超图对策的组内和组间位置值

doi:10.15960/j.cnki.issn.1007-6093.2022.04.009

运筹学学报 ›› 2022, Vol. 26 ›› Issue (4): 107-118.doi: 10.15960/j.cnki.issn.1007-6093.2022.04.009

超图对策的组内和组间位置值

韩佳玉¹, 于志强¹, 赵加贵², 单而芳^1*

1. 上海大学管理学院, 上海 200444;
2. 上海公安学院, 上海 200137

收稿日期:2018-12-28 发布日期:2022-11-28
通讯作者: 单而芳 E-mail:efshan@shu.edu.cn
基金资助:
国家自然科学基金(No. 11971298)

The within groups and the between groups Position values on hypergraph games

HAN Jiayu¹, YU Zhiqiang¹, ZHAO Jiagui², SHAN Erfang^1*

1. School of Management, Shanghai University, Shanghai 200444, China;
2. Shanghai Police College, Shanghai 200137, China

Received:2018-12-28 Published:2022-11-28

摘要/Abstract

摘要： 本文研究超图对策位置值的分解问题。1988年, Meessen考虑到以图为合作结构的对策中边在合作中的作用, 提出了一个重要的分配规则, 这个规则被称为位置值(Position value)。本文通过考虑超图的每条超边不仅对关联于它的联盟中的参与者的收益产生影响, 同时作为中介也对不关联于它的联盟中的参与者的收益产生间接影响, 引入超图对策的组内Position值和组间Position值, 以区分参与者收益的成分。本文首先给出这两类值的公理化刻画。其次, 通过案例对超图对策的组内Position值和组间Position值进行了分析, 并讨论了中介费用不合理情况下的改进分配方案。

关键词: TU对策, 超图, 超图对策, 位置值

Abstract: We study the additive decomposition of the Position value on hypergraph games. In 1988, Meessen considered the contributions of the links in the alliances and proposed an important allocation rule, called the Position value. By considering each conference in hypergraphs not only affects the benefit of the players in the alliances associated with it, but also affects the benefit of the players in the alliances that are not associated with it, we introduce the within groups Position value and the between groups Position value on hypergraph games to distinguish the components of each player’s benefit. We first give axiomatic characterizations for these two kinds of values. Secondly, we give an example to illustrate the within groups Position value and the between groups Position value. Finally, we propose an improved allocation rule by adjusting the proportion of the intermediary cost.

Key words: TU game, hypergraph, hypergraph game, Position value

中图分类号:

韩佳玉, 于志强, 赵加贵, 单而芳. 超图对策的组内和组间位置值[J]. 运筹学学报, 2022, 26(4): 107-118.

HAN Jiayu, YU Zhiqiang, ZHAO Jiagui, SHAN Erfang. The within groups and the between groups Position values on hypergraph games[J]. Operations Research Transactions, 2022, 26(4): 107-118.

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超图对策的组内和组间位置值

The within groups and the between groups Position values on hypergraph games

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