具有风险因素的多联盟部分合作对策

多联盟部分合作对策是指对策中的局中人通过引入合作函数,彼此合作或采取单独行动来对非合作对策规则进行更改,形成具有多联盟结构的扩展型部分合作对策.本文克服多联盟部分合作对策中不同局中人联盟单调递增约束,局中人加入联盟后可以退出加入到其他联盟中;同时考虑风险因素的影响,采用专家打分法和网络分析法(ANP)重新确定联盟局中人各自所占的权重,对多联盟部分合作对策中构造的合作子对策的联盟收益分配方式进行改进,从而建立具有风险因素的多联盟部分合作对策模型,并利用逆推归纳法得到对策解的算法.最后通过实例说明所建模型及结论的合理性,体现实际经济管理过程中结盟的变化和风险的影响.     

联盟剖分型单向流动态网络生成对策

通过定义联盟同质费用研究考察具有固定联盟剖分的单向流动态网络生成对策.局中人通过采取局部行动生成网络,行动的原则是最大化其所在联盟的整益.选择B&G函数作为局中人的基本支付函数,诱导产生联盟-局中人的B&G函数.在新的规则之下,分别给出了局部纳什网的存在性、结构特性及其动态生成进程的定理.     

拟阵上合作对策的Banzhaf函数

本文结合文[1,2]中关于拟阵上静态结构和动态结构合作对策Shapley函数的描述,探讨了两类拟阵上的Banzhaf函数.通过给出相应的公理体系,论述了两类拟阵上Banzhaf函数的存在性和唯一性,拓展了拟阵上分配指标的研究范围.同时讨论了两类合作对策上Banzhaf函数的有关性质.最后通过算例来说明局中人在此类合作对策中的Banzhaf指标.     

联盟收益不确定下合作博弈的多目标粒子群扩展算法求解

在传统的合作博弈求解中,通常假设联盟收益确定或者局中人对联盟收益取值意见一致.现实中,联盟收益往往不确定,局中人对联盟收益取值意见不一致,且联盟分配方案的达成通常是局中人基于个体理性与判断进行多轮谈判,互相影响、相互妥协、最终趋同的结果.针对这种情况,本文首先对联盟收益不确定时局中人的收益进行描述,建立合作博弈的扩展模型,再考虑局中人的理性互动与策略博弈,借鉴群智能的建模思想和求解思路,利用多目标粒子群扩展算法对模型进行求解.本文对于联盟收益不确定时合作博弈的求解提供了新的思路与方法.     

基于风险偏好与满意度的区间值合作对策

研究区间Shapley值一般是以超可加区间值合作对策或凸区间值合作对策为前提,但这限制了区间Shapley值的适用范围。本文以区间数的接受指标及局中人对风险的偏好水平为基础,提出了局中人满意度的概念,并利用满意度对区间值合作对策进行了探讨。通过计算区间值合作对策的局中人与联盟对其区间Shapley值的满意度,来判断区间Shapley值是否被局中人或联盟接受,形成的联盟是否稳定,拓展了区间值合作对策Shapley值的适用范围。同时,得到了当区间值合作对策满足一定条件时满意度的一些性质。     

微分对策中的联盟解

提出时间区间[t_0,∞)上的n人微分对策两阶段联盟解. 在第一阶段不能形成大联盟的假设是自然的,即源于这一思想. 在第一阶段以联盟作为局中人的对策中计算得到其纳什均衡,之后对每个联盟的收益按Shapley值进行分配. 一个n人微分减排模型的例子阐明了上述结果.     

