具有产品质量差异的扩展Hotelling模型

假定两家厂商生产的同种产品具有质量差异,及消费者对产品质量偏好服从[d,e]区间上的均匀分布情况,研究了二次运输成本Hotelling模型:两家厂商首先沿[0,1]线性城市同时选址,然后进行价格竞争.运用后退归纳法得到了子博弈精炼Nash均衡,此时厂商将选址于城市中心。     

Pricing policies for substitutable products in a supply chain with Internet and traditional channels

This study considers pricing policies in a supply chain with one manufacturer, who sells a product to an independent retailer and directly to consumers through an Internet channel. In addition to the manufacturer’s product, the retailer sells a substitute product produced by another manufacturer. Given the wholesale prices of the two substitute products, the manufacturer decides the retail price of the Internet channel, and the retailer decides the retail prices of the two substitute products. Both the manufacturer and the retailer choose their own decision variables to maximize their respective profits. This work formulates the price competition, using the settings of Nash and Stackelberg games, and derives the corresponding existence and uniqueness conditions for equilibrium solutions. A sensitivity analysis of an equilibrium solution is then conducted for the model parameters, and the profits are compared for two game settings. The findings show that improving brand loyalty is profitable for both of the manufacturer and retailer, and that an increased service value may alleviate the threat of the Internet channel for the retailer and increase the manufacturer’s profit. The study also derives some conditions under which the manufacturer and the retailer mutually prefer the Stackelberg game. Based on these results, this study proposes an appropriate cooperation strategy for the manufacturer and retailer.     

Dual-Role Based Pricing in a Dynamic and Competitive Environment

The dual role of price, as a product attribute signaling quality and as a measure of sacrifice, serving as a benchmark for comparing the utility gains from superior product quality, is now well established in the marketing and economic literature. However, knowledge about their long-run impact and the influence of competition on these effects still remains very sparse. In the current paper, with reference to a dynamic and competitive framework, an analytical model is proposed to help determining optimal decision rules for price incorporating both roles. The main results are as follows: (i) The optimal pricing policy is determined as a Nash equilibrium strategy. (ii) The resulting equilibrium price is higher than an equilibrium that disregards the carryover price effects. (iii) For a symmetric competition, we provide normative rules on how firms should set prices as a function of the perceived quality; particularly, how the price should be set initially, when there is little product familiarity and the perceived quality is low, and how this price should vary as the perceived quality increases. (iv) At steady state, we find that the level of equilibrium margin, in percentage terms, decreases with the elasticity of demand with respect to the brand price, but this decrease is moderated by the elasticity of demand with respect to the brand perceived quality, the cross elasticity of demand with respect to the competitor’s perceived quality and the effect of the competitor’s current price on the firm’s perceived quality deterioration. The author thanks Konstantin Kogan for helpful discussions and comments.     

Fighting strategies in a market with counterfeits

Counterfeiting is a widely spread phenomenon and has seen rapid growth in recent years. In this paper, we adopt the standard vertical differentiation model and allow consumers the choices of purchasing an authentic product, purchasing a counterfeit, or not buying. We focus on how non-deceptive counterfeits, which consumers know at time of purchase that the products are counterfeits with certainty, affect the price, market share and profitability of brand name products. We also consider the strategies for brand name companies to fight counterfeiting. We compare different fighting strategies in a market with one brand name product and its counterfeit, and derive equilibrium fighting strategies in a market with two competing brand name products and a counterfeit under general conditions.     

Pricing policies under direct vs. indirect channel competition and national vs. store brand competition

This paper analyzes channel pricing in multiple distribution channels under competition between a national brand (NB) and a store brand (SB), where an NB can be distributed both through a direct channel (e-channel) and an indirect channel (local stores) but an SB can be distributed only through an indirect channel. We first explore cross-brand and cross-channel pricing policies. Formulating the problem as a Nash pricing game, we reach two findings: (1) brand loyalty building is profitable for both an NB and an SB; and (2) marketing decisions are more restrictive for an NB channel than they are for the SB channel. We next assess supply chain coordination and reach two findings: (1) wholesale price change does not coordinate the supply chain and (2) an appropriate combination of markup and markdown prices can achieve both supply chain coordination and a win–win outcome for each channel.     

Competitive Price Equilibrium with Consumer Reservation Utility

This paper studies a competitive price equilibrium in the market of a product category where consumers are homogeneous with a reservation utility below which they will not purchase the product. The impact of the reservation utility on the price equilibrium is of particular interest, because the reservation utility may change according to the business cycle and economic environments. Using multinomial logit model to describe market response, we study the comparative statics of the prices, profits and market shares of firms, each of which produces one brand in the product category, with respect to the reservation utility in the Nash equilibrium. It is shown that, as the reservation utility increases, the prices as well as the profits at Nash equilibrium decrease. Also, in the case of duopoly market, the firm with lower cost structure will increase its market share as the reservation utility increases.     

