具有可行联盟的合作对策的最小二乘解
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(1. 北京理工大学管理与经济学院,北京100081;2. 广州中大控股有限公司,广州510275;3. 首都师范大学管理学院,北京100089)

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E-mail: zhengxingzou@126.com.

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O225;F224.32

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国家自然科学基金项目(71771025,71801016,71871002,71874112,71561022);教育部人文社会科学研究青年基金项目(17YJC630203).


The least square value for cooperative games with feasible coalitions
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(1. School of Management and Economics,Beijing Institute of Technology,Beijing100081,China;2. Guangzhou Zhongda Holding Company Limited,Guangzhou510275,China;3. School of Management,Capital Normal University,Beijing100089,China)

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    摘要:

    最小二乘解是基于最小平方优化方法得到的使联盟中局中人的分配值之和与联盟收益的期望偏差最小的分配方案.为了拓展最小二乘解的适用范围,构建可行联盟集合限制下最小二乘解的最优化模型,根据凸规划理论探讨该最小二乘解的存在性及唯一性条件,进而利用拉格朗日乘子法给出求解最小二乘解的矩阵方程,并基于此探讨解的具体表达式和一些重要性质.同时,基于不可分开的局中人获得相同分配值这一分配准则,在最小二乘解的基础上提出对称最小二乘解,并讨论其唯一性条件及相关性质.值得指出的是,当且仅当其可行联盟集合为非奇异时,具有可行联盟的合作对策存在唯一的最小二乘解.所提出的最小二乘解可为局中人合作具有限制时的收益分配问题提供理论依据和决策参考.

    Abstract:

    The least square value for classical cooperative games provides a kind of least square optimization method of allocating benefits to the players, which minimizes the expected deviation between the payoffs and the worths of all coalitions. This paper constructs an optimization model for the least square value of cooperative games in which cooperation among players is based on a set system of feasible coalitions. The existence and uniqueness of the least square value are investigated on the basis of the convex programming theory. Meanwhile, an equivalent matrix equation for solving the least square value is obtained by using the Lagrange multiplier method, and then, based on this equation, the expression and several important properties of the value are discussed. Besides, the so-called symmetric least square value is proposed by employing a distribution rule that the inseparable players gain the same payoffs, and its properties are also studied. It is worth noting that the class of cooperative games with feasible coalitions has a unique least square value if and only if the rank of the set of feasible coalitions is full. These results can provide theoretical perspective and decision-making reference for distributing the worth of players when not all coalitons can be formed.

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邹正兴,张强,吴佳颖,等.具有可行联盟的合作对策的最小二乘解[J].控制与决策,2020,35(4):965-972

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  • 在线发布日期: 2020-03-03
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