杨慧;丁正生;宋雪丽;

• 1:西北工业大学理学院
• 2:西安科技大学理学院

摘要(Abstract)：

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。

关键词(KeyWords)： 合作对策;加权不可分成本值;优化实现;加权对称性;公理化

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11601417);; 陕西省自然科学基金(2018JM1047)

作者(Author): 杨慧;丁正生;宋雪丽;

Email:

DOI: 10.13800/j.cnki.xakjdxxb.2020.0320

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