带层次结构效用可转移合作对策的collective值

胡勋锋,李登峰

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (1) : 172-185.

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PDF(443 KB)
系统科学与数学 ›› 2017, Vol. 37 ›› Issue (1) : 172-185. DOI: 10.12341/jssms13051
论文

带层次结构效用可转移合作对策的collective值

    胡勋锋,李登峰
作者信息 +

The Collective Value of Transferable Utility Cooperative Games with a Level Structure

    HU Xunfeng, LI Dengfeng
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文章历史 +

摘要

层次结构是比联盟结构更一般化的结盟限制形式. 文章给出了带层次结构效用可转移合作对策collective值的两种定义. 第一种类似于带层次结构效用可转移合作对策的ζ值, 从多步分配的角度定义了collective值; 第二种类似于带图结构效用可转移合作对策的Myerson值, 从交流限制的角度定义了collective值. 文中证明了这两种定义是等价的, 并给出了collective值的一个公理化刻画. 研究结果丰富了带层次结构效用可转移合作对策的解概念, 可为研究其它带结盟限制效用可转移合作对策的值函数提供借鉴.

Abstract

As an alliance restriction, a level structure is more general than a coalition structure. This paper proposes two definitions of the collective value of transferable utility cooperative games with a level structure. Similar to the ζ value of transferable utility cooperative games with a level structure, the first one defines the collective value from the perspective of multi-step allocation. And similar to the Myerson value of transferable utility cooperative games with a graph structure, the second one defines the collective value from the perspective of communication restriction. The equivalence of these two definitions is proved and an axiomatic characterization of the collective value is given in the paper. Research results enrich solution concepts of transferable utility cooperative games with a level structure, and they can be taken as references to investigate other solutions of transferable utility cooperative games with an alliance restriction.

关键词

合作对策 / 层次结构 /   / collective值 / Shapley值 / 加权Shapley值.

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胡勋锋 , 李登峰. 带层次结构效用可转移合作对策的collective值. 系统科学与数学, 2017, 37(1): 172-185. https://doi.org/10.12341/jssms13051
HU Xunfeng , LI Dengfeng. The Collective Value of Transferable Utility Cooperative Games with a Level Structure. Journal of Systems Science and Mathematical Sciences, 2017, 37(1): 172-185 https://doi.org/10.12341/jssms13051
中图分类号: 91A06    91A12    91A65   
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