具有不对称网络外部性和纵向差异化的产品竞争策略

在产品不完全覆盖市场中,研究具有不对称网络外部性的纵向差异化产品的Bertrand价格竞争或Cournot数量竞争策略.研究表明,两产品在Cournot数量竞争中的市场利润和社会福利都大于在Bertrand价格竞争中的市场利润和社会福利.在Bertrand价格竞争或Cournot数量竞争中,当低质量产品的网络外部性较大且满足一定条件时,低质量产品也可以获得较大的市场利润;当高质量产品具有较大网络外部性,或网络外部性虽然较小但满足一定条件条件,网络外部性相等或产品都不具有网络外部性时,高质量产品获得较大的市场利润.随着网络外部性的增强,Cournot-Nash均衡点并不稳定,在重复博弈以后,均衡点向Bertrand-Nash均衡点靠近.     

两阶段双寡头垄断市场Hotelling定价模型

激烈的双寡头垄断市场竞争环境下,单一定价和歧视定价成为厂商选择的两大定价策略.考虑到网络外部效用的广泛存在性与对称性,对传统的Hotelling模型加以改进,分价格竞争和策略选择两个阶段,对双寡头垄断厂商的定价策略进行了博弈分析,指出了各种均衡情况及需满足的条件,并验证了歧视定价相对单一定价的边际成本、网络外部效应、消费者对产品的忠诚度等因素对厂商进行定价策略选择的重要影响,为其制定最优定价策略提供了指导.     

基于风险管理的动态供应链超网络均衡模型

基于风险管理的动态供应链超网络均衡模型的研究有助于供应链超网络节点厂商在动态环境下优化其风险管理,降低风险损失,提升供应链网络在风险管理下的竞争优势。本文以三层供应链超网络为研究对象,采用风险发生概率和损失函数表达供应链超网络中节点厂商中断风险的特征,构建了基于风险管理的动态供应链超网络均衡模型。模型中包括三种类型的节点,产品生产商、零售商和需求市场,生产商考虑风险损失的情况下,基于动态变化的风险、需求和成本追求个体期望效益最优化。接着,通过进化变分不等式来表达动态供应链超网络风险管理下的均衡解,并采用投影动态系统求解进化变分不等式,通过数值算例验证方法的可靠性和合理性,通过投影动态系统解释某一个厂商趋近均衡解的过程。通过单一厂商趋近均衡解的过程,阐述其他厂商相应的最优决策。     

带有网络外部性的动态寡头垄断定价

给出了带有网络外部性的两阶段寡头垄断定价模型,并用博弈论方法求解.通过与带有网络外部性的完全垄断定价模型的比较,得出重要结论:在网络外部性足够大的情况下,①寡头竞争情况下与完全垄断下情况一样,“科斯假设”将得到克服,均衡定价将呈现先低后高的情况.②对于完全垄断厂商来说,网络外部性k的增加能够增加其利润,但对于寡头竞争的企业来说,正好相反,k的增加将导致其利润的下降.     

随机需求下直销多商品流供应链网络均衡模型

建立了随机需求下直销多商品流供应链网络均衡模型,导出了供应链网络达到均衡的条件,它等价于一个有限维变分不等式.通过构建修改拟牛顿法,获得了随机需求下直销多商品流供应链网络均衡模型的解(变分不等式的解),并给出了1个算例,验证了模型的正确性和算法的可行性.     

基于网络外部性的港口FDI企业与内资港口企业博弈策略研究

将港口服务产品的网络外部性和服务质量水平引入到发货人的效用函数中,通过Hotelling价格竞争模型分析港口FDI企业与内资港口企业的博弈策略行为,分别研究在Nash和Stackelberg博弈条件下,港口服务价格、收益与网络外部性系数、服务质量水平之间的关系.理论研究的结论表明:港口FDI企业与内资港口企业在Stackelberg条件下的最优定价、均衡收益均大于Nash条件下的最优定价、均衡收益;企业最优定价随网络外部性强度线性递减,随服务水平线性递增;企业均衡收益受服务水平和网络外部性强度的影响,呈现出一定的区间变化规律,处于相同港口外部市场环境下,内资港口企业与港口FDI企业的服务策略选择和侧重点不相同.     

无限维Hamilton系统稳态解的保结构算法

基于Hamilton变分原理和Bridges意义下的多辛积分理论,提出了保持无穷维Hamilton系统稳态解能流通量和动量通量的保结构分析方法.针对复杂的无穷维Hamilton系统的多辛对称形式,首先讨论了其稳态解所满足的对称形式的守恒律问题;随后,以一个典型的无穷维Hamilton系统——Zufiria方程为例,采用box离散格式,模拟了其稳态解,并验证了算法的保结构性能.研究结果显示:采用保结构算法能够较好地模拟无穷维Hamilton系统的稳态解,并保持了无穷维Hamilton系统稳态解的能流通量和动量通量两个重要力学参量.这一研究结果将为复杂无穷维Hamilton系统稳态解的数值分析提供新的途径.     

