{"title":"A new value for communication situations","authors":"Daniel Li Li, Erfang Shan","doi":"10.1007/s00186-024-00873-0","DOIUrl":null,"url":null,"abstract":"<p>A communication situation (<i>N</i>, <i>v</i>, <i>H</i>) consists of a cooperative game (<i>N</i>, <i>v</i>) and a communication hypergraph (<i>N</i>, <i>H</i>), for which the Myerson value and the position value are well-known allocation rules. The value defined in this paper treats links in <i>H</i> as imaginal players, for which we define a bipartite graph between <i>N</i> and <i>H</i> according to the structure given by <i>H</i>, and propose an allocation rule called the bipartite value. This value assigns payoff to each player with two parts: as a player and as a member in links. A characterization of the bipartite value is given.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"58 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods of Operations Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00186-024-00873-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A communication situation (N, v, H) consists of a cooperative game (N, v) and a communication hypergraph (N, H), for which the Myerson value and the position value are well-known allocation rules. The value defined in this paper treats links in H as imaginal players, for which we define a bipartite graph between N and H according to the structure given by H, and propose an allocation rule called the bipartite value. This value assigns payoff to each player with two parts: as a player and as a member in links. A characterization of the bipartite value is given.
通信情境（N，v，H）由合作博弈（N，v）和通信超图（N，H）组成，其中迈尔森值和位置值是众所周知的分配规则。本文定义的值将 H 中的链接视为意象玩家，为此我们根据 H 给出的结构定义了 N 和 H 之间的双向图，并提出了一种名为双向值的分配规则。该值将每个玩家的报酬分为两部分：作为玩家的报酬和作为链接中成员的报酬。本文给出了双向值的特征。
期刊介绍：
This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience.
All papers are refereed. The emphasis is on originality, quality, and importance.
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