基于Shapley-value法的联盟利益分配研究

联盟利益分配是否合理关乎联盟组织运营效率高低以及联盟目标能否实现,因此至关重要。以建筑业产业为例,技术创新战略联盟属于多方参与的联盟,各个单位情况皆有不同。考虑到建筑业产业技术创新战略联盟的特殊性,在对比分析多种联盟利益分配研究方法的基础上,又对联盟利益分配影响因素进行了分析,然后将夏普利值法运用到建筑业产业技术创新战略联盟的利益分配中,进而求得出相对公平的利益分配方案。

中国人均CO_2排放水平地区差异的成因分析——基于GINI系数和回归的Shapley Value分解方法

根据2000-2011年中国省际面板数据,以GINI系数为衡量指标,测算了人均CO2排放水平的地区差异,分析了人均CO2排放水平随时间的演变趋势,在此基础上采用基于回归的Shapley Value分解方法,对中国人均CO2排放水平地区差异形成原因进行了考察,探究各影响因素对差异程度的影响水平,从而为有效缩小地区差异和制定CO2减排政策提供有益的参考。结果表明：人均能源消费量因素的影响程度最大,平均贡献率为72.80%,各省份的经济发展水平和产业结构是人均CO2排放水平省际差异的第二大贡献因素,其平均贡献率依次为8.01%与10.20%,且在不同的时间段其结果有所不同。排在第四位和第五位的因素分别是城镇化水平和对外开放水平,二者都是影响人均CO2排放水平省际差异的重要因素,平均贡献率分别达到5.17%与3.81%。

基于Shapley Value方法的金融控股公司综合经营风险评估研究——以光大集团和中信集团为例

金融控股公司综合经营风险评估是审慎监管的重要内容。本文在微观层面上运用Shapley Value方法,评估了光大集团和中信集团等金融控股公司的金融子公司对整个集团的重要性程度,探讨了金融集团内部的风险结构,并对影响金融子公司重要性程度的因素进行了分析。结果表明,规模因素是影响金融子公司重要性程度的关键性因素,而规模调整重要性程度可以作为金融控股公司进行综合经营投资决策的依据。本文将对金融控股公司风险评估的研究从理论到实践推进了一步,提出了一套与实际数据相结合的评估方法,具有一定的现实意义。

基于TOPSIS-Shapley值法的梯级水电站补偿效益分摊研究

针对流域内联合电站数目众多但利益分配存在纠纷的情况,旨在提出一种更为合理的梯级电站利益分配方法。基于Shapley值法和TOPSIS法,综合考虑电站贡献及电站对不同客观分摊方法的相对满意程度,建立TOPSIS-Shapley值法梯级电站补偿效益分摊模型,同时为解决Shapley值法在求解多利益主体梯级电站联合调度增益分配问题中的局限性,引入聚合降维思想。模型思路如下:将上游电站联合调度前后梯级发电效益的增量作为补偿效益,首先采取四种不同的客观分摊方法对电站特性参数指标进行计算,构成TOPSIS的基础决策矩阵,利用TOPSIS原理得出电站对各个分摊方法的相对满意度,同时采用联盟博弈理论,计算电站所有可能联盟方式下的发电效益,得到基于Shapley值的补偿效益分摊结果,最后将TOPSIS原理得出的分摊系数与由Shapley值法所得的分摊系数结合形成综合分摊权重,应用于黑河上游的八级电站补偿效益分摊中。工程应用实例表明:该方法不仅考虑了联盟电站对整体的边际贡献和各电站的分摊满意程度,且兼顾了电站的特性指标差异,合理量化和分配了各电站间的发电补偿效益,分摊结果公平合理、易被各方接受,可促进流域各级电站参与联合调度从而达到整体效益最大的目标,对于数量较多的梯级水电站补偿效益分配问题具有重要参考意义。

基于Shapley-Value的梯级水库联合调度效益分配方法探讨

目前梯级水库在联合调度时由于补偿效益分配制度上的不合理,致使一些调节性能较好的电站在联合调度过程中得不到公正的对待,从而影响了这些电站对联合调度的积极性。针对上述问题,以三峡梯级和清江梯级五库联合调度为例,引入博弈论中的Shapley-Value法对联合调度所产生效益分配方法问题进行了探讨。结果表明:该方法不仅具有很强的操作性,并且在分配过程中充分考虑了调节性能好的清江梯级在系统参与调峰过程中的效益补偿,其分配结果对各参与方都是公平合理的,从而使各梯级都有参与合作的积极性,有利于实现梯级水库群总效益最优的目标。

Shapley值及其应用

Shapley值是合作博弈理论中最重要的概念之一,其在经济学、社会管理等领域具有十分广泛的应用.本文回顾了合作博弈的Shapley值的理论研究,并从Shapley-Shubik权力指数、拼车费用分摊、图博弈的Page-Shapley值以及SHAP方法与机器学习等4个方面介绍了Shapley值的应用进展.