网络效应影响下品牌商与模仿者的竞争策略

近年来,品牌商与模仿者的竞争问题引起了社会的广泛关注。本文构建了包含一个品牌商和一个潜在模仿者的两周期动态博弈模型,且消费者具有策略性行为。品牌商在第一周期是市场的垄断者,若模仿者在第二周期进入市场,那么第二周期会变成双寡头市场。模仿者入侵市场除了会引起竞争效应外,与品牌产品的相似性也会引起网络效应,从而增加品牌产品的市场接受度。因此,面对模仿者入侵,品牌商需要同时权衡竞争效应与网络效应两方面的影响。研究结果表明:(1)网络效应并不总是对品牌商和模仿者的价格和需求等产生积极影响。(2)模仿产品质量不可提升过高,当模仿产品质量和品牌产品质量过分接近时,两个企业的利润都会降低。(3)当网络效应较小或者模仿产品质量过高时,品牌商在双寡头市场的需求可能会高于垄断市场的需求。     

Dual role of price and myopia in a marketing channel

In this paper we study a dynamic two-player channel where the manufacturer controls the wholesale price and the investment in quality and the retailer chooses the retail price. We consider that the retail price affects both the demand and the perceived quality of the brand and that its variations contribute to the building of an internal reference price. One of the model’s distinctive features is that it accounts for the two meanings of price, i.e., its classical objective measure of the cost of acquiring a particular quantity of the product, and its subjective roles as an assessment of the quality of the product and an evaluation of gains or losses (deal vs. sacrifice) resulting from buying a “cheap” or an “expensive” product. This dual computation is done with respect to the internal reference price.     

Price and quality competition: The effect of differentiation and vertical integration

This paper studies an instance of price and quality competition between firms as seen in the recent Internet market. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. Characterizing this competition from a microeconomic viewpoint, we consider two possible business strategies that firms can utilize to overcome the competition—the differentiation and the vertical integration with another complementary firm. We show an interesting result not seen in the well-known Bertrand price competition: not only does the differentiation always increase the firms’ profits, but also it can increase the consumer’s welfare in a quality-sensitive market. We further derive that under some mild conditions the monopolistic vertical integration that excludes the combination-purchase with a competitor’s product is beneficial for both the integrated firm and its consumers.     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Advertising and quality improving strategies in a supply chain when facing potential crises

In this paper, we consider a supply chain that faces a potential brand crisis, with one manufacturer deciding quality improvement and global advertising levels, and one retailer determining local advertising effort. The goodwill model proposed by Nerlove and Arrow (1962) is adopted here under the assumption that when the crisis happens, the companies suffer a sharp decrease in the goodwill. We characterize the feedback Nash equilibrium, and then we compare the corresponding quality and advertising strategies and outcomes with those of the case where the potential crises are absent, and where the companies do not invest in quality. The effects of the instantaneous crisis rate and the short-term and long-term damages are also evaluated. Our results reveal that the pre-crisis quality improvement accelerates the goodwill build-up before the crisis, and also helps the recovery in post-crisis regime. Its twofold function suggests that one of the pre- and post-crisis regimes/instants ought to be matched with more intense investment in both quality and global advertising, depending on the overall effect of instantaneous crisis rate, short-term damage and long-term damage. This carryover effect also brings a non-monotonicity of quality improvement effort and value functions with respect to the instantaneous crisis rate. These properties leave the chance to mitigate the loss by anticipating crisis for both members under certain circumstances.     

Optimal pricing in a diffusion model with concave price-dependent market potential

Using optimal control theory, a diffusion model of new product acceptance is studied. We consider a profit-maximizing firm faced with the problem of determining its optimal pricing policy under the assumption that the total market potential is a concave decreasing function of price. For an infinite planning horizon it is shown by phase portrait analysis that the optimal price is steadily increasing and converging to a saddle point equilibrium.     

Brand value in horizontal alliances: the case of twin-cars

Rival firms often cooperate horizontally in order to share risks and achieve scale advantages in production or in their research and development projects. The output of these strategic alliances is usually sold by the individual ally company under its own brand and using its own marketing mix strategies. Marketing strategies create a cumulative effect that is reflected in brand value. Although horizontal alliances often have a significant overall impact on firm profitability, undesired brand value dilution is a worrisome possibility for the partners and therefore a relevant subject of study. In this paper, we consider brand value to be the economic added value of a brand, and propose two market-based measures of brand value: (1) price premia (which are relevant for a unit sale) and (2) revenue premia (which also account for the premia in sales volume). We apply this analysis to the Spanish market for new automobiles, in which successful and long-lasting horizontal alliances have formed. Our findings suggest that, during the introduction stage of the product life cycle, horizontal allies did not charge different price premia, but that horizontal allies profit from differences in brand reputation obtained from demand side effects such as revenue premia (specifically, the impact on sales volume). Consequently, horizontal cooperation among brands does not dilute their value at the introduction stage. Furthermore, our results suggest that horizontal allies do charge different price premia during the growth stage of the product life cycle. Consequently, horizontal allies have recognized strategies that do not dilute brand value in intense competition mitigating the brand value diluting risk.     

