运筹学学报 >
2023 , Vol. 27 >Issue 3: 159 - 168
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.03.013
具有超图合作结构的Banzhaf值
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
Received date: 2019-10-08
Online published: 2023-09-14
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
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.
Key words: TU-game; graph game; hypergraph; hypergraph game; Banzhaf value
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