具有边际贡献权重的位置值
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摘要
先通过交流局势中交流结构的边邻接关系,确定了边邻接交流局势。再利用边邻接交流局势的Myerson值,以及边的端点的边际联盟贡献比例,定义了具有边际贡献权重的位置值。并利用分支有效性和边均衡贡献性,在一类交流局势下刻画了具有边际贡献权重的位置值。
In this paper,we determine link 's adjacent communication situation by the adjacent relationship between links in communication structure. Then,using Myerson value of the link's adjacent communication situation and the proportion of the marginal contribution of two vertices in their link,we define the position value with weight of marginal contribution. Furthermore,in some communication situations,the weighted position value is characterized by component efficiency and balanced link contributions.
In this paper,we determine link 's adjacent communication situation by the adjacent relationship between links in communication structure. Then,using Myerson value of the link's adjacent communication situation and the proportion of the marginal contribution of two vertices in their link,we define the position value with weight of marginal contribution. Furthermore,in some communication situations,the weighted position value is characterized by component efficiency and balanced link contributions.
引文
[1]Myerson R B.Graphs and cooperation in games[J].Mathematics of Operations Research,1977,2:225-229.
[2]Owen G.Values of graph-restricted games[J].SIAM Journal of Algebraic Discrete Methods,1986,7:210-220.
[3]Meessen R.Communication games[D].Master’s thesis,Department of mathematics,University of Mijmegen,The Netherlands,1988.
[4]Borm P,Owen G,Tijs S.On the position value for communication situations[J].SIAM Journal on Discrete Mathematics,1992,5:305-320.
[5]Slikker M.A characterization of the position value[J].International Journal of Game Theory,2005,33:505-514.
[6]Casajus A.The position value is the myerson value,in a sense[J].International Journal of Game Theory,2007,36:47-55.
[7]Hamiache G.A value with incomplete information[J].Games and Economic Behavior,1999,26:59-78.
[8]Herings P J J,Van der Laan G,Talman A J J.The average tree solution for cycle-free graph games[J].Games and Economic Behavior,2008,62:77-92.
[9]Herings P J J,Van der Laan G,Talman A J J,Yang Z.The average tree solution for cooperative games with communication structure[J].Games and Economic Behavior,2010,68:626-633.
[10]Jiménez-Losada A,Fernández J R,Ordó1ez M.Myerson values for games with fuzzy communication structure[J].Fuzzy Sets and Systems,2013,213:74-90.
[11]Talman D,Yamamoto Y.Average tree solution and subcore for acyclic graph games[J].Journal of the Operations Research Society of Japan,2008,51:203-212.
[12]聂翠平,张强.模糊联盟图对策的平均树解[J].运筹学学报,2012,16:77-85.
[13]Shapley L S.A value for-person games[C].In:Kuhn H.,Tucker A.(eds)Contributions to the theory of games,vol II,Princeton University Press,Princeton:307-317.
[2]Owen G.Values of graph-restricted games[J].SIAM Journal of Algebraic Discrete Methods,1986,7:210-220.
[3]Meessen R.Communication games[D].Master’s thesis,Department of mathematics,University of Mijmegen,The Netherlands,1988.
[4]Borm P,Owen G,Tijs S.On the position value for communication situations[J].SIAM Journal on Discrete Mathematics,1992,5:305-320.
[5]Slikker M.A characterization of the position value[J].International Journal of Game Theory,2005,33:505-514.
[6]Casajus A.The position value is the myerson value,in a sense[J].International Journal of Game Theory,2007,36:47-55.
[7]Hamiache G.A value with incomplete information[J].Games and Economic Behavior,1999,26:59-78.
[8]Herings P J J,Van der Laan G,Talman A J J.The average tree solution for cycle-free graph games[J].Games and Economic Behavior,2008,62:77-92.
[9]Herings P J J,Van der Laan G,Talman A J J,Yang Z.The average tree solution for cooperative games with communication structure[J].Games and Economic Behavior,2010,68:626-633.
[10]Jiménez-Losada A,Fernández J R,Ordó1ez M.Myerson values for games with fuzzy communication structure[J].Fuzzy Sets and Systems,2013,213:74-90.
[11]Talman D,Yamamoto Y.Average tree solution and subcore for acyclic graph games[J].Journal of the Operations Research Society of Japan,2008,51:203-212.
[12]聂翠平,张强.模糊联盟图对策的平均树解[J].运筹学学报,2012,16:77-85.
[13]Shapley L S.A value for-person games[C].In:Kuhn H.,Tucker A.(eds)Contributions to the theory of games,vol II,Princeton University Press,Princeton:307-317.