具有超图合作结构的Banzhaf值

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  • 1. 上海大学管理学院, 上海 200444
单而芳, E-mail: efshan@shu.edu.cn

收稿日期: 2019-10-08

  网络出版日期: 2023-09-14

基金资助

国家自然科学基金(11971298)

The Banzhaf value for hypergraph communication situations

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  • 1. School of Management, Shanghai University, Shanghai 200444, China

Received date: 2019-10-08

  Online published: 2023-09-14

摘要

2006年,Alonso-Meijide和Fiestras-Janeiro考虑了以图作为合作结构的可转移效用对策模型(简称为图对策),提出了图对策Banzhaf值,它是经典Banzhaf值的一类推广。本文进一步将Banzhaf值推广到超图对策中,定义了超图对策Banzhaf值。其次,证明了超图对策Banzhaf值满足分支可分解性、分支总贡献性、公平性、平衡贡献性以及隔离性,并给出了该值的两种公理性刻画。最后,举例分析了超图对策Banzhaf值所满足的性质。

本文引用格式

吕文蓉, 单而芳 . 具有超图合作结构的Banzhaf值[J]. 运筹学学报, 2023 , 27(3) : 159 -168 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.03.013

Abstract

Alonso-Meijide and Fiestras-Janeiro(2006) introduced TU games with restricted cooperative structure represented by an undirected graph, or simple graph games, and present the Banzhaf value of the graph game, that extend the Banzhaf value. In this paper, we first generalize the Banzhaf value to the hypergraph game, define the Banzhaf value of the hypergraph game. Secondly, we prove that the Banzhaf value of the hypergraph game satisfies the property of component decomposability, component total contribution, fairness, balanced contribution, and isolation, and propose two characterizations of this value. Finally, we give an example to illustrate the properties satisfied by the Banzhaf value of the hypergraph game.

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