基于矩阵方法的Myerson值的一种规范化

发布时间：2018-05-27 16:39

本文选题：合作对策 + 图结构　；参考：《应用数学学报》2017年03期

【摘要】：在合作对策中,将一个值规范化意味着让其满足有效性.Hamiache利用矩阵方法得到了带图结构效用可转移合作对策Myerson值的一种规范化.通过给出一种新的满足最小划分唯一性的集合簇,本文利用矩阵方法得到了Myerson值的另一种规范化.特殊地,当所考虑的图结构在各连通分支上的限制均为完全图时,文中给出了带联盟结构效用可转移合作对策AumannDrèze值的一种规范化.与其它Myerson值规范化的比较分析表明本文规范化与van den Brink等的等价.由此van den Brink等的规范化与Hamiache的规范化都可用矩阵方法来描述,而它们之间的区别则被归结于满足最小划分唯一性的集合簇之不同.
[Abstract]:In the cooperative game, the normalization of a value means that it satisfies the validity. Hamiache uses the matrix method to obtain a normalization of the Myerson value of the cooperative game with graph structure utility transferable. By giving a new set family which satisfies the uniqueness of minimal partition, another normalization of Myerson value is obtained by using matrix method. In particular, when the restriction of the graph structure on each connected branch is a complete graph, a normalization of the AumannDr 猫 ze value of the utility transferable cooperative game with alliance structure is given in this paper. The comparison with other Myerson values shows that the normalization of this paper is equivalent to that of van den Brink et al. The normalization of van den Brink and Hamiache can be described by matrix method, and the difference between them can be attributed to the difference of sets satisfying the uniqueness of minimal partition.
【作者单位】：福州大学经济与管理学院;海南师范大学数学与统计学院;
【基金】：国家自然科学基金重点(71231003);国家自然科学基金(71572040) 福建省社会科学规划项目(FJ2015C230) 福建省自然科学基金(2016J05169)资助项目
【分类号】：O225

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