基于灰矩阵的合作博弈研究——以古诺寡头模型为例

针对两寡头单独决策时市场效率不高的问题,通过引入政府奖励(惩罚)值,建立带有合作约束的灰得益矩阵博弈模型.首先,增加合作约束,根据政府掌握信息的不完全性,将其奖惩力度设为灰数,得到区间灰数型得益信息.然后,采用区间灰数优势度和劣势度比较的方法实现灰数白化的过程,得到满足条件的政府奖励(惩罚)值,并求出博弈模型的均衡解.最后,应用算法实例对模型的有效性进行验证,结果表明政府调控下市场效率得到提高.     

基于偏好序列的“三方两边”威慑问题的谈判解

本文从合作博弈的角度对于"三方两边"威慑问题进行讨论,首先对局中人分类并利用不完全信息博弈的思想构造效用函数,其次构造合作双矩阵博弈,进而求出合作双矩阵博弈的谈判解,给出弱方到底该与哪一强方结盟以及结盟后双方进行恐吓的理论分析方法。最后求解具体实例,并对研究做出总结。     

不同博弈框架下多竞争零售商的双渠道供应链定价决策研究

在Bertrand竞争、Stackelberg竞争及集中决策下,研究由单制造商与多竞争零售商组成的双渠道供应链的定价决策问题。运用两阶段优化技术、博弈论及矩阵论,讨论了多竞争零售商与单制造商在价格方面相互竞争的问题,给出不同市场竞争模式及集中决策下供应链成员的博弈均衡解。对比不同博弈框架及集中决策下供应链成员的定价决策,通过数值实验分析了价格敏感度及零售商个数对最优定价决策和最大利润影响,给出一些管理学理论与见解,为双渠道供应链中各成员的管理者制定最优决策提供理论支持。     

考虑决策者风险态度的三角直觉模糊双矩阵博弈均衡及应用

在现实博弈问题中,行动方案的选择不可避免的需要对预期支付值(收益值)进行估计和排序,且选择结果往往受到决策者风险态度有的影响。针对决策者具有不同风险态度的博弈环境,基于模糊值指标和模糊度指标确定的三角直觉模糊数排序关系,研究了具有风险态度的三角直觉模糊双矩阵博弈模型,并利用双线性规划方法,给出了该环境下的均衡策略确定方法,为现实博弈均衡的确定提供了有效的途径。最后通过企业营销策略选择的应用研究,对方法的现实有效性予以说明。     

双渠道供应链协调及价值扰动

本文研究了消费者选择行为给出的需求模型下双渠道供应链的协调与价值扰动问题.利用Stackelberg博弈对系统建模及其应急管理方法考虑价值扰动问题,获得了扰动前的Stackelberg博弈系统的均衡解和中心决策系统的最优解对价值扰动具有一定的橹棒性的结果,推广了供应链中的应急管理研究结果.     

腐败的三方动态博弈模型及其治理对策

本建立了腐败问题的三方动态博弈模型，并求出博弈模型的均衡解模型，根据均衡解，提出了治理腐败问题的对策。     

不确定偏好序下的双边匹配博弈

针对带有不确定偏好序的双边匹配问题,现有方法大都仅注重整体收益之和,忽略了参与人的个体收益以及在交互选择中的策略运用.基于最大满意度准则,给出不确定序下的收益（满意度）矩阵的推导过程;然后,从个体理性视角,结合矩阵博弈的思想构建一种兼顾整体和个体收益的博弈匹配优化模型,并证明模型最优解满足纳什均衡.最后,进一步探讨各种策略选择及其优劣分析.     

相位阻尼信道条件下量子斗鸡博弈模型均衡解分析

利用量子博弈的相关理论,以噪音强度和记忆强度为参量,建立了相位阻尼信道条件下的量子斗鸡博弈模型,求出了模型的量子纳什均衡解,讨论了两参量对均衡解稳定性的影响,得出在无记忆相位阻尼信道条件下,当噪音强度小于阈值0.24时,纳什均衡仍然为帕累托最优解,当噪音强度大于0.24时,均衡解演变为另2个均衡解,不再是帕累托最优;在有记忆相位阻尼信道条件下,当噪音强度小于0.24,且记忆强度大于0.5时,均衡解是稳定的.特殊地,当信道是完全记忆时,均衡解的稳定性与噪音强度无关.     

区间合作博弈Shapley值的矩阵计算方法

在合作博弈中,Shapley单点解按照参与者对联盟的边际贡献率对联盟的收益进行分配.联盟收益具有不确定性,往往不能用精确数值表示,更多学者关注特征函数取值为有限区间的合作博弈(区间合作博弈)的收益分配.文章利用矩阵半张量积,研究区间合作博弈中含有折扣因子的Shapley区间值的矩阵计算.首先利用矩阵的半张量积将合作博弈的特征函数表示为矩阵形式,得到特征函数区间矩阵.然后通过构造区间合作博弈Shapley矩阵,将区间合作博弈的Shapley值(区间)计算转化为矩阵形式.最后利用区间合作博弈Shapley值矩阵公式计算分析航空公司供应链联盟收益的Shapley值.文章给出的区间合作博弈Shapley值的矩阵计算公式形式简洁,为区间合作博弈的研究提供了新的思路.     

