Product Assortment and Price Competition under Multinomial Logit Demand

The role of assortment planning and pricing in shaping sales and profits of retailers is well documented and studied in monopolistic settings. However, such a role remains relatively unexplored in competitive environments. In this study, we study equilibrium behavior of competing retailers in two settings: (i) when prices are exogenously fixed, and retailers compete in assortments only; and (ii) when retailers compete jointly in assortment and prices. For this, we model consumer choice using a multinomial Logit, and assume that each retailer selects products from a predefined set, and faces a display constraint. We show that when the sets of products available to retailers do not overlap, there always exists one equilibrium that Pareto‐dominates all others, and that such an outcome can be reached through an iterative process of best responses. A direct corollary of our results is that competition leads a firm to offer a broader set of products compared to when it is operating as a monopolist, and to broader offerings in the market compared to a centralized planner. When some products are available to all retailers, that is, assortments might overlap, we show that display constraints drive equilibrium existence properties.     

A Choice‐Based Dynamic Programming Approach for Setting Opaque Prices

Opaque pricing is a form of pricing where certain characteristics of the product or service are hidden from the consumer until after purchase. In essence, opaque selling transforms a differentiated good into a commodity. Opaque pricing has become popular in service pricing as it allows firms to sell their differentiated product at higher prices to regular brand loyal customers while simultaneously selling to non‐brand loyal customers at discounted prices. We use a nested logit model in combination with logistic regression and dynamic programming to illustrate how a service firm can optimally set prices on an opaque sales channel. The choice model allows the characterization of consumer trade‐offs when purchasing opaque products while the dynamic programming approach allows the characterization of the optimal pricing policy as a function of inventory and time remaining. We compare optimal prices and expected revenues when dynamic pricing is restricted to daily price changes. We provide an illustrative example using data from an opaque selling mechanism ( Hotwire.com ) and a Washington DC‐based hotel.     

考虑策略性消费者的生鲜农产品定价和库存决策

消费者的策略性行为使零售商的生鲜农产品的定价和库存决策面临更大挑战。本文基于报童模型，综合考虑消费者的策略性行为，对生鲜农产品价值下降进行离散化处理。刻画策略性消费者的决策行为，构建零售商的单阶段和两阶段定价及库存决策模型，分析了产品价值剩余率对消费者行为、零售商最优定价、最优库存水平以及零售商利润的影响机理。研究发现，在单阶段模型中零售商最优价格和最优库存水平均随产品价值剩余率的递增而递增；而在两阶段模型中，第二阶段最优价格随价值剩余率的变化趋势可能存在阈值。     

Coordinating a Supply Chain System with Retailers Under Both Price and Inventory Competition

We investigate a supply chain system with a common supplier selling to downstream retailers who are engaged in both price and inventory competition. We establish the existence and uniqueness of the pure‐strategy Nash equilibrium for the retailer game and study how a supplier can coordinate the system to achieve the best performance. Our main conclusions are as follows: First, a buyback contract can be used to coordinate retailers competing on both price and inventory in a sense that optimal retail prices and inventory levels arise as the Pareto‐dominant equilibrium. With symmetric retailers, the system optimum arises as the unique symmetric equilibrium. Second, the particular type of competition experienced by retailers (price versus inventory competition) affects the characteristics of the contract. Specifically, strong price competition leads to a coordination mechanism with a positive buyback rate, where the supplier subsidizes retailers for leftover inventories; however, strong inventory competition leads to a negative buyback rate, where retailers are punished for overstocking. Using a linear expected demand function, we further explore the impact of system parameters on the coordination contract and the competitive equilibrium. We also find that the performance of the supplier's optimal contract is asymptotic to the system optimal coordination contract as competition becomes fierce.     

