{"title":"On Integer Imputations of the Core of Totally Balanced Cooperative Games","authors":"V. V. Morozov, S. I. Romanov","doi":"10.1134/S1064562424702399","DOIUrl":null,"url":null,"abstract":"<p>We consider totally balanced cooperative games in which the characteristic function takes integer values. It is proved that any three- or four-person game has an integer imputation from the core. A similar result, with the exception of one degenerate case, is obtained for five-person games. An example of a five-person game is given in which the core consists of a single noninteger imputation.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S376 - S382"},"PeriodicalIF":0.6000,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424702399","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider totally balanced cooperative games in which the characteristic function takes integer values. It is proved that any three- or four-person game has an integer imputation from the core. A similar result, with the exception of one degenerate case, is obtained for five-person games. An example of a five-person game is given in which the core consists of a single noninteger imputation.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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