在消费者偏好不确定下双寡头定位定价博弈

本文通过建立在企业对消费者偏好信息不确定情形下,双寡头企业动态定位、定价博弈模型,研究企业的定位策略、定价策略以及产品差异化问题。证明了该动态博弈存在唯一的子博弈精炼均衡。均衡结果表明,偏好不确定性是一种差异化力量,与消费者偏好信息确定情形相比,企业的不确定性能够提高均衡价格、增加均衡利润。最后,分析了偏好不确定性对社会最优定位和社会最优差异化的影响。     

考虑跟随企业搭便车行为的创新企业定价策略研究

文章通过构建博弈模型探讨了存在跟随企业搭便车行为时创新企业的定价策略及定价模式(稳定定价或动态定价),并分析了忠实消费者规模及需求溢出效应等特征对创新企业定价决策与利润的影响.结果表明,无论创新企业采用稳定定价或动态定价模式,跟随企业搭便车行为均会降低创新企业利润,需求溢出效应的增强总能使创新企业和跟随企业均获得更高的利润.动态定价模式下,当需求溢出效应较大时,创新企业会采用渗透定价策略;反之会采用撇脂定价策略.无论垄断或竞争市场情形下,均存在消费者规模阈值效应,即创新企业的利润随着忠实消费者规模的增大而先增大后减小.垄断市场下,动态定价模式能让创新企业获得更高利润;竞争市场下,当跟随企业质量处于较中间水平时,稳定定价模式能让创新企业获得更多优势.     

消费者偏好驱动的制销供应链利润分配策略

从企业社会责任对消费者偏好的影响入手,运用博弈论的基本思想,对制销供应链中,制造商与分销商一次性博弈的定价和利润分配策略进行了研究,并在此基础上对不同情况下制销双方重复性博弈的均衡结果进行了讨论.结果表明:在两类制销供应链中,联盟定价都是制销双方一次性博弈的唯一纳什均衡结果,且在制销双方商定的利润分配因子的取值范围内双方联盟后所得的利润高于联盟之前;在两类制销供应链中,制造商与分销商坚持联盟定价对双方的长期利润都是最优的.     

基于策略型消费者购买习惯的产品动态定价决策研究

消费者具有浏览销量和评论的购买习惯.为分析此购买习惯对零售商定价的影响,以策略型消费者为研究对象,建立了受产品价格、销量与评论内容影响的效用函数,并构建了策略型消费者和零售商的两阶段博弈模型.同时,基于消费者购买习惯对零售商公布和调整价格的两种策略进行博弈和比较分析.结论表明,消费者通过浏览评论信息对产品质量的感知达到一定程度时,购买习惯改变了零售商总是降价的定价策略;零售商在公布价格策略中产品定价和收益高于调整价格策略;当消费者较具有耐心且对产品质量感知显著时,能提高消费者需求.研究结果对零售商的定价决策具有指导意义.     

考虑消费者转移的双渠道定价决策研究

产品的双渠道销售不仅给企业带来更多的利润收益,同时给企业在应对市场复杂需求方面带来冲突和挑战.以拥有双渠道销售的制造商为研究对象,基于消费者对制造商线下渠道和线上渠道存在的策略型行为,研究了渠道之间考虑存在消费者转移的双渠道产品定价及协调策略.首先,构建了"线下主导"和"线上主导"的Stackelberg分散决策博弈模型,得到分散决策模式下的双渠道最优定价均衡解,并分析了策略型消费者所占比例、线上消费者购买到产品概率、消费者转移概率对最优定价和总利润的影响.然后,构建了双渠道集中决策定价模式,通过分析得出存在唯一的双渠道最优定价策略,并给出其解析解表达式.最后,通过数值算例仿真分析进行验证.     