Why Do We Observe Stockless Operations on the Internet? Stockless Operations Under Competition

Due to the proliferation of electronic commerce and the development of Internet technologies, many firms have considered new pricing‐inventory models. In this paper, we study the role of stockless (i.e., zero‐inventory) operations in online retailing by a considering duopoly competition in which two retailers compete to maximize profit by jointly optimizing their pricing and inventory decisions. In our model, the retailers are allowed to choose either an in‐stock policy or stockless operations with a discounted price. We first present the characteristics and properties of the equilibrium. We then demonstrate that the traditional outcome of asymmetric Bertrand competition is observed under head‐to‐head competition. However, when the two firms choose different operational policies, with corresponding optimal pricing, they can share the market under certain conditions. Finally, we report interesting observations on the interaction between pricing and inventory decisions obtained from an extensive computational study.     

Browse‐and‐Switch: Retail‐Online Competition under Value Uncertainty

Although online shopping is becoming popular, consumers who are unsure about whether to buy a product may find it advantageous to visit a brick‐and‐mortar retail store to first examine the product before purchasing it. But, after browsing at the store, consumers have the option of switching to an e‐tailer to purchase the item at a cheaper price rather than buying at the store. Recent business press refers to this browse‐and‐switch behavior as “showrooming,” and attributes to it the declining profits of brick‐and‐mortar retailers. To study the effect of the browse‐and‐switch option on retail and online pricing strategies and profits, we analyze a stylized economic model that incorporates uncertainty in consumers' valuation of the product, captures the heterogeneity among consumers in their inclination to purchase online, and permits product returns. We consider various equilibrium scenarios for different combinations of consumer shopping behaviors, characterize the parameter ranges for each scenario, and demonstrate that browse‐and‐switch behavior can indeed occur under equilibrium. Our analysis further shows that the option for consumers to browse‐and‐switch intensifies competition, reducing the profits for both firms.     

Early Sales of Seasonal Products with Weather‐Conditional Rebates

Some retailers of seasonal products adopt weather‐conditional rebate programs to induce early sales and increase profits. In such promotions, customers who buy the product in an advance preselling period are offered rebates if a pre‐specified weather condition is realized during the later normal selling season. We investigate the potential benefits of these programs for retailers. We show that the weather‐conditional rebate program can increase sales by price discriminating among a customer's post‐purchase states. Taking advantage of the early sales, it can also reduce the inventory holding cost and ordering cost, and hence can increase the retailer's expected profits. In addition, we numerically investigate the sensitivity of the rebate program's effectiveness to the model parameters and illustrate its advantages over an advance‐discount policy.     

The Dynamics of Domestic Gray Markets and Its Impact on Supply Chains

Gray markets are created by unauthorized retailers selling manufacturer's branded products. Similar to international gray markets, domestic gray markets are a growing phenomenon whose impact on supply chains is not clear. We consider a supply chain with one manufacturer and several authorized retailers who face a newsvendor problem and a domestic gray market. While a gray market provides an opportunity for retailers to clear their excess inventory (inventory‐correction effect), it also can be a threat to their demand (demand‐cannibalization effect). We first characterize the emerging equilibrium by assuming an MSRP environment. Comparing a decentralized and centralized system, we show that a wholesale pricing contract is quite efficient in a gray market environment; we explain the underlying mechanism and note some of the operational decisions that could hurt that efficiency. We show that the gray market price determines the degree of both the negative effects of demand‐cannibalization and the positive effects of inventory correction, which in turn determines the net impact of gray markets on the retailer's stocking choice and, ultimately, the manufacturer's profit. We then study the authorized retailers' problem as a price‐setting newsvendor. We observe that the gray market creates price competition between the authorized and unauthorized retailers, causing a drop in the primary market price. However, this price competition can be counteracted by the authorized retailers' stocking decision. Finally, we extend our model to consider the cases where the demand can be correlated across retailers.     

Joint Inventory and Pricing Coordination with Incomplete Demand Information

In retailing operations, retailers face the challenge of incomplete demand information. We develop a new concept named K‐approximate convexity, which is shown to be a generalization of K‐convexity, to address this challenge. This idea is applied to obtain a base‐stock list‐price policy for the joint inventory and pricing control problem with incomplete demand information and even non‐concave revenue function. A worst‐case performance bound of the policy is established. In a numerical study where demand is driven from real sales data, we find that the average gap between the profits of our proposed policy and the optimal policy is 0.27%, and the maximum gap is 4.6%.     

