非合作-合作两型博弈的Shapley值纯策略纳什均衡解求解方法

在合作中又有竞争的"经济全球化"时代背景下,经济实体之间越来越多地体现出竞争与合作交织的特点,既有策略的选择,同时也有利益的分配或者成本的分摊,即竞争与合作相互联系。为此,Brandenburger和Stuart提出了非合作-合作两型博弈模型为这类博弈提供了有效的工具。目前非合作-合作两型博弈研究较少,且Brandenburger和Stuart提出的非合作-合作两型博弈存在一些不足：合作博弈用核心求解可能为空或者不唯一。Shapley值是一种重要的合作博弈单值解,满足匿名性、有效性、可加性和虚拟性,表达形式简单且唯一,对一些成本分摊问题和利益分配问题,给决策者提供了一个公平满意的分配方案。因此本文研究将Shapley值作为合作博弈的解时非合作-合作两型博弈解存在的条件。为了分析本文提出的基于Shapley值的非合作-合作两型博弈的新理论框架,首先给出了其特征函数满足的联盟无外部性条件。在满足此条件下,我们进一步证明了非合作-合作两型博弈解存在的条件及性质。结合数值实例比较分析合作博弈用核心和Shapley值求解非合作-合作两型博弈解的优缺点。研究表明：当用Shapley值求解合作博弈解,降低了非合作-合作两型博弈解存在条件。因此,本文的研究不仅弥补了Brandenburger和Stuart提出的非合作-合作两型博弈中合作博弈的核心为空或者不唯一的情况,而且为非合作-合作两型博弈的解提供新的理论框架,从而为既有竞争又有合作的博弈问题提供新的求解方法,因此,本文的研究具有一定的理论价值和应用价值。     

The vertex cover game: Application to transport networks

As communications are progressing, transport networks need to be monitored, more specifically, camera surveillance of violations is needed. Standards are being developed on how to install cameras, and the question of efficiently distributing surveillance devices across the road network ensue. This task is addressed in this paper by using the methods of the cooperative game theory. The vertex cover game is introduced, and its properties are studied. Since surveillance cameras are to cover all areas of the network, the characteristic function depends on the vertex covers of the graph. The Shapley–Shubik index is used as the measure of centrality. The Shapley–Shubik index is shown to be efficient in a vertex cover game for the allocation of cameras in a transport network. Proceeding from the Shapley–Shubik indices calculated in this study, recommendations were given for the allocation of surveillance cameras in a specific transport network in a district of the City of Petrozavodsk, Russia.     

Simulation of a police patrol activity

This paper describes the use of the Patrol Car Allocation Model to structure the relationships which exist between the utilization of patrol resources and various measures of performance. The relationships depict the cost vs service trade-offs that are present in patrol allocation decisions. The results of an actual study are presented along with a discussion of their potential value to the police patrol allocation function.     

基于合作博弈的易腐性产品运输设施选择的费用分配

易腐性产品的价值会随着时间而损失,运输易腐性产品时,客户除了支付运输费用外还需要承担产品的价值损失。本文把易腐性产品的价值损失和运输费用之和作为总费用,应用合作博弈理论,把易腐性产品的运输设施选择的费用分配问题构造成费用分配博弈,证明了在易腐性产品线性价值损失的情况下,运输设施选择博弈的核心非空,且为子模博弈,并讨论核仁、夏普利值、τ-值等解。论文最后讨论了有约束运输的设施选择的费用分配博弈的解的情况,说明其核心也许为空,并提出了进一步研究的方向。     

Qualitative differences in men and women police officers' experience of occupational stress

Gender differences in exposure to sources of occupational stress and experience of adverse consequences are explored in a study of 358 male and 139 female police constables engaged in uniformed patrol or detective duties from one large provincial English police force. Stressors were divided into those arising tiom police operational duties and those deriving tioni organizational and management issues. Women uniformed constables are less likely to be exposed to police operational stresson involving the potential for violence, but ifexposed they report more severe adverse reactions than uniformed policemen. Women unifomied officers and women detectives are more likely to be involved with victims ofviolence or sexual offences and the former report higher levels ofassociated self-perceived stress than their male counterparts. There are relatively few differences in exposure to organizational stressors except that women detectives and uniformed officers report higher rates of sex discrimination and prejudice than policemen. Multivariate analyses show gender and occupational role differences in qualitative features that contribute to reported psychologal distress. Results are discussed in terms of possible explanations for gender differences.     