基于匹配序的合作对策联盟形成决策方法及其应用

合作对策中,联盟的形成过程是联盟一切活动的基础,直接影响着合作的稳定性与可持续发展。本文在分析局中人心理,情感,现实等因素对联盟形成所产生影响的基础上,首先定义了主观偏好标度值量化了心理、情感等因素,定义了收益分配函数将现实因素量化,构建了综合匹配函数作为局中人选择合作伙伴的一个序标准,通过定义匹配请求、交互匹配、直接交互匹配等概念,构建了基于匹配序的联盟形成决策模型,并证明了在特定情况下直接交互匹配的存在必然性。其次,给出了基于匹配序的联盟形成方法步骤,演化了大联盟的形成过程。最后通过具体实例验证了该决策方法的有效性与合理性。结果表明,该方法能有效的形成一系列可行且稳定的联盟结构,能快速演化联盟的形成过程,为有效解决联盟形成问题奠定了良好基础。     

具有多联盟结构的扩展型部分合作对策

通过定义新的合作函数,得到具有多联盟结构的扩展型部分合作对策,并运用逆推归纳法建立部分合作对策解的概念,构造出相应的最优路径. 模型克服了经典合作对策模型中对策树上任意结点处只能形成简单联盟结构的局限性.     

优先联盟间有权限结构限制的合作对策的联盟限制Owen值

考虑局中人结成优先联盟参与合作,并且优先联盟之间具有权限结构限制的合作对策,利用Owen值的两阶段分配思路并考虑到优先联盟之间权限结构对合作的限制,定义这类合作对策一个解,证明了解的公理化结论,并验证了公理化条件的独立性.最后给出了算例分析,说明解在合作收益分配问题的应用.     

区间支付图对策上的平均树解

结合图对策和具有区间支付的模糊合作对策理论,引入区间支付图对策,提出区间平均树解,此解可以看做是经典图对策中平均树解的推广,并通过算例说明区间平均树解的应用性.分析了区间平均树解的相对分支有效性.当区间支付图对策满足严格超可加性时,每个局中人参加联盟得到的收益不小于其单干所得支付.最后,讨论了经典平均树解与区间平均树解之间的关系.     

The Myerson value for directed graph games

A directed graph game consists of a cooperative game with transferable utility and a digraph which describes limited cooperation and the dominance relation among the players. Under the assumption that only coalitions of strongly connected players are able to fully cooperate, we introduce the digraph-restricted game in which a non-strongly connected coalition can only realize the sum of the worths of its strong components. The Myerson value for directed graph games is defined as the Shapley value of the digraph-restricted game. We establish axiomatic characterizations of the Myerson value for directed graph games by strong component efficiency and either fairness or bi-fairness.     

A ranking for the nodes of directed graphs based on game theory (Poster Presentation)

We introduce a value that allows us to emphasize the importance of each player in a cooperative game when the cooperation possibilities are limited according to the links of an oriented network. The proposed concept of accessibility tries to conjugate the marginal contributions of each node as a game player with the cooperation geometry imposed by the directed graph that models the network. As a consequence, it is possible to offer a ranking for the nodes of directed graphs. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Iterative Procedure for Evaluating Digraph Competitions

A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.     

Inducing cooperation by reciprocative strategy in non-zero-sum games

In this paper, we investigate the use of reciprocative strategy to induce cooperative behavior in non-zero-sum games. Reciprocative behavior is defined mathematically in the context of a two-person non-zero-sum game in which both the players have a common set of pure strategies. Conditions under which mutual cooperative behavior results when one of the players responds optimally to reciprocative behavior by the other player are described. Also, the desirability of playing the reciprocative strategy is investigated by stating conditions under which reciprocative strategy by one of the players or by both the players leading to mutual cooperative behavior is a Nash equilibrium outcome.     

A recognition algorithm for the intersection graphs of directed paths in directed trees

Consider a finite family of non-empty sets. The intersection graph of this family is obtained by representing each set by a vertex, two vertices being connected by an edge if and only if the corresponding sets intersect. The intersection graph of a family of directed paths in a directed tree is called a directed path graph. In this paper we present an efficient algorithm which constructs to a given graph a representation by a family of directed paths on a directed tree, if one exists. Also, we prove that a graph is a proper directed path graph if and only if it is a directed path graph.     