Profit Allocation Scheme Among Players in Supply-Chain Based on Shapley Value of Fuzzy Bi-cooperative Games

The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.

Profit Allocation Scheme among Partners in Virtual Enterprises Based on Fuzzy Shapley Values

Fuzzy Shapley values are developed based on classical Shapley values and used to allocate profit among partners in virtual enterprises （VE）. Axioms of the classical Shapley value are extended to Shapley values with fuzzy payoffs by using fuzzy sets theory. Fuzzy Shapley function is defined based on these extended axioms. From the viewpoint the allocation for each partner should be a crisp value rather a fuzzy membership function at the end of cooperation, a crisp allocation scheme based on fuzzy Shapley values is proposed.

Shapley Value for Cooperative Games with Fuzzy Coalition

Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable to both supperadditive and subadditvie cooperative games while other kinds of fuzzy cooperative games can only be superadditive. An explicit form of the Shapley function on fuzzy games with λ-fuzzy measure was also proposed.

On the Coalitional Rationality and the Inverse Problem for Shapley Value and the Semivalues

In cooperative game theory, a central problem is to allocate fairly the win of the grand coalition to the players who agreed to cooperate and form the grand coalition. Such allocations are obtained by means of values, having some fairness properties, expressed in most cases by groups of axioms. In an earlier work, we solved what we called the Inverse Problem for Semivalues, in which the main result was offering an explicit formula providing the set of all games with an a priori given Semivalue, associated with a given weight vector. However, in this set there is an infinite set of games for which the Semivalues are not coalitional rational, perhaps not efficient, so that these are not fair practical solutions of the above fundamental problem. Among the Semivalues, coalitional rational solutions for the Shapley Value and the Banzhaf Value have been given in two more recent works. In the present paper, based upon a general potential basis, relative to Semivalues, for a given game and a given Semivalue, we solve the connected problem: in the Inverse Set, find out a game with the same Semivalue, which is also coalitional rational. Several examples will illustrate the corresponding numerical technique.

效用可转移合作博弈的Shapley值公理化研究进展综述

随着全球经济融合和国际关系日益紧密,合作共赢已然成为当今时代的核心趋势。合作博弈理论作为研究合作问题的有力工具,主要探讨如何在参与者之间分配合作所产生的收益。Shapley值作为合作博弈中最重要的单值解之一,具有重要研究意义与价值。本文将主要介绍目前Shapley值公理化的研究工作,从可加性、均衡贡献性、边际性、公平性、简约一致性、相关一致性和一些特殊的参与者性的角度,分别归纳整理了Shapley值基于这些性质的公理化研究结论。最后对未来研究进行了展望。

基于Shapley值与全局和声搜索算法的电网投资组合策略

随着新型电力系统建设的加速推进,电网投资的力度持续攀升,企业须探索更加合理高效的电网投资策略,以实现最优的综合效益。为此,从经济、社会、环保和安全的维度出发,以电网项目投资的综合效益为优化目标,对投资组合策略进行研究。首先,应用Shapley值法对各效益函数的占比进行分摊,以呈现不同效益指标的特性。其次,在考虑投资能力、负荷需求等关键约束的基础上,设计了电网项目投资组合优化模型,并采用全局和声搜索算法进行求解。最后,构建算例对投资组合策略进行验证。算例结果表明,所提方法能够协助决策者在新形势下制定最优的电网投资策略。

Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators

Two interval-valued intuitionistic uncertain linguistic hybrid operators cal ed the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging （I-IIULHSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric （I-IIULHSG） operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley averaging （I-IIULHλSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley geometric （I-IIULHλSG） operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.

基于改进Shapley值法的风-光-水-储多主体互补发电系统合作增益分配策略

为了充分发挥系统中可调节资源的自身优势,利用变速抽水蓄能机组配合小水电机组进行常规调节,并考虑变速抽水蓄能机组的快速响应特性,提出了兼顾系统小时级以及秒级安全性的风-光-水-储多主体互补发电系统的联合优化调度模型。为了降低合作博弈高效性算法线性增长的计算复杂度,基于改进Shapely值法提出了一种大规模利益主体的合作增量效益(增益)分配策略。通过资源聚合,对高维度问题进行降维处理,利用Shapley值法进行初始分配;构建合作增益贡献指标,采用非对称纳什谈判理论对同类型的不同主体进行细化分配。以某流域风-光-水-储10主体互补发电系统为仿真算例,结果表明:抽水蓄能机组与小水电机组互补运行可以提升系统的灵活性和安全性;基于改进Shapley值法的合作增益分配策略具有计算高效性以及应用可行性。