基于Stackelberg博弈均衡的双寡头企业竞争策略

在具有网络外部性的Hotelling模型中，放松厂商定位必须局限于消费者空间的假设，运用Sackelberg博弈来研究产品具有不同边际成本结构的企业竞争策略。相比较于传统的Nash博弈价格均衡结果，当不局限厂商定位空间时，两厂商通过Sackelberg价格博弈可以选择更大的产品差异性。如果边际成本相等，两厂商在Stackelberg博弈均衡中都获得比在Nash博弈均衡中更大的市场利润，当不局限厂商定位空间时，市场先进人者获得先动优势，当局限厂商定位空间时，市场后动者获得后动优势。     

双渠道双目标的多期供应链网络均衡问题研究

以变分不等式为工具建立双渠道双目标的多期供应链网络均衡模型.在传统实体交易和电子网上交易的双渠道环境下,考虑时间因素与库存变量的影响,提出由制造商、零售商和需求市场组成的三层多期供应链网络均衡问题,其中制造商和零售商均追求经济利润最大化与风险最小化的双重目标.分别对各系统成员的独立决策行为及其相互作用进行分析,得到各层决策成员的均衡条件并给出相应经济解释,推导与双渠道双目标的多期供应链网络均衡问题等价的有限维变分不等式模型.在证明其解在一定的假设条件下存在的基础上,构造数值算例以验证模型的正确性与合理性.     

无限维Hillbert空间中单调变分不等式解的近似迭代算法

在无穷维Hillbert空间中研究了一类单调型变分不等式，把求单调型变分不等式解的问题转化为求强单调变分不等式的解，建立了一种新的迭代算法，并证明了由算法生成的迭代序列强收敛于单调变分不等式的解，从而推广了所列文献中的许多重要结果．     

Forcing strong convergence of Korpelevich’s method in Banach spaces with its applications in game theory

We develop a variant of Korpelevich’s method for solving variational inequality problems with pseudomonotone operators in Banach spaces. We establish the strong convergence of the sequence generated by the method under reasonable assumptions on the problem data. Finally, we justify the motivation of our theory by including compelling examples of infinite dimensional variational inequality problems for which our method is applicable.     

Lipschitz continuity and duality for dynamic oligopolistic market equilibrium problem with memory term

We are concerned with an infinite dimensional variational inequality which is connected with the dynamic oligopolistic market equilibrium problem. We will provide existence theorems and show, under minimal assumptions on the data, the Lipschitz continuity of the solution. Moreover a general duality theory is provided overcoming the difficulty of the voidness of the interior of the ordering cone which defines the cone constraints.     

A New Extragradient Method for Strongly Pseudomonotone Variational Inequalities

This article proposes a new extragradient solution method for strongly pseudomonotone variational inequalities. A detailed analysis of the iterative sequences’ convergence and of the range of applicability of the method is provided. Moreover, an interesting class of strongly pseudomonotone infinite dimensional variational inequality problems is considered.     

Direct pseudo‐spectral method for optimal control of obstacle problem – an optimal control problem governed by elliptic variational inequality

In this paper, a computational technique based on the pseudo‐spectral method is presented for the solution of the optimal control problem constrained with elliptic variational inequality. In fact, our aim in this paper is to present a direct approach for this class of optimal control problems. By using the pseudo‐spectral method, the infinite dimensional mathematical programming with equilibrium constraint, which can be an equivalent form of the considered problem, is converted to a finite dimensional mathematical programming with complementarity constraint. Then, the finite dimensional problem can be solved by the well‐developed methods. Finally, numerical examples are presented to show the validity and efficiency of the technique. Copyright © 2017 John Wiley & Sons, Ltd.     

An existence theorem for generalized variational inequalities with discontinuous and pseudomonotone operators

This paper gives a solution existence theorem for a generalized variational inequality problem with an operator which is defined on an infinite dimensional space, which is C-pseudomonotone in the sense of Inoan and Kolumbán [D. Inoan, J. Kolumbán, On pseudomonotone set-valued mappings, Nonlinear Analysis 68 (2008) 47-53], but which may not be upper semicontinuous on finite dimensional subspaces. The proof of the theorem provides a new technique which reduces infinite variational inequality problems to finite ones. Two examples are given and analyzed to illustrate the theorem. Moreover, an example is presented to show that the C-pseudomonotonicity of the operator cannot be omitted in the theorem.     

界定用户平衡及Logit型随机用户平衡下的混合平衡交通网络效率损失

考虑一个具有两类用户的交通网络,一类用户按照用户平衡原则选择出行路径,另一类用户按照Logit型随机用户平衡原则选择出行路径.建立了描述这种混合平衡出行行为的变分不等式模型,给出了满足此种混合平衡的交通网络效率损失上界,结果表明,效率损失上界与被研究的交通网络拓扑结构,交通需求及两类用户的划分比例系数有关.     

Lexicographic variational inequalities with applications

In this article, we consider equivalence properties between various kinds of lexicographic variational inequalities. By employing various concepts of monotonicity, we show that the usual sequential variational inequality is equivalent to the direct lexicographic variational inequality or to the dual lexicographic variational inequality. We establish several existence results for lexicographic variational inequalities. Also, we introduce the lexicographic complementarity problem and establish its equivalence with the lexicographic variational inequality. We illustrate our approach by several examples of applications to vector transportation and vector spatial equilibrium problems.     

A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.     

On the differential variational inequalities of parabolic‐elliptic type

We consider a model of infinite dimensional differential variational inequalities formulated by a parabolic differential inclusion and an elliptic variational inequality. The existence of global solution and global attractor for the semiflow governed by our system is proved by using measure of noncompactness. Copyright © 2017 John Wiley & Sons, Ltd.     

Super Efficiency of Multicriterion Network Equilibrium Model and Vector Variational Inequality

The super efficiency of a vector variational inequality is considered in this paper. We show that for both the single and multiple criteria cases, a network equilibrium model can be recast as super efficient solutions to a kind of variational inequality. For the network equilibrium model with a vector-valued cost function, we derive the necessary and sufficient condition in terms of the super efficiency of a vector variational inequality by using the Gerstewitz’s function without any convex assumptions.