联盟结构和交流网络限制下合作博弈的Shapley值研究进展  

The Shapley Values for Cooperative Games with a Communication Ggraph or a Coalition Structure: A Survey

作　　者：胡勋锋 单而芳[3] 李登峰 Hu Xunfeng;Shan Erfang;Li Dengfeng(School of Business,Guangxi University,Nanning 530004,China;Center for Applied Mathematics of Guangxi(Guangxi University),Shanghai 200444,China;School of Management,Shanghai University;School of Management and Economics,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]广西大学工商管理学院,广西南宁530004 [2]广西应用数学中心(广西大学),广西南宁530004 [3]上海大学管理学院,上海200444 [4]电子科技大学经济与管理学院,四川成都611731

出　　处：《中国管理科学》2025年第1期140-152,共13页Chinese Journal of Management Science

基　　金：国家自然科学基金项目(71901076,72071032,72271046,72371151);广西科技基地和人才专项基金项目(AD22080047)。

摘　　要：合作博弈通过指定所有潜在局中人联盟的价值来描述现实中的分配问题,它的解旨在将最大联盟的价值公平地分配给所有局中人。Shapley值是合作博弈最重要的解概念之一,本文关注联盟结构和交流网络限制下合作博弈的Shapley值。Shapley值在联盟博弈和网络博弈中都有多种扩展。文中首先对Shapley值在联盟博弈和网络博弈中的扩展进行梳理总结。联盟博弈部分,不仅关注传统联盟结构,还关注联盟组合和层次结构这两种推广形式。网络博弈部分,不仅关注传统交流网络,还关注超网络这一推广形式。随后,进一步梳理Shapley值在联盟结构和交流网络双重限制下合作博弈中的扩展。不仅关注联盟结构和交流网络相互独立的联盟网络博弈,还关注二者相互关联的两层网络博弈。研究结果厘清了Shapley值在各领域的发展脉络,可为现实中的分配问题提供决策参考。A cooperative game describes real-world allocation problems by specifying the worth of all potential coalitions of players. A solution of cooperative games aims to distribute the worth of the grand coalition among all players fairly. The Shapley value is one of the most important solution concepts in cooperative game theory.The paper focuses on the Shapley values for cooperative games with a coalition structure or a communication network. A coalition structure is a partition of the player set, where each component acts as an intermediary node during the allocation process. The Aumann-Drèze value, the Owen value, and the two-step Shapley value are well-known extensions of the Shapley value to cooperative games with a coalition structure. A communication network consists of nodes and edges, where nodes and edges represent players and communication relationships between players, respectively. Only connected players in the network can communicate with each other.The Myerson value, the position value, and the average tree solution are well-known extensions of the Shapley value to cooperative games with a communication graph. The underlying paper aims to review these extensions. For coalition games, both the traditional coalition structure and the extended forms of coalition configurations and level structure are concerned. For network games, the extended form of hyper-network is also studied. Moreover, the extensions of the Shapley value to cooperative games with both a coalition structure and a communication network are also reviewed, where two cases are considered: 1) coalition network games in which the coalition structure and the communication network are independent;2) two-layer network games in which the two are interrelated. According to these reviews, the relationship between different Shapley value extensions are more clear, which may support decision making in reality.

关 键 词：合作博弈 联盟结构 交流网络 SHAPLEY值 

分 类 号：C931[经济管理—管理学]