超图结构上合作博弈的赋权Position值

在合作博弈的一般模型中总是假设所有联盟都能形成。不过,在实际中由于受到一些因素的制约,有些联盟是不能形成的。基于此,Myerson提出了具有图通讯结构的合作博弈。Myerson值和Position值是超图博弈上的两个重要分配规则。2005年,Slikker给出了在图博弈上Position值的公理化刻画。但超图博弈上Position值的公理化刻画一直悬而未决。本文通过引入 “赋权平衡超边贡献公理”,并结合经典的“分支有效性”,提出了超图博弈上赋权Position值的公理化刻画。作为推论,解决了超图博弈上Position值的公理化刻画问题。     

On some balanced, totally balanced and submodular delivery games

This paper studies a class of delivery problems associated with the Chinese postman problem and a corresponding class of delivery games. A delivery problem in this class is determined by a connected graph, a cost function defined on its edges and a special chosen vertex in that graph which will be referred to as the post office. It is assumed that the edges in the graph are owned by different individuals and the delivery game is concerned with the allocation of the traveling costs incurred by the server, who starts at the post office and is expected to traverse all edges in the graph before returning to the post office. A graph G is called Chinese postman-submodular, or, for short, CP-submodular (CP-totally balanced, CP-balanced, respectively) if for each delivery problem in which G is the underlying graph the associated delivery game is submodular (totally balanced, balanced, respectively). For undirected graphs we prove that CP-submodular graphs and CP-totally balanced graphs are weakly cyclic graphs and conversely. An undirected graph is shown to be CP-balanced if and only if it is a weakly Euler graph. For directed graphs, CP-submodular graphs can be characterized by directed weakly cyclic graphs. Further, it is proven that any strongly connected directed graph is CP-balanced. For mixed graphs it is shown that a graph is CP-submodular if and only if it is a mixed weakly cyclic graph. Finally, we note that undirected, directed and mixed weakly cyclic graphs can be recognized in linear time. Received May 20, 1997 / Revised version received August 18, 1998?Published online June 11, 1999     

Inheritance of properties in communication situations

In this paper we consider cooperative games in which the possibilities for cooperation between the players are restricted because communication between the players is restricted. The bilateral communication possibilities are modeled by means of a (communication) graph. We are interested in how the communication restrictions influence the game. In particular, we investigate what conditions on the communication graph guarantee that certain appealing properties of the original game are inherited by the graph-restricted game, the game that arises once the communication restrictions are taken into account. We study inheritance of the following properties: average convexity, inclusion of the Shapley value in the core, inclusion of the Shapley values of a game and all its subgames in the corresponding cores, existence of a population monotonic allocation scheme, and the property that the extended Shapley value is a population monotonic allocation scheme. Received May 1998/Revised version January 2000     

Colouring games based on autotopisms of Latin hyper-rectangles

Abstract

Every partial colouring of a Hamming graph is uniquely related to a partial Latin hyper-rectangle. In this paper we introduce the Θ-stabilized (a, b)-colouring game for Hamming graphs, a variant of the (a, b)-colouring game so that each move must respect a given autotopism Θ of the resulting partial Latin hyperrectangle. We examine the complexity of this variant by means of its chromatic number. We focus in particular on the bi-dimensional case, for which the game is played on the Cartesian product of two complete graphs, and also on the hypercube case.     

考虑延迟现象的质量改进投入和营销努力动态协同策略

利用时滞微分方程刻画质量改进投入对品牌商誉提升的延迟现象,分别构建了制造商和零售商采取非合作博弈、合作博弈以及成本分担的部分合作博弈(制造商参与营销的单向部分合作博弈、零售商参与生产的单向部分合作博弈、制造商参与营销及零售商参与生产的双向部分合作博弈)五种决策模式下的微分博弈模型。借助哈密尔顿极大值原理,求解得到五种情形下的制造商最优质量改进投入策略和零售商的最优营销努力策略以及供应链利润。对比五种博弈模式下的结果发现:1)延时现象会降低制造商进行质量改进投入的积极性,但对零售商营销努力无影响;品牌商誉在延迟现象影响下出现先衰减后提升的演进规律;2)合作博弈对于供应链绩效总是最优的,三种成本分担的部分合作博弈契约虽不能实现供应链的完全协调,但可以对非合作博弈情形进行帕累托改进;3)对比两种单向部分合作博弈,在提高供应链利润方面,制造商参与营销的成本分担契约优于零售商参与生产的成本分担契约;4)三种成本分担契约中,双向合作的部分合作博弈是供应链的最优选择,但随着延迟时间增大,其帕累托改进效果将不再明显。