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.     

信息不对称条件下的企业集团转移定价研究

本文研究了信息不对称条件下企业集团的转移定价决策问题,提出了歧视转移定价法。即在信息不对称条件下,当上游子企业对中间产品具有完全垄断能力时,企业集团将转移定价决策权下放给上游子企业,上游子企业根据内外部市场需求的差异,采用差别定价策略。通过与市场基础转移定价和边际成本转移定价相比较,得出歧视转移定价可以增加企业集团的整体利润。     

航空客运平行航班动态定价模型

航空公司在同一航线上,提供多个不同时刻起飞的航班,我们称这样的航班为平行航班。本文应用随机控制理论建立了两个平行航班动态定价连续时间数学模型,证明了最优策略的性质,得到了最优动态定价综合策略,并给出了最优控制的时间阈值点。数值实验结果表明,这种时间阈值点的综合控制策略不仅易于实施,而且,应用该优化模型得到的总收入比两个平行航班独立决策时得到的总收入大。     

数据优势会使平台企业提高定价吗？——模型推导与理论分析

数字经济时代,数据成为平台企业的重要生产要素。本文分析了垄断环境与差异化竞争环境下,数据对平台企业定价行为的影响。研究结果表明：在垄断环境下,数据会降低平台企业产品或服务的价格;差异化竞争环境下,数据的丰富使市场中的平台企业可以自发地形成两种定价方式：对于为主流领域提供产品或服务的企业而言,数据会使其提高价格获取利润,而对于面临长尾需求的企业而言,数据会使其降低价格,采取"薄利多销"的手段获取利润。同时,本文也提出了对数据优势作用的进一步思考——数据有助于完全价格歧视的实现与产生新价格歧视场景;数据有助于企业识别自身特征,进一步使平台市场自发形成"主流层次"与"长尾层次"两个层次;数据有弱化市场势力的作用。     

Grocery Perishables Management

In this article, we study the joint pricing and inventory control problem for perishables when a retailer does not sell new and old inventory at the same time. At the beginning of a period, the retailer makes replenishment and pricing decisions, and at the end of a period, the retailer decides whether to dispose of ending inventory or carry it forward to the next period. The objective of the retailer is to maximize the long‐run average profit. Assuming zero lead time, we propose an efficient solution approach to the problem, which is also generalized to solve three extensions to the basic model. A feature of the present study is that we consider explicitly the influence of perishability on the demand. Among the insights gathered from the numerical analysis, we find that dynamic pricing aids extending shelf life and when disposal incurs a lower cost, or even a positive salvage value, the retailer is induced to dispose earlier since the benefit of selling new inventory offsets the loss due to disposal. We also observe that the faster the perceived rate of deterioration, the lower the threshold of the ending inventory for disposal. Perhaps a bit counter‐intuitive, maximizing profits does not mean eliminating disposals or expirations.     

消费者锚定效应下的动态定价与库存控制研究

在零售商-消费者两级供应链中, 零售商垄断销售市场, 研究基于消费者锚定效应的动态定价与库存问题。将消费者的锚定效应纳入决策模型中, 探讨消费者锚定的参考价格与产品的市场需求、价格的动态变化关系;利用动态规划理论建立了消费者锚定效应的动态定价与库存模型;在此基础上考虑利润折现和库存积压问题, 并分别构建了相应模型。数值分析表明, 消费者会根据市场价格的变化决定最佳的购买时机, 零售商的期望收益随着销售时间的延长而增加。     

On the Benefit of Inventory‐Based Dynamic Pricing Strategies

We study the optimal pricing and replenishment decisions in an inventory system with a price‐sensitive demand, focusing on the benefit of the inventory‐based dynamic pricing strategy. We find that demand variability impacts the benefit of dynamic pricing not only through the magnitude of the variability but also through its functional form (e.g., whether it is additive, multiplicative, or others). We provide an approach to quantify the profit improvement of dynamic pricing over static pricing without having to solve the dynamic pricing problem. We also demonstrate that dynamic pricing is most effective when it is jointly optimized with inventory replenishment decisions, and that its advantage can be mostly realized by using one or two price changes over a replenishment cycle.     