具有联盟优先关系的模糊合作博弈的目标规划求解模型

用合作博弈研究实际管理问题中的分配方案时，常常存在一些不重要联盟或无效联盟，这些联盟影响公平合理的分配方案。因此，联盟的重要程度成为求解合作博弈必不可少的因素。本文考虑了联盟的重要性和局中人参与联盟的不确定性，研究了具有优先关系的模糊联盟合作博弈(简称为模糊合作博弈)。首先，借助于目标规划模型的优先因子可以表征联盟重要程度的思想，通过构建多优先级目标规划模型，得到模糊合作博弈新的解。其次，证明了构建的多优先级目标规划模型的解和模糊合作博弈的核心之间具有重要对应关系。最后，通过数值实例和比较分析，说明本文提出的多优先级目标规划模型求解模糊合作博弈问题的合理性和有效性。研究表明：(1)本文提出的多优先级目标规划模型考虑不同联盟重要程度，得到的解符合“多劳多得”原则，能够更公平合理解决实际管理中的分配问题。(2)本文的目标规划模型同时适用于求解存在联盟特征函数值缺失的合作博弈。与已有合作博弈的解进行比较分析，该模型无需估算无效联盟的特征函数缺失数据得到的分配值更为准确。从而，说明本文给出的目标规划求解模糊合作博弈解的模型，更符合许多管理学问题的实际情况。(3)通过多优先级目标规划模型最优解是否存在可判断模糊合作博弈的核心存在情况，若核心存在则该模型通过目标规划软件包可得到核心内的一个解，这样也得到了一个判断合作博弈核心是否存在的标准。(4)目标规划模型可弥补已有合作博弈解的一些不足，如核心可能为空集，Shapley值和最小二乘预核仁可能不满足个体合理性等。本文构建的多优先级目标规划模型不仅能求解联盟具有优先关系的模糊合作博弈，而且能够求解一般合作博弈的解，该目标规划模型作为合作博弈一种新的求解方法，能更有效地解决实际管理中的分配问题，具有更加广泛的应用价值。     

国家风险动态性的多尺度特征提取与识别:以OPEC国家为例

国家风险是经济活动主体在国际业务中所面临的来自其他国家的风险, 深入研究其内在特征, 对于理解和把握国家风险的动态演化规律有着重要意义。鉴于国家风险复杂易变的特点, 本文提出了一种基于"分解重构"思想的多尺度特征提取与识别的研究框架, 利用Ensemble EMD方法将原始国家风险值分解到短期、中期和长期三个时间尺度上, 引入方差贡献率、相关系数和Shapley值刻画各尺度与原始国家风险序列间的波动特征、模态特征以及全局重要度。以12个OPEC石油输出国为样本, 实证结果发现:利用各尺度的模态特征和波动特征可以很好地实现样本国国家风险的分类管理, 且分类具有较好的一致性;由Shapley值获得不同尺度的全局重要度, 对于全部样本国呈现出一致且稳定的内在固有特征, 即短期、中期和长期三尺度对国家风险的"贡献度"约为1:1:3。这不仅能够为国家风险管理提供了更为丰富的动态特征信息, 而且对于更为全面的国家风险特征识别、监测与预测提供了一种新的研究方法。     

基于Choquet延拓n人模糊对策的Shapley值

由于n人对策任意联盟可由它的特征向量来等价地表示,利用Choquet积分,将n人对策从集合{0,1}n延拓到[0,1]n上,通过建立公理化体系,对具有Choquet延拓形式n人模糊对策的Shapley值进行深入研究,证明了这类n人模糊对策Shapley值存在性与惟一性,并给出了此模糊对策Shapley值的解释表达式.最后将此模糊对策的Shapley值作为收益分配方案应用到供应链协作企业收益分配的实例中.     

