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Operations Research Transactions >

2023 , Vol. 27 >Issue 3: 159 - 168

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.03.013

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

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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.

Key words： TU-game; graph game; hypergraph; hypergraph game; Banzhaf value

Cite this article

Wenrong LYU, Erfang SHAN . The Banzhaf value for hypergraph communication situations[J]. Operations Research Transactions, 2023 , 27(3) : 159 -168 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.03.013

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