非线性定价的贝叶斯均衡策略研究

本文利用贝叶斯均衡策略研究非线性定价问题,将消费需求类型推广到三种,设计一个非线性价格机制博弈,推导出该博弈的贝叶斯均衡,得出结论:当消费者类型满足不同假设条件时,得到贝叶斯均衡策略也不同.文中还将贝叶斯均衡与纳什均衡进行比较,并从博弈角度为一类企业(如电信公司等)的定价提供理论依据.     

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.     

随机需求下竞争零售商的定价策略研究

本文研究了随机需求下两竞争零售商的定价策略选择(响应性定价或清仓定价)、产品订货量及响应性价格的联合决策问题。通过将问题转化为一个三阶段的博弈模型,基于Kuhn-Tucker条件求解了两零售商不同定价策略子博弈下的均衡产品订货量及响应性定价决策,分析了不同定价策略子博弈下产品订货量及价格决策的差别以及潜在市场需求不确定(期望和方差变动)对订货量和定价策略的影响。数值分析结果表明,当潜在市场需求服从均匀分布时,响应性定价子博弈是帕累托最优策略,清仓定价子博弈是零售商的均衡策略,混合定价子博弈下两零售商的收益差距较大。     

双寡头动态定位定价博弈分析

本分析双寡头两阶段动态定位定价策略，首先两个企业同时选择地址，然后进行价格竞争。市场上有两种类型的消费，对企业提供的产品有不同的偏好，每个企业预测它对地址的选择会影响它的需求和竞争密度，给出了使企业利润最大的子博弈精练Nash均衡。     

实行BOPS模式是否总是有益的？与传统双渠道的对比研究

针对企业线上线下渠道融合战略中提出的BOPS(buy-online-and-pick-up-in-store)模式,在集中式和分散式两情境下分别构建并对比了BOPS和传统双渠道模型,探讨了在传统双渠道基础之上引入BOPS服务是否对企业而言总是有好处的,并分析了传统型消费者占比和消费者的服务敏感性程度对企业实施BOPS的影响。研究表明,企业是否在传统双渠道模式基础上增设BOPS服务,取决于市场中传统型消费者占比规模(即偏好传统零售的消费者)以及各类型消费者对线下服务的敏感性程度;BOPS模式下,当消费者BOPS行为的真正动机是出于欲体验线下零售服务时,对实施BOPS的制造商企业而言更为有利;同时,企业的产品定价和线下服务水平不仅需要考量生产、服务成本,同样需对消费者的服务敏感性有准确的了解和定位。     

On price competition in location-price models with spatially separated markets

In this paper we study price competition for two types of location-price models in which facility locations are set up and price decisions have to be made in order to maximise profit. We discuss the existence and determination of equilibrium prices in a general location space when facilities have different production costs. It is assumed that each price is bounded from below and demand for a single homogeneous product is price-inelastic. When facilities set mill prices, a price equilibrium rarely exists and necessary conditions for existence are obtained. In particular, when the location space is a tree network, we give a characterisation of the locations for which a unique equilibrium exists for two competitors. With spatial price discrimination, though equilibrium prices might not exist, it is shown that ε-equilibrium prices always exist for any locations of the facilities. A characterisation of ε-equilibrium is also given. Then the location-price problem is reduced to a location problem. A comparison of results with the two types of price determination is also presented. This work has been supported by the Ministry of Science and Technology of Spain under the research project BEC2002-01026, in part financed by the European Regional Development Fund (ERDF).     

Finding all pure strategy Nash equilibria in a planar location game

In this paper, we deal with a planar location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. If firms set the equilibrium prices in the second stage, the game is reduced to a location game for which pure strategy Nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the customer and the facility from which it is served. We present characterizations of local and global Nash equilibria. Then an algorithm is shown in order to find all possible Nash equilibrium pairs of locations. The minimization of the social cost leads to a Nash equilibrium. An example shows that there may exist multiple Nash equilibria which are not minimizers of the social cost.     