Pricing Policy in a Supply Chain: Negotiation or Posted Pricing

This article examines the choice of pricing policy (posted pricing or negotiation) toward end customers in a supply chain. Many retailers actively decide whether or not to encourage negotiation on the shop floor. Of course, the retailer's pricing policy influences not only the retailer's profit, but also the profits of the manufacturers who sell through the retailer. However, little is known about the forces that shape the pricing policy when two self‐interested parties interact in a supply chain. We consider two alternative models depending on who has the power to decide the pricing policy: the manufacturer or the retailer. We find that an increase in the wholesale price weakens the retailer's ability to price discriminate through negotiation. Therefore, the retailer prefers negotiation at lower wholesale prices and posted pricing at higher wholesale prices. We also find that whenever the retailer prefers negotiation, the manufacturer does too. Therefore, the retailer's discretion over the pricing policy causes friction only when the retailer wants to use posted pricing, while the manufacturer wishes the retailer to use negotiation. We show that such friction arises only when product availability or the cost of negotiation is moderate. In this case, we show that the manufacturer may offer a substantial discount to persuade the retailer to negotiate. Surprisingly, in this region of friction, a decrease in the supply chain's capacity or an increase in negotiation costs (both of which are typically considered as worsening the retailer's business environment) translates into higher profit for the retailer.     

考虑退货的定价和订货优化及信息发布美化策略

考虑顾客由感知差异引起的退货行为，以及促销期与日常销售期不同的行为特点，对日常销售期和促销期顾客购买率和退货率分别进行了解析表述.在此基础上分析了确定需求下信息发布美化策略对最大利润的影响.建立了随机需求下在线零售商的期望利润模型，对定价和订货量进行联合优化.最后通过算例分析了在感知价值和感知差异服从更为一般的分布形式且存在相关性条件下，最优策略下的预期利润随信息发布美化程度的变化规律，以及相关性对信息发布美化策略有效性的影响.研究结果表明，基于感知价值和感知差异构建的购买率和退货率模型可较好解释已有实证研究结果，以此为基础对定价和库存进行联合优化更符合实际，优化条件下的最大利润随信息发布美化程度的提高先增后降，取得最大利润的信息美化值促销期大于日常销售期，且线性相关程度越高的产品取得最大利润的信息美化值越大。     

存在战略购买需求的定价、供给、机制选择和配给研究

本文研究存在战略购买需求的易逝资产销售策略问题。垄断厂商基于利润最大化目标确定易逝资产定价、供给、机制选择和配给策略,战略消费者通过锚定预期价格安排战略购买时机。不同于通常基于效用理论研究定价的思路,本文首先基于锚定效应和跨期价格均衡思想探寻不同战略等待购买规模的市场预期需求曲线和动静态定价区域;其次在众多预期需求曲线中寻找市场有效定价前沿（即有效预期需求曲线）;再次在利润曲面上找出与有效定价前沿对应的容量扩展线（即最大利润曲线）;最后沿容量扩展线和有效定价前沿搜寻最大期望利润及相应策略。研究表明,消费者保留价异质和需求不确定性是动态定价和战略购买存在的根本原因;市场在不同战略等待购买规模状态拥有不同预期需求曲线,最大战略等待购买规模状态预期需求曲线是市场有效定价前沿。动静态定价机制各有其所适用的容量和价格空间,消费者保留价水平和战略消费者规模决定动态定价空间大小,随机需求分布差异只影响动态定价空间形状（即影响需求弹性）。在跨期价格均衡区域内,提价和扩容都会加剧消费者战略购买程度,供给越大定价往往越低。战略购买不仅会降低厂商供给、定价和利润水平,改变不同类型消费者之间高低价购买机会,甚至还可能影响定价机制选择和配给策略。压缩过度供给和虚高价格空间可降低战略购买导致的利润损失。本文研究结果可为考虑消费者行为的需求价格理论研究和运营管理实践提供参考。     

