[1]杨 慧,丁正生,宋雪丽.加权不可分成本值的优化实现及公理化[J].西安科技大学学报,2020,(03):518-524.[doi:10.13800/j.cnki.xakjdxxb.2020.0320]
 YANG Hui,DING Zheng-sheng,SONG Xue-li.Optimization implementation and axiomatization of the weighted nonseparable cost value[J].Journal of Xi'an University of Science and Technology,2020,(03):518-524.[doi:10.13800/j.cnki.xakjdxxb.2020.0320]
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加权不可分成本值的优化实现及公理化(/HTML)
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西安科技大学学报[ISSN:1672-9315/CN:61-1434/N]

卷:
期数:
2020年03期
页码:
518-524
栏目:
出版日期:
2020-05-15

文章信息/Info

Title:
Optimization implementation and axiomatization of the weighted nonseparable cost value
文章编号:
1672-9315(2020)03-0518-07
作者:
杨 慧12丁正生2宋雪丽2
(1.西北工业大学 理学院,陕西 西安 710072; 2.西安科技大学 理学院,陕西 西安 710054)
Author(s):
YANG Hui12DING Zheng-sheng2SONG Xue-li2
(1.School of Natural and Applied Sciences,Northwestern Polytechnical University,Xi'an 710072,China; 2.School of Science,Xi'an University of Science and Technology,Xi'an 710054,China)
关键词:
合作对策 加权不可分成本值 优化实现 加权对称性 公理化
Keywords:
cooperative games the weighted nonseparable cost value optimization implementation weighted symmetry axiomatization
分类号:
O 225
DOI:
10.13800/j.cnki.xakjdxxb.2020.0320
文献标志码:
A
摘要:
合作对策研究如何公平合理地分配参与者通过相互合作形成联盟后获得的最大收益。将权重系统引入合作对策,定义了加权不可分成本值,首先分配给每个参与者其大联盟边际贡献,再将不可分成本值依据权重系数进行分配。构造去权平方抱怨度优化模型,证明其最优解与加权不可分成本值一致,优化实现了加权不可分成本值。其次定义大联盟边际标准对策的加权对称性,用公理化的方法研究了加权不可分成本值是合作对策中唯一同时满足有效性、 可加性、非本质对策性和大联盟边际标准对策的加权对称性的解。用协变性替代非本质对策性对不可分成本值做出新的公理化证明。最后在实际应用中对比研究不同的分配规则,分析了加权不可分成本值的合理性。结果表明:加权不可分成本值有效地综合了分配问题中的平均主义原则和功利主义原则,可以均衡地最小化所有参与者的去权平方抱怨度,是去除权重影响后距离理想收益最近的分配方案。
Abstract:
The cooperative game aims at studying how to fairly distribute the maximum payoff that is acquired by players'mutual cooperation.The weighted nonseparable cost value was defined through introducing a weight system.This value firstly allocated to each player his grand marginal contribution,then divided the remaining nonseparable cost value based on the weight coefficient.The optimization model of the dis-weighted square complaint was constructed applying the optimization theory.The model's unique optimal solution was proved to be coincide with the weighted nonseparable cost value,which exhibited the optimization implementation for this value.Through defining the weighted symmetry restricted in the grand marginal normalized game and applying the axiomatization method,the paper proved that the weighted nonseparable cost value was the unique value that possessed efficiency,additivity,inessential game property and the weighted symmetry restricted in the grand marginal normalized game.A new axiomatization was put forward by substituting the axiom of covariance for inessential game property.Based on the comparing result with other solutions,the paper validated the reasonable of the weighted nonseparable cost value.The results indicate that the weighted nonseparable cost value not only efficiently compromises the relationship between the egalitarianism and utilitarianism but also equilibratedly minimizes the dis-weighted square complaint.The weighed nonseparable cost value is therefore proved to be the closest solution to the ideal payoff after removing the effect of the weight.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2019-11-06 责任编辑:刘 洁
基金项目:国家自然科学基金(11601417); 陕西省自然科学基金(2018JM1047)
通信作者:杨 慧(1981-),女,山西长治人,博士研究生,讲师,E-mail:yangh816@mail.nwpu.edu.cn
更新日期/Last Update: 2020-05-15