基于图对策的收益分配  

Profit Allocation Based on Graph Games

作　　者：聂翠平[1,2] 张强[1] 赵璇[1] 

机构地区：[1]北京理工大学管理与经济学院,北京100081 [2]石家庄学院数学与信息科学系,河北石家庄050035

出　　处：《运筹与管理》2013年第4期1-5,共5页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(70771010;71071018;70801064);高等学校博士学科点专项科研基金(20111101110036);石家庄市科学技术研究与发展计划课题(135790075A)

摘　　要：基于具有交流结构的合作对策,即图对策,对平均树解拓展形式的特征进行刻画,提出此解满足可加性公理。进一步地,分析了对于无圈图对策此解是分支有效的。并且当连通分支中两个局中人相关联的边删掉后,此连通分支的收益变化情况可用平均树解表示。这一性质是Shapley值和Myerson值所不具有的。最后,我们给出了模糊联盟图对策中模糊平均树解的可加性和分支有效性。We study cooperative games with communication structure, called graph games. The generalization of the average tree solution is considered in the game. We propose that additivity axiom characterizes the solution. Furthermore, on the class of cycle-free graph games the solution satisfies component efficiency. The change in payoff can be represented by the average tree solution when a link between two players is deleted for a component that does not hold for Shapley value and the Myerson value. Finally, we show that there are similar properties in graph games with fuzzy coalitions.

关 键 词：图对策 平均树解 模糊联盟 分支有效性 分配 

分 类 号：O225[理学—运筹学与控制论]