Centralized versus Decentralized Competition for Price and Lead‐Time Sensitive Demand

We study two firms that compete on price and lead‐time decisions in a common market. We explore the impact of decentralizing these decisions, as made by the marketing and production departments, respectively, with either marketing or production as the leader. We compare scenarios in which none, one, or both of the firms are decentralized to see whether decentralization can be the equilibrium strategy. We find that under intense price competition, with intensity characterized by the underlying parameters of market demand, firms may suffer from a decentralized structure, particularly under high flexibility induced by high capacity, where revenue‐based sales incentives motivate sales/marketing to make aggressive price cuts that often erode profit margins. In contrast, under intense lead‐time competition, a decentralized strategy with marketing as the leader can not only result in significantly higher profits, but also be the equilibrium strategy. Moreover, decentralization may no longer lead to lower prices or longer lead‐times if the production department chooses capacity along with lead‐time.      

Committed Versus Contingent Pricing Under Competition

Should capacitated firms set prices responsively to uncertain market conditions in a competitive environment? We study a duopoly selling differentiated substitutable products with fixed capacities under demand uncertainty, where firms can either commit to a fixed price ex ante, or elect to price contingently ex post, e.g., to charge high prices in booming markets, and low prices in slack markets. Interestingly, we analytically show that even for completely symmetric model primitives, asymmetric equilibria of strategic pricing decisions may arise, in which one firm commits statically and the other firm prices contingently; in this case, there also exists a unique mixed strategy equilibrium. Such equilibrium behavior tends to emerge, when capacity is ampler, and products are less differentiated or demand uncertainty is lower. With asymmetric fixed capacities, if demand uncertainty is low, a unique asymmetric equilibrium emerges, in which the firm with more capacity chooses committed pricing and the firm with less capacity chooses contingent pricing. We identify two countervailing profit effects of contingent pricing under competition: gains from responsively charging high price under high demand, and losses from intensified price competition under low demand. It is the latter detrimental effect that may prevent both firms from choosing a contingent pricing strategy in equilibrium. We show that the insights remain valid when capacity decisions are endogenized. We caution that responsive price changes under aggressive competition of less differentiated products can result in profit‐killing discounting.     

中小制造企业在线直销与传统分销双渠道定价决策研究

针对传统渠道中处于非主导地位的中小制造企业开展双渠道销售时存在的价格冲突问题,考虑产品数字属性对渠道需求的影响,构建了制造商与零售商独立决策和制造商占非主导地位两种情况下的双渠道定价决策模型,给出了两种情况下的双渠道最优定价,并分别考察了产品数字属性变化以及决策权利结构不同对最优定价的影响。研究结果表明,处于非主导地位的中小制造企业应采用依从强势零售商的定价策略,该策略有利于制造商和零售商以及渠道整体收益的增加;随着产品数字属性的增大,制造商的最优定价相应地提高,而零售商的最优定价则相应地降低;制造商占非主导地位时的双渠道最优定价高于制造商与零售商独立决策时的双渠道最优定价。     

顾客策略行为下差异产品两阶段定价模型研究

互联网和信息技术的发展,为零售商收集顾客信息带来方便的同时,也使得消费者变得越来越具有策略性和选择性。首先,构建零售商只销售一种高质量产品的情形,研究其两阶段的定价策略,并分析产品的跨期折扣因子对产品的零售价格、销售量和零售商利润的影响。然后,考虑零售商可提供高质量和低质量两种产品的情形,顾客在第一销售期、第二销售期都可以选择两种产品。构建两阶段的定价决策模型,并分析产品的跨期折扣因子、顾客对低质量产品的接受度等参数对产品两阶段的零售价格、销售量的影响。最后,用数值算例分析了第二种模型下顾客对低质量产品的接受度等模型参数对零售商两阶段总利润的影响,然后比较了第一种和第二种模型下高质量产品的零售价格和销售量。研究结论较全面的分析了顾客策略行为对差异产品两阶段销售期的定价决策的影响,为零售商进行定价优化决策提供了十分重要的参考。     

