超图结构上合作博弈的赋权Position值  

The Weighted Position Value for HypergraphGames

作　　者：单而芳[1] 谢娜娜 王光明 SHAN Er-fang;XIE Na-na;WANG Guang-ming(School of Management,Shanghai University,Shanghai 200444,China;School of Mathematical Sciences,University of Jinan,Jinan 250022,China)

机构地区：[1]上海大学管理学院,上海200444 [2]济南大学数学科学学院,山东济南250022

出　　处：《运筹与管理》2022年第9期28-33,共6页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(11971298)。

摘　　要：在合作博弈的一般模型中总是假设所有联盟都能形成。不过,在实际中由于受到一些因素的制约,有些联盟是不能形成的。基于此,Myerson提出了具有图通讯结构的合作博弈。Myerson值和Position值是超图博弈上的两个重要分配规则。2005年,Slikker给出了在图博弈上Position值的公理化刻画。但超图博弈上Position值的公理化刻画一直悬而未决。本文通过引入“赋权平衡超边贡献公理”,并结合经典的“分支有效性”,提出了超图博弈上赋权Position值的公理化刻画。作为推论,解决了超图博弈上Position值的公理化刻画问题。In the general model of cooperative game,it is always assumed that all coalitions can be formed.However,in practice,due to the constraints of some factors,some coalitions can not be formed.Based on this,Myerson proposed a cooperative game with graph communication structures.The Myerson value and position value are two important allocation rules in hypergraph games.In 2005,Slikker gave an axiomatic characterization of position values on graph games.However,the axiomatic characterization of position values in hypergraph games is still up in the air.In this paper,by introducing the axiom of weighted balanced conference contributions,and combining with the classical component efficiency,the axiomatic characterization of weighted positioning values on hypergraph games is proposed.As a corollary,the problem of axiomatic characterization of position values on hypergraph games is solved.

关 键 词：超图 TU-博弈 超图博弈 Myerson值 赋权Position值 

分 类 号：F224.32[经济管理—国民经济] F224.33