具有联盟和概率图结构合作对策的分配规则及其应用  

The Allocation Rule for TU-games with Coalition and Probabilistic Graph Structures and Its Applications

作　　者：单而芳[1] 史纪磊 蔡蕾 Shan Erfang;Shi Jilei;Cai Lei(School of Management,Shanghai University,Shanghai 200444,China;School of Business,Jiangsu Ocean University,Lianyungang 222005,China)

机构地区：[1]上海大学管理学院,上海200444 [2]江苏海洋大学商学院,江苏连云港222005

出　　处：《中国管理科学》2024年第1期137-145,共9页Chinese Journal of Management Science

基　　金：国家自然科学基金项目(72371151);国家社会科学资助基金项目(19BGL001);江苏高校哲学社会科学项目(2023SJYB1805);宁波市自然科学基金项目(2021J235)。

摘　　要：van den Brink等^([24])考虑了具有联盟结构和图结构合作对策的分割-图值,该值虽然反映了联盟结构和图结构对分配结果的双重影响,但忽略了合作结构的不确定性。本文从图结构的不确定性出发,提出了具有联盟结构和概率图结构的合作对策模型,并引入了新的分配规则——分割-概率图值。证明了分割-概率图值是满足概率分割分支有效性和概率公平性的唯一解。最后,以跨国材料运输为例,将分割-概率图值和其他值做了比较分析。A cooperative game with transferable utility,shortly TU-game,is a pair consisting of a finite set of players and a characteristic function assigning a worth to each coalition of players.However,in many situations cooperation is restricted by cooperation structures such as hierarchical,technical or communicational structure.Aumann and Drèze(1974)first considered the situation in which there exists an exogenous coalition structure.Later,Myerson(1977)introduced TU-games with restricted cooperation possibilities represented by an undirected graph.In practice,there are some situations of cooperative decision making in which the cooperation between agents is restricted by both a communication structure and an organizational structure.van den Brink et al.(2015)considered the partition-graph value for TU-games with coalition and graph structures.The partition-graph value reflects not only the coalition structure but also the graph structure of the game will influ⁃ence the allocation process,but disregards the uncertainty of cooperation structure.In this paper the TU-games with coalition and probabilistic graph structure are proposed and the partition-probabilistic graph value for the game model in introduced by considering the uncertainty of graph structure.It is shown that the partitionprobabilistic graph value is uniquely determined by probabilistic partition component efficiency and probabilistic fairness.Finally,the partition-probabilistic graph value is illustrated by an example of transnational material transportation and compare it with other values.

关 键 词：TU-对策 分配规则 联盟结构 概率图 分割-概率图值 

分 类 号：C934[经济管理—管理学] O225[理学—运筹学与控制论]