| 具有图结构和联盟结构的Banzhaf值及应用 |
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| 引用本文： | 单而芳,刘贺宇,吕文蓉,史纪磊.具有图结构和联盟结构的Banzhaf值及应用[J].运筹与管理,2023,32(1):73-78. |
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| 作者姓名： | 单而芳 刘贺宇 吕文蓉 史纪磊 |
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| 作者单位： | 上海大学 管理学院,上海 200444 |
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| 基金项目： | 国家自然科学基金资助项目(11971298);浙江省社科联研究课题(2018B08) |
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| 摘 要： | Banzhaf值是经典可转移效用合作对策中一个著名的分配规则，可以用来评估参与者在对策中的不同作用。本文将Banzhaf值推广到具有联盟结构和图结构的TU-对策中，首先提出并定义了具有联盟结构和图结构的Banzhaf值(简称PL-Banzhaf值),证明了PL-Banzhaf值满足公平性、平衡贡献性和分割分支总贡献性，并给出了该值的两种公理性刻画。其次，讨论了PL-Banzhaf值在跨国天然气管道案例中的应用，并和其他分配规则进行了比较分析。
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| 关 键 词： | TU-对策 图 通讯情境 联盟结构 Banzhaf值 |
| 收稿时间： | 2020-10-25 |
The Banzhaf Value with Graph and Coalition Structures |
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| SHAN Erfang,LIU Heyu,LÜ,Wenrong,SHI Jilei.The Banzhaf Value with Graph and Coalition Structures[J].Operations Research and Management Science,2023,32(1):73-78. |
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| Authors: | SHAN Erfang LIU Heyu LÜ Wenrong SHI Jilei |
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| Affiliation: | School of Management, Shanghai University, Shanghai 200444, China |
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| Abstract: | As one of the well-known allocation rules in the classic transferable utility cooperative game, the Banzhaf value can be used to evaluate the different roles of players in the game. In this paper, firstly, we extend the Banzhaf value to a TU-game with coalition and graph structures, and define the Banzhaf value with coalition and graph structures(PL-Banzhaf value for short). It is also proved that PL-Banzhaf value satisfy the fairness, balanced contributions and partition component total power, and it can be characterized by these properties in two different forms. Secondly, we discuss an application of the PL-Banzhaf value in a case on transnational natural gas pipelines, and compare the value with several others. |
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| Keywords: | TU-game graph communication situation coalition structures banzhaf value |
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