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).     

���ģ���¾��ж�̬ΥԼ�߽��ծȯ����

In this paper, a pricing problem for corporate bond with dynamic default barrier is studied under a hybrid model. Firstly, a mathematical model for the pricing problem is set up by applying risk-free equilibrium principle. Then, a closed-form formula for the pricing model is obtained by using the variable transformation technique and the image method, which extends the relevant literature's results. Finally, a numerical experiment is presented to analyze the effect of the dynamic barrier on the bond price. Our studies show that the different shape curve of a bond's price can be obtained by adjusting the relevant parameter on the default boundary, and then can control the risk or get a higher bond's yield     

Massively parallel computation of large-scale spatial price equilibrium models with discriminatory ad valorem tariffs

In this paper, we develop a perfectly competitive spatial equilibrium model in price and quantity variables in the presence of discriminatory ad valorem tariffs, a widely used trade policy instrument. We derive the equilibrium conditions and formulate them as a variational inequality problem. An algorithm is then proposed for the computation of the equilibrium pattern and convergence results established. The algorithm resolves the problem into very simple subproblems, each of which can be solved simultaneously and in closed form. Finally, the algorithm is implemented on the massively parallel Thinking Machines CM-2 and CM-5 architectures, known as the Connection Machines, and numerical results presented.     

基于两阶段动态博弈的服务外包定价分析

本文通过引入动态博弈模型,从完全竞争市场博弈定价、税收减免下博弈定价、人才补贴下博弈定价三个角度定量研究了服务外包企业的最优定价策略及其影响因素。研究表明,服务外包均衡价格受企业需求函数和竞争对手决策等因素影响,并得出了在政府行业扶持政策下的服务外包均衡价格与各参数之间的关系。依据研究结果,本文对政府给予服务外包行业的相关扶持政策提出了若干合理性建议。     

Bicriterion Weight Varying Spatial Price Networks

We consider a spatial price equilibrium problem in which the consumers take their decisions according to the transportation cost and transportation time necessary for obtaining a given commodity. In particular, each consumer market can give a different weight to each component of a generalized cost, and we suppose that this weight can depend on time. Thus, we are faced with a time-dependent equilibrium problem which we cast within the framework of variational inequalities. We give existence results and, by using the example of a linear operator, we propose also a discretization procedure for equilibrium problems which can be modeled by the same type of variational inequality.     

非线性非均衡蛛网模型的动态分析

描述单商品市场价格波动的蛛网模型是动态经济分析中的经典模型 ,证明了由模型 ( )所生成的价格序列在一定的条件下不会出现 3以上周期运动和混沌现象 ,并对其进行稳定性分析 ,得到模型关于均衡价格稳定的六个判别定理 .     

A solution condition for complementarity problems: with an application to spatial price equilibrium

A sufficient condition is developed for the existence of solutions to complementarity problems, which is applicable to all continuous functions. In addition, it is shown to imply a number of simpler conditions, including the well-known coerciveness condition. Finally, this condition is applied to an existence problem in spatial price equilibrium, where it is shown to yield not only a more general result, but also a simpler method of proof.     

Time-consistent investment strategy under partial information

This paper considers a mean–variance portfolio selection problem under partial information, that is, the investor can observe the risky asset price with random drift which is not directly observable in financial markets. Since the dynamic mean–variance portfolio selection problem is time inconsistent, to seek the time-consistent investment strategy, the optimization problem is formulated and tackled in a game theoretic framework. Closed-form expressions of the equilibrium investment strategy and the corresponding equilibrium value function under partial information are derived by solving an extended Hamilton–Jacobi–Bellman system of equations. In addition, the results are also given under complete information, which are need for the partial information case. Furthermore, some numerical examples are presented to illustrate the derived equilibrium investment strategies and numerical sensitivity analysis is provided.     

DIFFERENTIAL INVERSE VARIATIONAL INEQUALITIES IN FINITE DIMENSIONAL SPACES

In this article,a new differential inverse variational inequality is introduced and studied in finite dimensional Euclidean spaces.Some results concerned with the linear growth of the solution set for the differential inverse variational inequalities are obtained under different conditions.Some existence theorems of Caratheodory weak solutions for the differential inverse variational inequality are also established under suitable conditions.An application to the time-dependent spatial price equilibrium control problem is also given.     

Utility Indifference Pricing: A Time Consistent Approach

Abstract

This article considers the optimal portfolio selection problem in a dynamic multi-period stochastic framework with regime switching. The risk preferences are of exponential (CARA) type with an absolute coefficient of risk aversion that changes with the regime. The market model is incomplete and there are two risky assets: tradable and non-tradable. In this context, the optimal investment strategies are time inconsistent. Consequently, the subgame perfect equilibrium strategies are considered. The utility indifference ask price of a contingent claim written on the risky assets is computed through an indifference valuation algorithm. By running numerical experiments, we examine how this price varies in response to changes in model parameters.     

A differential oligopoly game with differentiated goods and sticky prices

We investigate a dynamic oligopoly game where goods are differentiated and prices are sticky. We study the open-loop and the closed-loop memoryless Nash equilibrium, and show that the latter equilibrium entails a larger level of steady state production as compared to the former; both equilibria entail a larger level of production in steady state than the static game. We also study the effects of price stickiness and product differentiation upon the steady state equilibrium allocation and profits. The per-firm equilibrium output is increasing in both product differentiation and price stickiness, while profits are increasing in both product differentiation and the speed of price adjustment. The steady state social welfare monotonically increases in the speed of price adjustment, and the overproduction entailed by dynamic competition has beneficial effect from a social standpoint.     