A comparison of fixed and dynamic pricing policies in revenue management

We consider the problem of selling a fixed capacity or inventory of items over a finite selling period. Earlier research has shown that using a properly set fixed price during the selling period is asymptotically optimal as the demand potential and capacity grow large and that dynamic pricing has only a secondary effect on revenues. However, additional revenue improvements through dynamic pricing can be important in practice and need to be further explored. We suggest two simple dynamic heuristics that continuously update prices based on remaining inventory and time in the selling period. The first heuristic is based on approximating the optimal expected revenue function and the second heuristic is based on the solution of the deterministic version of the problem. We show through a numerical study that the revenue impact of using these dynamic pricing heuristics rather than fixed pricing may be substantial. In particular, the first heuristic has a consistent and remarkable performance leading to at most 0.2% gap compared to optimal dynamic pricing. We also show that the benefits of these dynamic pricing heuristics persist under a periodic setting. This is especially true for the first heuristic for which the performance is monotone in the frequency of price changes. We conclude that dynamic pricing should be considered as a more favorable option in practice.     

网络外部性与产品垄断定价策略研究

当产品存在网络外部性时,垄断厂商在一个较长的时期内如何分阶段提供产品并制定一个合理的价格以获得最大的利润是一个重要问题,因为网络外部性可能会对消费者的预期有着重要的影响,从而影响垄断厂商的定价策略和利润.为了探讨这一问题,本文通过构造一个两阶段的动态模型,分垄断厂商可以在不同的阶段提供同质产品和差异产品两种情形来分析了存在网络外部性条件下垄断厂商的动态价策略.研究表明,若垄断厂商在不同阶段提供同质产品,则第一时段的价格要高于第二时段价格的贴现值;若垄断厂商在第二阶段提供差异产品,则产品的价格会比没有网络外部性的情况下有所降低.     

考虑广告影响下的新产品垄断动态定价研究

针对垄断零售商的新产品定价问题,提出了一个新产品动态定价策略。在顾客对以往的价格和广告具有"学习"能力的条件下,提出了具有"学习"功能的需求函数。在给定各周期广告水平下,给出了零售商最优的动态定价策略,分析了零售商定价规律,发现其定价规律具有"振荡"性,并趋近于一定值。在零售商要同时决策零售价格和广告水平的条件下,给出了各周期最优的零售价格和广告水平。在一定条件下,当周期数趋近无穷大时零售价格趋近于顾客的保留价格或者单位成本。     

双渠道下库存与定价策略的研究

为分析实体店零售商建立自己网络渠道存在的两个基本问题,本文探讨了为满足网络渠道需求网络渠道是自持有库存、还是共享实体店的库存问题,及如何解决网络渠道与实体渠道的销售冲突问题。在总结动态库存配给策略相关研究基础上,采用了动态定价策略的思路分析解决渠道冲突的问题;通过对双渠道是否共享库存的两种方案进行模拟对比,分析讨论了相关库存决策问题,并评价了共享库存所带来的共享效应的大小,以期使实体店零售商建立网络销售渠道取得更大的收益。研究结果表明,共享库存有比较显著的优势,库存共享效应能使需求波动更平滑、需求预测更精准;动态定价会带来更大的收益,在验证该结果时,对动态定价策略也进行了结构特征的分析。该思路可为相关研究提供借鉴。     

Technical Note – Pricing Below Cost Under Exchange‐Rate Risk

Pricing below cost is often classified as “dumping” in international trade and as “predatory pricing” in local markets. It is legally prohibited from practice because of earlier findings that it leads to predatory behavior by either eliminating competition or stealing market share. This study shows that a stochastic exchange rate can create incentives for a profit‐minded monopoly firm to set price below marginal cost. Our result departs from earlier findings because the optimal pricing decision is based on a rational behavior that does not exhibit any malicious intent against the competition to be considered as violating anti‐trust laws. The finding is a robust result, because our analysis demonstrates that this behavior occurs under various settings such as when the firm (i) is risk‐averse, (ii) can postpone prices until after exchange rates are realized, (iii) is capable of manufacturing in multiple countries, and (iv) operates under demand uncertainty in addition to the random exchange rate.     

