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。
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.
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