带策略约束的区间数双矩阵博弈的双线性规划求解方法

传统区间数双矩阵博弈理论研究局中人支付值为区间数的策略选择问题,但没有考虑局中人策略选择可能受到各种约束.创建一种求解局中人策略选择受约束且支付值为区间数的双矩阵博弈（简称带策略约束的区间数双矩阵博弈）的简单、有效的双线性规划求解方法.首先,将局中人的博弈支付看作支付值区间中数值的函数.通过证明这种函数具有单调性,据此利用支付值区间的上、下界,构造了一对辅助双线性规划模型,可分别用于显式地计算任意带策略约束的区间数双矩阵博弈中局中人区间数博弈支付的上、下界及其相应的最优策略.最后,利用考虑策略约束条件下企业和政府针对发展低碳经济策略问题的算例,通过比较其与不考虑策略约束情形下的结果,说明了提出的模型和方法的有效性、优越性及可应用性.     

Estimating a survival function with incomplete cause-of-death data

We propose a random censorship model which permits uncertainty in the cause of death assessments for a subset of the subjects in a survival experiment. A nonparametric maximum likelihood approach and a “self-consistency” approach are considered. The solution sets corresponding to both approaches are found. They are infinite and identical. Only some of the solutions are consistent; i.e., the MLEs and self-consistent estimators are not consistent in general. Two estimates are thus proposed and their asymptotic properties are studied. It is shown that both estimates are strongly consistent and converge to Gaussian processes. The covariance structures of these Gaussian processes are derived.     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

Morse decompositions of nonautonomous dynamical systems

The global asymptotic behavior of dynamical systems on compact metric spaces can be described via Morse decompositions. Their components, the so-called Morse sets, are obtained as intersections of attractors and repellers of the system. In this paper, new notions of attractor and repeller for nonautonomous dynamical systems are introduced which are designed to establish nonautonomous generalizations of the Morse decomposition. The dynamical properties of these decompositions are discussed, and nonautonomous Lyapunov functions which are constant on the Morse sets are constructed explicitly. Moreover, Morse decompositions of one-dimensional and linear systems are studied.

     

Subinverses of fuzzy matrices

A matrix operation is examined for fuzzy matrices and interesting properties of fuzzy matrices are obtained using the operation. Particularly some properties concerning subinverses and regularity of fuzzy matrices are given and the largest subinverse is shown by the properties. The properties are closely related to inverses of fuzzy matrices and fuzzy equations. Moreover fuzzy preorders are examined using the matrix operation and basic properties are obtained. The results are considered to be useful for the theory of fuzzy matrices.     

Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems

Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.     

横观各向同性多孔超弹性矩形板的单向拉伸

利用横观各向同性超弹性材料的广义neo-Hookean应变能函数研究了含有多个微孔的超弹性矩形板在单向拉伸作用下的有限变形和受力分析.给出了含有某种对称性分布的多个微孔的矩形板的变形模式,通过求解该变形模式满足的微分方程,将它用两个参数表示出来.可应用最小势能原理导出变分近似解,从而得到矩形板的变形和应力分布的解析解.分析了板中微孔的增长及微孔边缘应力的分布情况,讨论了板的各向异性程度及微孔的大小和孔间距离的影响,得到了单个、三个及五个微孔板中微孔的增长变形和孔边应力分布的一些基本规律规律,并进行了相互比较.     

On the Geometry of Liouville Equation: Symmetries, Conservation Laws, and Bäcklund Transformations

Various geometrical structures related to the Liouville equation are considered. Properties of the symmetry algebra are discussed and local conserved currents are constructed. Bäcklund transformations for the Liouville equation are integrated and nontrivial generalizations of the latter are studied as well as the structures on them.     

Differential sensitivity of solutions of convex constrained optimal control problems for discrete systems

A family of optimal control problems for discrete systems that depend on a real parameter is considered. The problems are strongly convex and subject to state and control constraints. Some regularity conditions are imposed on the constraints.The control problems are reformulated as mathematical programming problems. It is shown that both the primal and dual optimal variables for these problems are right-differentiable functions of a parameter. The right-derivatives are characterized as solutions to auxiliary quadratic control problems. Conditions of continuous differentiability are discussed, and some estimates of the rate of convergence of the difference quotients to the respective derivatives are given.     

Enumeration of point-determining graphs

Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the combinatorial theory of species to enumerate these graphs as well as the connected cases.     

具有双裂纹的弹性复合材料板承受剪切冲击时的动应力强度因子

本文研究了两个材半限弹性的接合面附近存在与接合面平行的双裂纹，并承受剪切冲击时的瞬态应力，运用付里叶（Ｆｏｕｒｉｅｒ）和拉普拉斯（Ｌａｐｌａｃｅ）变换，将问题归结为求解二元积分方程，求解时将裂纹所在面上，下的位移差展成级数，并让其自动满足裂纹面外的位移差为零的条件，利用裂纹面上的边界条件和施密特（Ｓｃｈｍｉｄｔ）方法求解级数中的待定系数，在拉普拉斯像空间中，求得动应力强度因子，并将其数值地逆变换至