Pareto‐Improving Contracts for Express Package Delivery Services

We address the problem of an express package delivery company in structuring a long‐term customer contract whose terms may include prices that differ by day‐of‐week and by speed‐of‐service. The company traditionally offered speed‐of‐service pricing to its customers, but without day‐of‐week differentiation, resulting in customer demands with considerable day‐of‐week seasonality. The package delivery company hoped that using day‐of‐week and speed‐of‐service price differentiation for contract customers would induce these customers to adjust their demands to become counter‐cyclical to the non‐contract demand. Although this usually cannot be achieved by pricing alone, we devise an approach that utilizes day‐of‐week and speed‐of‐service pricing as an element of a Pareto‐improving contract. The contract provides the lowest‐cost arrangement for the package delivery company while ensuring that the customer is at least as well off as he would have been under the existing pricing structure. The contract pricing smoothes the package delivery company's demand and reduces peak requirements for transport capacity. The latter helps to decrease capital costs, which may allow a further price reduction for the customer. We formulate the pricing problem as a biconvex optimization model, and present a methodology for designing the contract and numerical examples that illustrate the achievable savings.     

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.     

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.     

考虑退货风险的制造商双渠道供应链定价决策研究

针对事前不确定性导致的退货问题，从消费者行为出发，建立考虑定价差异和退货风险双重因素的市场需求函数，通过Stackelberg博弈模型研究四种不同市场需求情形在不同定价模式下双渠道供应链的最优决策。在数值仿真部分，对不同情形决策之间比较、供应链收益进行比较分析。研究表明：电子渠道销售价格与电子渠道的市场基本需求成正比，批发价和传统渠道销售价格与传统渠道的市场基本需求成正比，实体店体验服务水平和传统渠道的市场基本需求的关系（线性关系）则根据某些条件而定；退货风险对供应链决策的影响与定价模式、市场需求影响因素相关；制造商偏好于定价不相等模式，零售商偏好于定价相等模式；退货风险与定价差异对供应链成员收益的影响与定价模式相关，对整体供应链收益的影响与定价模式和退货率大小有关。     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

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.     

Competitive Pricing in a Multi‐Product Multi‐Attribute Environment

We address the problem of simultaneous pricing of a line of several products, both complementary products and substitutes, with a number of distinct price differentiation classes for each product (e.g., volume discounts, different distribution channels, and customer segments) in both monopolistic and oligopolistic settings. We provide a generic framework to tackle this problem, consider several families of demand models, and focus on a real‐world case‐study example. We propose an iterative relaxation algorithm, and state sufficient conditions for convergence of the algorithm. Using historical sales and price data from a retailer, we apply our solution algorithm to suggest optimal pricing, and report on numerical results.     

限制性定价策略中在位厂商的最优产量选择

Milgrom-Roberts模型及相关研究证明了不完全信息条件下限制性定价策略均衡的存在,但对存在的具体形式却没有说明。本文通过对Milgrom-Roberts限制性定价模型的进一步研究,指出不完全信息条件下不同成本类型的在位厂商阻止潜在竞争厂商进入的策略均衡可以在一个产量区间内存在;并且由于利润最大化原则,实际上形成在位厂商生产最优产量即阻止进入的均衡产量区间内的利润最大化产量、潜在竞争厂商不进入的唯一策略均衡结果。由于潜在的进入威胁,在位厂商要想成功实施限制性定价策略,其最优产量只能大于或等于垄断产量,而利润只能小于或等于垄断利润。