Bargaining and Cooperation in Strategic Form Games

In this paper we view bargaining and cooperation as an interaction superimposed on a game in strategic form. A multistage bargaining procedure for N players, the “proposer commitment” procedure, is presented. It is inspired by Nash's two‐player variable‐threat model; a key feature is the commitment to “threats.” We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies, the traditional coalitional function may not be adequate when utilities are not transferable. (JEL: C70, C71, C78, D70)     

模糊合作对策的Shapley值

考虑合作对策中支付函数是模糊数的情形,利用模糊数学相关理论,对Shapley提出的三条公理进行拓广,并构造了模糊Shapley值.针对局中人在合作完成后需要对具体的联盟收益进行分配的情况,文中利用构造的模糊Shapley值隶属函数给出了确定的收益分配方案.最后将该方法应用到动态联盟伙伴企业收益分配的实例中.     

基于EOQ的集成供应成本分摊问题研究

第三方物流的集成供应是降低供应链成本的有效途径,而集成供应成本在各供应商企业之间的分摊是需要解决的核心问题.本文详细阐述了第三方物流的集成供应问题,基于合作博弈理论建立了第三方物流集成供应的成本分摊模型.在采用夏普利值法对该模型进行求解的过程中,针对夏普利值法难以赋值的问题,引入集成供应的经济订货批量模型,有效解决了了第三方物流供应成本分摊问题.最后,用算例对该方法进行了说明.     

Backward Induction Foundations of the Shapley Value

We present a noncooperative game model of coalitional bargaining, closely based on that of Gul (1989) but solvable by backward induction. In this game, Gul's condition of “value additivity” does not suffice to ensure the existence of a subgame perfect Nash equilibrium that supports the Shapley value, but a related condition—“no positive value‐externalities”—does. Multiple equilibria can arise only in the event of ties, and with a mild restriction on tie‐break rules these equilibria all support the Shapley value.     

联合订货区间值EOQ模型及变权Shapley值成本分摊方法

研究多个销售商企业组成联盟向一个供应商订购同种商品的联合订货问题。考虑到实际问题中很难预测到精确的需求，本文用区间表示单位时间需求量，研究允许缺货的销售商企业联合订货区间值EOQ模型，其中缺货完全回补。以联合订货平均成本最小为目标，结合连续有序加权集结算子求解出联合订货的周期、区间值订货量和区间值平均成本。定义变权Shapley值，给出区间值合作博弈的区间值变权Shapley值的求解方法，得出区间值变权Shapley值的表达式可直接利用相关联盟值的左、右端点计算得到。考虑联盟和局中人的相对重要性，结合需求率确定合成权重，提出基于区间值变权Shapley值的联合订货成本分摊方法。利用数值算例验证模型和方法的有效性。本文可为解决联合订货成本分摊问题提供决策参考。     

供应链不同合作模式下合作利益分配机制研究——以煤电企业供应链为例

供应链合作模式直接决定合作利益形成机理,并由此影响合作利益分配,针对不同合作模式研究合作利益分配机制十分必要。根据煤电企业供应链合作实际,运用无限阶段讨价还价博弈方法建立了基于利润分配因子的合作利益分配模型,该模型适合一方向另一方投资的合作利益分配;运用Shapley值法和风险期望原理,建立了基于合作贡献和风险补偿原则确定的合作利益分配模型,该模型适合对长期合同、战略合作等合作利益分配。本文研究结果不仅对煤电企业,而且对其他生产商与供应商之间的供应链合作利益分配机制的建立具有指导意义。     

面向价值网络的企业协同竞争博弈模型研究

运用演化博弈理论的方法,分析价值网络模式下企业的协同竞争机制,构建企业主体间协同竞争的演化博弈模型,指出价值网络模式下企业协同竞争行为的博弈过程及特点,揭示出系统的初始状态、发展阶段及利益分配机制对演化博弈过程的影响机理。     

