pages 48-59\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Social Sciences\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165489623000793\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Social Sciences","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165489623000793","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
Weighted fair division with matroid-rank valuations: Monotonicity and strategyproofness
We study the problem of fairly allocating indivisible goods to agents with weights corresponding to their entitlements. Previous work has shown that, when agents have binary additive valuations, the maximum weighted Nash welfare rule is resource-, population-, and weight-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time. We generalize these results to the class of weighted additive welfarist rules with concave functions and agents with matroid-rank (also known as binary submodular) valuations.
期刊介绍：
The international, interdisciplinary journal Mathematical Social Sciences publishes original research articles, survey papers, short notes and book reviews. The journal emphasizes the unity of mathematical modelling in economics, psychology, political sciences, sociology and other social sciences.
Topics of particular interest include the fundamental aspects of choice, information, and preferences (decision science) and of interaction (game theory and economic theory), the measurement of utility, welfare and inequality, the formal theories of justice and implementation, voting rules, cooperative games, fair division, cost allocation, bargaining, matching, social networks, and evolutionary and other dynamics models.
Papers published by the journal are mathematically rigorous but no bounds, from above or from below, limits their technical level. All mathematical techniques may be used. The articles should be self-contained and readable by social scientists trained in mathematics.
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