效用可转移合作博弈的Shapley值公理化研究进展综述  

Axiomatizations of the Shapley value in cooperative games with transferable utility:A review

作　　者：李文忠 徐根玖[1] LI Wenzhong;XU Genjiu(School of Mathematics and Statistics,Northwest-ern Polytechnical University,Xi'an 710072,Shaanxi,China)

机构地区：[1]西北工业大学数学与统计学院,陕西西安710072

出　　处：《运筹学学报（中英文）》2024年第3期63-80,共18页Operations Research Transactions

基　　金：国家自然科学基金(Nos.72301214,72071159);智能博弈重点实验室创新工作站开放课题(Nos.ZBKF-24-07,ZBKF-24-11)。

摘　　要：随着全球经济融合和国际关系日益紧密,合作共赢已然成为当今时代的核心趋势。合作博弈理论作为研究合作问题的有力工具,主要探讨如何在参与者之间分配合作所产生的收益。Shapley值作为合作博弈中最重要的单值解之一,具有重要研究意义与价值。本文将主要介绍目前Shapley值公理化的研究工作,从可加性、均衡贡献性、边际性、公平性、简约一致性、相关一致性和一些特殊的参与者性的角度,分别归纳整理了Shapley值基于这些性质的公理化研究结论。最后对未来研究进行了展望。With the increasing integration of global economy and closer international relations,win-win cooperation has become a core trend in today.As a powerful tool for studying cooperative issues,cooperative game mainly explores how to allocate the benefits generated by cooperation among players.The Shapley value,as one of the most important solutions in cooperative games,has significant research significance and value.This paper mainly introduce some research on the axiomatization of the Shapley value from the point of additivity,balanced contribution,marginality,fairness,reduced consistency,associated consistency and some special player properties.We finally give a brief summary from the perspective of future research.

关 键 词：合作博弈 SHAPLEY值 公理化方法 

分 类 号：O225[理学—运筹学与控制论]