The social construction of the meaning of acute stressors: a qualitative study of the personal accounts of police officers using a stress counselling service

The police profession is one in which acute stressors are encountered more frequently than in other occupations. Using the personal accounts of 35 police officers attending an in-house stress counselling clinic, the aim of the present study was to provide a qualitative examination of how the institutional context of policing influenced the ways in which acute stressors signified to individual police officers experiencing felt distress. Using the framework of Rational Emotive Behaviour Therapy as an analytical tool, it is argued that beliefs contributing to the experience of felt distress are related to the way in which policing as both an identity and an activity is constructed through the police organizational culture. Not only do these constructions influence the ways in which officers perceive themselves and their environments, but they also operate at the collective level to 'normalize' some emotional responses and to 'pathologize' others which, it is argued, could impact upon the outcomes of interventions such as stress counselling.     

协作车辆路径成本分摊问题的 B-T Shapley 方法

多个企业协作配送能显著地降低物流配送成本和减少尾气排放, 研究协作配送模型与成本分摊方法是亟需解决的关键问题.传统经典成本分摊方法需要计算所有子联盟的协作成本, 在本问题中等价于需要求解2N-1个 (N为企业数量) 复杂的车辆路径问题.本文建立了多方协作车辆路径问题模型, 分析了协作配送成本分摊问题的属性.基于经典的Shapley成本分摊方法, 提出了B-T (Binary Tree) Shapley近似方法, 不仅将成本分摊本身计算复杂度由O (N22N) 降为O (N2log2N) , 而且将需要求解的车辆路径问题数量由2N-1个锐减至2N-1个, 从而能够在合理时间内完成协作配送问题的成本分摊.通过求解算例和实际案例, 计算结果表明, B-T Shapley的耗时与Shapley方法相比几乎可以忽略不计, 更重要的是B-T Shapley与Shapley的成本分摊结果之间仅有细微的偏差, 其平均准确度可以达到95%左右.     

The social construction of the meaning of acute stressors: A qualitative study of the personal accounts of police officers using a stress counselling service

The police profession is one in which acute stressors are encountered more frequently than in other occupations. Using the personal accounts of 35 police officers attending an in-house stress counselling clinic, the aim of the present study was to provide a qualitative examination of how the institutional context of policing influenced the ways in which acute stressors signified to individual police officers experiencing felt distress. Using the framework of Rational Emotive Behaviour Therapy as an analytical tool, it is argued that beliefs contributing to the experience of felt distress are related to the way in which policing as both an identity and an activity is constructed through the police organizational culture. Not only do these constructions influence the ways in which officers perceive themselves and their environments, but they also operate at the collective level to 'normalize' some emotional responses and to 'pathologize' others which, it is argued, could impact upon the outcomes of interventions such as stress counselling.     

Differentiating conflicts in beliefs versus value tradeoffs in the domestic intelligence policy debate

Since the 9/11 terrorist attacks, there has been an increase in public discussion regarding U.S. domestic intelligence activities. Domestic intelligence activities focus on gathering information about potential threats from individuals within the United States, and completely rational members of the public can have different opinions about the acceptability of various alternatives depending on one's values toward privacy, civil liberty, and security. Past studies have demonstrated that construction of a multiobjective value model can help clarify public values in controversial risk debates. This research explores a range of domestic intelligence alternatives that vary on multiple objectives, and applies value-focused thinking to develop a multiattribute utility model to evaluate and compare the alternatives. The process demonstrates the feasibility of eliciting model parameters from individuals and provides a method for identifying the locus of possible disagreements among individuals. The development of the model is described first, followed by insights found from participants who provided both value tradeoffs and performance scores for six different domestic intelligence alternatives. The participants were two student groups and a group of police officers. The analysis showed differences among weights for an additive model for different stakeholder groups and differences among the performance scores. In particular, there is a "halo" effect for alternatives, such that its supporters ranked the alternative higher on all attributes compared to respondents who find the alternative unacceptable. This modeling approach and results offer organizations such as the Department of Homeland Security insights into the debate surrounding new policy initiatives, particularly those requiring sensitive value tradeoffs.