基于矩阵方法的Myerson值的一种规范化

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基于矩阵方法的Myerson值的一种规范化胡勋锋¹, 李登峰¹, 张庆^1,21. 福州大学经济与管理学院, 福州 350108;
2. 海南师范大学数学与统计学院, 海口 571158 A Normalization of the Myerson Value with the Matrix Approach HU Xunfeng¹, LI Dengfeng¹, ZHANG Qing^1,21. School of Economics and Management, Fuzhou University, Fuzhou 350108, China;
2. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China

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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Aumann-Drèze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.

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收稿日期: 2016-04-22

PACS:

O225

基金资助: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.

引用本文:

胡勋锋, 李登峰, 张庆. 基于矩阵方法的Myerson值的一种规范化[J]. 应用数学学报, 2017, 40(3): 321-330. HU Xunfeng, LI Dengfeng, ZHANG Qing. A Normalization of the Myerson Value with the Matrix Approach. Acta Mathematicae Applicatae Sinica, 2017, 40(3): 321-330.

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