Pareto Optimal Allocation and Price Equilibrium for a Duopoly with Negative Externality

A spatial competition model involving decisions made by consumers and firms is proposed. A regulating agent assigns the demand, taking into account the price, transport and externality cost, and minimizing the joint consumer cost to obtain a Pareto optimal allocation. Assuming the Pareto optimal allocation, firms fix prices in order to maximize the profit. An equilibrium problem is studied and some results are presented. The problem and results are illustrated with an example.     

Dynamic lot-sizing with price changes and price-dependent holding costs

This paper proposes a new formulation of the dynamic lot-sizing problem with price changes which considers the unit inventory holding costs in a period as a function of the procurement decisions made in previous periods. In Section 1, the problem is defined and some of its fundamental properties are identified. A dynamic programming approach is developed to solve it when solutions are restricted to sequential extreme flows, and results from location theory are used to derive an O(T²) algorithm which provides a provably optimal solution of an integer linear programming formulation of the general problem. In Section 2, a heuristic is developed for the case where the inventory carrying rates and the order costs are constant, and where the item price can change once during the planning horizon. Permanent price increases, permanent price decreases and temporary price reductions are considered. In Section 3, extensive testing of the various optimal and heuristic algorithms is reported. Our results show that, in this context, the two following intuitive actions usually lead to near optimal solutions: accumulate stock at the lower price just prior to price increase and cut short on orders when a price decrease is imminent.     

Dynamic pricing with uncertain production cost: An alternating-move approach

This article studies a two-firm dynamic pricing model with random production costs. The firms produce the same perishable products over an infinite time horizon when production (or operation) costs are random. In each period, each firm determines its price and production levels based on its current production cost and its opponent’s previous price level. We use an alternating-move game to model this problem and show that there exists a unique subgame perfect Nash equilibrium in production and pricing decisions. We provide a closed-form solution for the firm’s pricing policy. Finally, we study the game in the case of incomplete information, when both or one of the firms do not have access to the current prices charged by their opponents.     

竞争环境下风险规避的航班动态定价

以同一航线上的多个竞争航班为研究对象,在假设各竞争航班之间具有完全信息的基础上,利用马尔可夫决策过程和博弈论,建立了竞争环境下风险规避的航班动态定价的数学模型,证明了均衡价格的存在性。在此基础上,进一步讨论了信息不完全情况下风险规避的竞争航班的动态定价问题。数值实验表明:在竞争环境下,各风险规避航班的均衡价格随自身剩余座位数量和风险规避系数的增加而下降,随其他竞争航班的剩余座位数量和风险规避系数的增加而提高。     

Single facility location on a network under mill and delivered pricing

^** E-mail: pelegrin{at}um.es Firms normally use either a mill price or a delivered pricepolicy, depending on market conditions (type of good, transportationway, customers location, costs, etc). In this paper, the problemof selecting the best location for an entering firm in competitionwith some pre-existing firms, under each price policy, is studiedon a network for the first time. With mill pricing, an equilibriumin price rarely exists and it is assumed that all competingfirms set a common mill price for all customers. With deliveredpricing, there exists a Nash equilibrium in price and it isassumed that the equilibrium price in each area is offered tothe customers in that area. In both cases, we consider thatcustomers buy from the cheapest facility and the same rulesare used for tie breaking in the lowest cost. While the profitmaximization problem for the entering firm always has optimalsolutions under mill pricing, this problem might not have anoptimal solution under delivered pricing. We show some discretizationresults and give procedures to find the full set of optimal,or -optimal, solutions to the problem under the two price policies.A comparison of results with the two price policies is givenby using an illustrative example.     

Time—Dependent Spatial Price Equilibrium Problem: Existence and Stability Results for the Quantity Formulation Model

This paper concerns with the study of the time–dependent variational inequality associated to the spatial price equilibrium model related to the quantity formulation. In particular existence the -orems of the solution to the associated variational inequality and a stability analysis of the equilibrium pattern is reported.     

蛛网模型收敛的一些充要条件

蛛网模型刻画了某种商品在市场中的供求波动,是一种重要的典型动态经济学模型.本文对传统的蛛网模型加以改进,建立了需求函数和供给函数可以为线性函数或非线性函数的广义蛛网模型.并对其进行了动态分析与稳定性分析,得到了模型存在稳定均衡点的一些充要条件.     

寡头垄断市场三度价格歧视动态博弈分析

对两寡头厂商2元市场用完全信息动态博弈的方法分析了实施三度价格歧视情形和统一定价情形的均衡产量,均衡价格和均衡总收益,并研究了这两种情形三个指标之间的关系.结果显示,在两个子市场的需求函数为线性需求的条件下,统一定价的市场均衡产量等于歧视定价的市场均衡产量;统一定价的均衡价格是歧视定价时两个子市场均衡价格的加权平均;统一定价的市场均衡总收益小于歧视定价的市场均衡总收益.     

基于GMCR的双渠道供应链价格冲突动态交互模型

在冲突分析图模型中,稳定性分析的均衡结果和决策者偏好信息之间存在一个动态反复的交互过程。为此,本文提出了基于GMCR的冲突分析动态交互理论,在偏好信息和均衡结果之间引入决策者的风险认知系统,以动态模拟冲突中决策者的风险认知、偏好信息与均衡解之间的交互关系。然后,构建了基于GMCR的双渠道供应链价格冲突动态交互模型,从冲突分析动态交互视角解释了价格战背后制造商和零售商的博弈行为,并有效预测了风险规避情况下双渠道供应链价格冲突的均衡结果,为供应链管理者提供了一套系统有效的冲突分析工具。