带层次结构效用可转移合作对策的多步Shapley值  

The multi-step Shapley value of transferable utility cooperative games with a level structure

作　　者：胡勋锋[1] 李登峰[1] 

机构地区：[1]福州大学经济与管理学院,福州350108

出　　处：《系统工程理论与实践》2016年第7期1863-1870,共8页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金重点项目(71231003);国家自然科学基金(71572040);高等学校博士学科点专项科研基金资助课题(20113514110009);福建省社会科学规划项目(FJ2015C230)~~

摘　　要：作为一种局中人结盟形式,层次结构比联盟结构更具一般性.本文致力于给出带层次结构效用可转移合作对策的多步Shapley值,具体给出了其分配过程及公理化刻画.另外,作为一个等价分配过程,本文还证明了它等价于一个特殊效用可转移合作对策的加权Shapley值.研究结果扩展了带联盟结构效用可转移合作对策的两步Shapley值,可为研究其它带结盟限制合作对策的解提供借鉴.As an alliance form for players, a level structure is more general than a coalition structure. This paper devotes to propose the multi-step Shapley value of transferable utility cooperative games with a level structure. Concretely, an allocation procedure and an axiomatic characterization of it are given. Additionally, as an equivalent allocation procedure, this paper proves that it is identical with the weighted Shapley value of an appropriate transferable utility cooperative game. Research results extend the two- step Shapley value of transferable utility cooperative games with a coalition structure, and they can be taken as references to investigate other solutions of transferable utility cooperative gaines with an alliance restriction.

关 键 词：合作对策 层次结构 联盟结构 两步Shapley值 SHAPLEY值 加权Shapley值 

分 类 号：O225[理学—运筹学与控制论]