Abstract: A well-known component efficient solution for graph games is the position value, which fully reflects the role of the links to cooperate in graph games, and is applied to measure centrality of networks. Based on the cooperative games with coalition and graph structures proposed by van den Brink et al., this paper extends the position value to graph games with coalition structure, and proposes the position value with coalition structure. Thisvaluecanbeusedasameasureforofcentrality constrained by priority coalitions in networks. First, we show that the position value with coalition structur isdeter ineuni uely ypartiti ncom onentefficiencyandbalancedlinkcontribution.Secondly, byacaseontransnationalnaturalgas pipelines, wecomparethevalue with several others.

Key words: cooperative games, coalition structures, graph games, position value

摘要： position值是图对策中著名的分支有效解, 该值充分体现了图的边在合作中的贡献, 因而也可作为网络中心性的一种测度方法。本文基于van den Brink等提出的具有联盟结构与图结构的合作对策, 将position值推广到具有联盟结构的图对策上, 提出了具有联盟结构的position值, 该值可以作为受优先联盟约束的网络中心性的一种测度方法。本文首先证明了具有联盟结构的position值可以由分割分支有效性和平衡边贡献性所唯一刻画。其次, 以跨国天然气管道网的收益分配为例, 对这个值与其他值做了比较分析。

关键词: 合作对策, 联盟结构, 图对策, Position值