产出不确定条件下“公司+农户”型订单农业供应链协商模型研究

在农产品产出不确定性及零售价格受农产品产出率影响的条件下,研究了一类由风险规避农户和风险中性公司组成“公司+农户”型订单农业农产品供应链协调问题。在该农产品供应链中,农户和公司通过Nash协商谈判来分别决策最优的生产量和订单价格。研究结果表明,在农产品产出不确定及零售市场价格受农产品产出率影响的条件下,风险规避型农户和公司的Nash协商合作博弈存在均衡解。Nash协商谈判所达成的最优农产品产出量和订单价格均高于分散决策情形下的最优农产品产出量和订单价格。最优农产品产出量是关于农户风险规避度的单调增函数,而最优的订单价格是关于农户风险规避度的单调减函数。最后,通过与分散决策情形相比,证明了Nash协商谈判机制能够促使风险规避型农户和风险中性型公司均达到帕累托改进。     

Establishing Nash equilibrium of the manufacturer–supplier game in supply chain management

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier's profit depends not only on its own delivery frequency, but also on other suppliers' frequencies through their impact on manufacturer's purchase allocation to the suppliers. We first solve the follower's (manufacturer's) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders' (suppliers') game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved.     

Components of optimal price under logit demand

Demand for durables can be modeled using a logit framework in which a customer chooses one brand from several alternatives, or buys nothing at all. In this framework, optimal prices for competing brands can be expressed as a system of non-linear equations, which, however, do not have closed form solutions. Although the optimal price can be determined by numerical search, the solution offers limited understanding of its components. In this article, we develop a linear approximation of the Nash equilibrium optimal price of a brand as its marginal cost plus a weighted sum of: (1) the inverse of the price sensitivity of the market, (2) the average value added by all brands in the market, and (3) the value advantage (or disadvantage) of the brand. The weights depend primarily upon the number of competing brands, with price insensitivity having the strongest impact, followed by value advantage of the brand, and average value added by all brands. This approximation for optimal price is found to be robust under a wide range of conditions. Additionally, we demonstrate that using the approximation results in only marginal deviation of profits from the theoretical Nash optimal.     

Market sharing dynamics between two service providers

We study the market partition between two distinct firms that deliver services to waiting time sensitive customers. In our model, the incoming customers select a firm on the basis of its posted price, the expected waiting time and its brand. More specifically, we quantify by a cost any departure from the ideal brand expected by each incoming customer. Considering that the two underlying queueing processes operate under high traffic regimes, we analyze the market sharing dynamics by using a diffusion process. As a function of control parameters, such as the waiting and brand departure costs or the incoming traffic intensity, we are able to analytically characterize a transition between an Hotelling-like regime (dominated by brand considerations) and a deadline type regime (dominated by waiting time considerations). The market sharing dynamics is described by the time evolution of a boundary point, which time evolution belongs to the class of noise-induced phase transitions, so far widely discussed in physics, chemistry and biology. Explicit illustrations for both symmetric (i.e. identical servers) and asymmetric cases are worked out.     

A discrete long-term location–price problem under the assumption of discriminatory pricing: Formulations and parametric analysis

We consider a competitive location problem in which a new firm has to make decisions on the locations of several new facilities as well as on its price setting in order to maximise profit. Under the assumption of discriminatory prices, competing firms set a specific price for each market area. The customers buy one unit of a single homogeneous price-inelastic product from the facility that offers the lowest price in the area the consumers belong to. Three customer choice rules are considered in order to break ties in the offered prices. We prove that, considering long-term competition on price, this problem can be reduced to a problem with decisions on location only. For each one of the choice rules the location problem is formulated as an integer programming model and a parametric analysis of these models is given. To conclude, an application with real data is presented.     

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.     

Optimal warranties,reliabilities and prices for durable goods in an oligopoly

This paper addresses the problem of durable goods manufacturers in an oligopoly seeking optimal values for three decision variables: product warranty, reliability and price. Each firm seeks a warranty-reliability-price combination that maximizes expected profit subject to quite general constraints on the firm's decision variables. Warranty serves as a signal of product reliability, which is not observable by consumers. We present a game-theoretic model of warranty-reliability-price competition in such a market and examine Nash equilibria for this game. We show that under fairly general assumptions each firm can optimally set its warranty and reliability independently of price and competitors' actions. In addition, we show that optimal warranties and reliabilities are complementary, and we explore the impact of different market factors on the optimal warranty and reliability. Finally, we show that optimal warranties are longer and products more reliable when consumers are risk averse.