Price Incentives and Coordination in a Two‐Product Decentralized Supply Chain

We investigate pricing incentives for competing retailers who distribute two variants of a manufacturer's product in a decentralized supply chain. Under a two‐dimensional Hotelling model, we derive decentralized retailers' prices for the products, and distortions in pricing when compared to centrally optimal prices. We show that price distortions decrease as consumers' travel cost between retailers increases, due to less intense competition. However, price distortions do not change monotonically in consumers' switching cost between products within stores. To fix decentralized retailers' price distortions, we construct a two‐part pricing contract that coordinates the supply chain. We show that the coordinating contract is Pareto‐improving and analyze increase in the supply chain profit under coordination.     

Supply Chain Coordination in a Market with Customer Service Competition

We consider a market with two competing supply chains, each consisting of one wholesaler and one retailer. We assume that the business environment forces supply chains to charge similar prices and to compete strictly on the basis of customer service. We model customer service competition using game‐theoretical concepts. We consider three competition scenarios between the supply chains. In the uncoordinated scenario, individual members of both supply chains maximize their own profits by individually selecting their service and inventory policies. In the coordinated scenario, wholesalers and retailers of each supply chain coordinate their service and inventory policy decisions to maximize supply chain profits. In the hybrid scenario, competition is between one coordinated and one uncoordinated supply chain. We discuss the derivation of the equilibrium service strategies, resulting inventory policies, and profits for each scenario, and compare the equilibria in a numerical study. We find that coordination is a dominant strategy for both supply chains, but as in the prisoner's dilemma, both supply chains are often worse off under the coordinated scenario relative to the uncoordinated scenario. The consumers are the only guaranteed beneficiaries of coordination.     

Sales Force and Competition in Financial Product Markets: The Case of Mexico's Social Security Privatization

This paper examines how sales force impacts competition and equilibrium prices in the context of a privatized pension market. We use detailed administrative data on fund manager choices and worker characteristics at the inception of Mexico's privatized social security system, where fund managers had to set prices (management fees) at the national level, but could select sales force levels by local geographic areas. We develop and estimate a model of fund manager choice where sales force can increase or decrease customer price sensitivity. We find exposure to sales force lowered price sensitivity, leading to inelastic demand and high equilibrium fees. We simulate oft proposed policy solutions: a supply‐side policy with a competitive government player and a demand‐side policy that increases price elasticity. We find that demand‐side policies are necessary to foster competition in social safety net markets with large segments of inelastic consumers.     

Joint Ordering and Pricing Strategies for Managing Substitutable Products

Starr and Rubinson (1978) develop a model to establish the relationship between product demand and relative prices. The notion of relative prices motivates us to consider a situation in which a retailer would either charge the same retail price for all products if he adopts a ‘fixed’ pricing strategy or charge different prices for different products if he adopts a ‘variable’ pricing strategy. In this paper, we develop a base model with deterministic demand that is intended to examine how a retailer should jointly determine the order quantity and the retail price of two substitutable products under the fixed and variable pricing strategies. Our analysis indicates that the optimal retail price under the variable pricing strategy is equal to the optimal retail price under the fixed pricing strategy plus or minus an adjustment term. This adjustment term depends on product substitutability and price sensitivity. We also present two different extensions of our base model. In the first extension, our analysis indicates that the underlying structure of the optimal retail price and order quantity is preserved when there is a limit on the total order quantity. The second extension deals with the issue of retail competition. Relative to the base case, we show that the underlying structure of the optimal retail price and order quantity is preserved in a duopolistic environment. Moreover, our analysis suggests that both retailers would adopt the variable pricing strategy at the equilibrium.