{"title":"Characterizations of the \\(\\textbf{u}\\)-prenucleolus by dually-\\(\\textbf{u}\\)-essential coalitions","authors":"Zsófia Dornai, Miklós Pintér","doi":"10.1007/s10479-025-06549-0","DOIUrl":null,"url":null,"abstract":"<div><p>We extend the theory of TU-games with utility functions, which is a generalization of TU-games with restricted cooperation, to include dual games. By using the theory of dual games, we define dually-<span>\\(\\textbf{u}\\)</span>-essential coalitions and show that they characterize the <span>\\(\\textbf{u}\\)</span>-prenucleolus of <span>\\(\\textbf{u}\\)</span>-balanced games. Additionally, we demonstrate that the intersection of <span>\\(\\textbf{u}\\)</span>-essential and dually-<span>\\(\\textbf{u}\\)</span>-essential coalitions also forms a characterization set for the <span>\\(\\textbf{u}\\)</span>-prenucleolus, provided that the <span>\\(\\textbf{u}\\)</span>-least-core is a proper subset of the <span>\\(\\textbf{u}\\)</span>-core.\n</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1575 - 1607"},"PeriodicalIF":4.5000,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10479-025-06549-0.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06549-0","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We extend the theory of TU-games with utility functions, which is a generalization of TU-games with restricted cooperation, to include dual games. By using the theory of dual games, we define dually-\(\textbf{u}\)-essential coalitions and show that they characterize the \(\textbf{u}\)-prenucleolus of \(\textbf{u}\)-balanced games. Additionally, we demonstrate that the intersection of \(\textbf{u}\)-essential and dually-\(\textbf{u}\)-essential coalitions also forms a characterization set for the \(\textbf{u}\)-prenucleolus, provided that the \(\textbf{u}\)-least-core is a proper subset of the \(\textbf{u}\)-core.
期刊介绍:
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.