基于Shapley值的作战体系单元价值评估

现代战争是体系与体系的对抗,如何根据作战体系特征进行有效建模,分析拓扑结构及作战功能,准确评估复杂作战体系中各军事单元的实际价值,不仅能够对敌方目标进行有效打击,也可用于己方作战单元的有效防护。将作战体系按照“侦、控、打、保、评”功能域进行划分,将其归纳为包括侦察网、指挥网、战斗网、通讯网4个核心子网的耦合作战体系,继而转化为4层多路复用网络,在充分考虑网络结构以及军事特征的基础上,构建了基于Shapley值的体系作战单元价值评估算法,并提出基于系统功能损毁曲线的效能仿真验证方法。经过与其他节点重要性计算方法比较,所提出的方法具有较高的准确度和较低的计算复杂度,可以迅速获得可靠的评估结果。

On the Coalitional Rationality of the Shapley Value and Other Efficient Values of Cooperative TU Games

In the theory of cooperative transferable utilities games, (TU games), the Efficient Values, that is those which show how the win of the grand coalition is shared by the players, may not be a good solution to give a fair outcome to each player. In an earlier work of the author, the Inverse Problem has been stated and explicitely solved for the Shapley Value and for the Least Square Values. In the present paper, for a given vector, which is the Shapley Value of a game, but it is not coalitional rational, that is it does not belong to the Core of the game, we would like to find out a new game with the Shapley Value equal to the a priori given vector and for which this vector is also in the Core of the game. In other words, in the Inverse Set relative to the Shapley Value, we want to find out a new game, for which the Shapley Value is coalitional rational. The results show how such a game may be obtained, and some examples are illustrating the technique. Moreover, it is shown that beside the original game, there are always other games for which the given vector is not in the Core. The similar problem is solved for the Least Square Values.

Egalitarian Allocations and the Inverse Problem for the Shapley Value

In a cooperative transferable utilities game, the allocation of the win of the grand coalition is an Egalitarian Allocation, if this win is divided into equal parts among all players. The Inverse Set relative to the Shapley Value of a game is a set of games in which the Shapley Value is the same as the initial one. In the Inverse Set, we determined a family of games for which the Shapley Value is also a coalitional rational value. The Egalitarian Allocation of the game is efficient, so that in the set called the Inverse Set relative to the Shapley Value, the allocation is the same as the initial one, but may not be coalitional rational. In this paper, we shall find out in the same family of the Inverse Set, a subfamily of games with the Egalitarian Allocation is also a coalitional rational value. We show some relationship between the two sets of games, where our values are coalitional rational. Finally, we shall discuss the possibility that our procedure may be used for solving a very similar problem for other efficient values. Numerical examples show the procedure to get solutions for the efficient values.

基于AHP-Shapley的家电制造业供应链收益分配研究

收益分配是影响家电制造业供应链能否顺利运行的重要因素。针对现阶段供应链收益分配存在的问题以及传统的Shapley值法的不足之处,综合考虑影响家电制造业供应链收益分配的主要因素,将风险承担、成本投入和努力程度考虑在收益分配策略之中,提出基于AHP(层次分析法)-Shapley值法的收益分配修正模型,结合算例对改进前后的收益分配方案进行比较。结果显示,改进后的Shapley值法能够得出更加公平合理的收益分配方案,有利于促进家电制造业供应链的长远发展。

The Mechanism Research of Green Supply Chain Synergy Profit Distribution Based on the Shapley Value Method

Under green supply chain mode, how to Carry out the distribution of profits between subjects is an important problem. Through the comparison of the green supply chain benefit allocation of non-cooperative game and cooperative game the payoffmatrix, it is clearly that the necessity of interest distribution cooperative game. Put general manufacturing enterprises of green supply chain as the research object, using Shapley value method for theory analysis and example verification, vertifys that enterprise synergy gains more than their own separate management, and puts forward a feasible path of supply chain collaboration through the construction of the distribution of interests coordination model.

Risk Sharing Method of PPP Model for Rural Sewage Treatment - Based on Interval Fuzzy Shapley Value

Rural sewage treatment is in need of more capital investment,in which the financing model of PPP(public-private partnership)is able to encourage the investment of social capital in this sector.Risk sharing is one of the core features in the PPP model.In view that the risk loss of projects cannot be accurately estimated,this article describes the uncertainty of risk loss with fuzzy numbers and allocates the distribution of risk loss among the participants of rural sewage treatment PPP projects with interval fuzzy Shapley value to ensure a more reasonable and effective risk distribution.