Finding location equilibria for competing firms under delivered pricing

We address the problem of finding location equilibria of a location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. Assuming that firms set the equilibrium prices in the second stage, the game is reduced to a location game for which a global minimizer of the social cost is a location equilibrium if demand is completely inelastic and marginal production cost is constant. The problem of social cost minimization is studied for both a network and a discrete location space. A node optimality property when the location space is a network is shown and an Integer Linear Programming (ILP) formulation is obtained to minimize the social cost. It is also shown that multiple location equilibria can be found if marginal delivered costs are equal for all competitors. Two ILP formulations are given to select one of such equilibria that take into account the aggregated profit and an equity criterion, respectively. An illustrative example with real data is solved and some conclusions are presented.     

Determination of Lagrangians from Equations of Motion and Commutator Brackets

The question as to whether a given set of equations, which govern the dynamical evolution of a system, determine a Lagrangian is considered. This problem, which has come to be known as the inverse problem of the calculus of variations, is reviewed and theorems which contain systems of partial differential equations which determine a type of self-adjointness are developed. It is shown that, given a reasonable form for the classical correspondence, the usual quantum commutator brackets can be expressed in terms of classical quantities which satisfy a particular form of these equations.     

The Friedrichs Extension of a Pair of Operators

Abstract

An extension of a pair of linear unbounded operators which map from a Banach space X to a Hilbert space Y is constructed and studied. The purpose of the extension is to obtain a pair of jointly closed operators which will be the generating pair of a B-evolution similar to the classical Friedrichs extension of a single operator which generates a holomorphic semigroup. The construction is based on spectral methods.     

Cycles of covers

We initially consider an example of Flynn and Redmond, which gives an infinite family of curves to which Chabauty’s Theorem is not applicable, and which even resist solution by one application of a certain bielliptic covering technique. In this article, we shall consider a general context, of which this family is a special case, and in this general situation we shall prove that repeated application of bielliptic covers always results in a sequence of genus 2 curves which cycle after a finite number of repetitions. We shall also give an example which is resistant to repeated applications of the technique. E. V. Flynn thanks the International Center for Transdisciplinary Studies at Jacobs University Bremen for its hospitality during July 2007, and thanks EPSRC for support: grant number EP/F060661/1.     

On the optimal control of the growth of a forest in a special case

In Ref. 1, the author considered the following large-scale forest management problem. There is a system consisting of several factories which all use, as raw material, wood obtained from a large forest region. This forest is divided into a large number of subforests, each of which is felled after it has reached a given age, after which a new forest is immediately planted. The instants in time at which each subforest is felled are assumed to form a stationary point process. In Ref. 1, it was demonstrated how the parameters of the system must be chosen in order to achieve a flow of raw material such that the probability that a shortage will occur is less than a preset value. In the present paper, we consider the problem of maximizing the yield of a single subforest.     

Cycles of covers

We initially consider an example of Flynn and Redmond, which gives an infinite family of curves to which Chabauty’s Theorem is not applicable, and which even resist solution by one application of a certain bielliptic covering technique. In this article, we shall consider a general context, of which this family is a special case, and in this general situation we shall prove that repeated application of bielliptic covers always results in a sequence of genus 2 curves which cycle after a finite number of repetitions. We shall also give an example which is resistant to repeated applications of the technique.     

Almost diagonal systems of linear difference equations

Linear homogeneous difference systems of equations on an infinite interval are considered. Conditions are given which allow to represent a fundamental solution as a product of two square matrices. The product is made of a diagonal matrix and a matrix which is a perturbation of the identity. The diagonal matrix being on the left in the proposed product rather than on the right as it has been traditionally represented. A self contained theorem of asymptotic approximation is provided which is applied to a special family of difference systems. A theorem, utilizing a linear transformation, which is best possible in a certain sense, is also given.     

Uniform Convergence of Spectral Expansions in the Terms of Root Functions of a Spectral Problem for the Equation of a Vibrating Beam

In this paper we consider a spectral problem which describes bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is fixed rigidly and on the right end is concentrated an elastically fixed load. We study the uniform convergence of spectral expansions in terms of root functions of this problem.