Differential Pricing for Information Sharing Under Competition

We consider a two‐echelon supply chain with a manufacturer supplying to multiple downstream retailers engaged in differentiated Cournot competition. Each retailer has private information about uncertain demand. The manufacturer is the Stackelberg leader who sets the contract terms with the retailers, and benefits from retailers sharing their private information. When all retailers are given the same wholesale price, truthful information sharing is not an equilibrium outcome. We propose two variants of differential pricing mechanisms that induce truthful information sharing by all retailers. The first variant rewards a retailer for providing optimistic information and achieves truthful information sharing as a unique equilibrium. The differential pricing mechanism is optimal in the class of linear‐price, incentive‐compatible, direct mechanisms. The second variant, which incorporates provision for a fixed payment in addition to wholesale prices, preserves all the equilibrium properties of the first variant and additionally “nearly coordinates” the supply chain. Our analysis of differential pricing with a fixed payment provides interesting observations regarding the relationship between product substitutability, number of retailers, information precision, and market power. As products become closer substitutes and/or number of retailers increase, the manufacturer's market power increases, enabling her to extract a larger fraction of the supply chain surplus.     

Dynamic Pricing with Constant Demand Elasticity

The celebrated model of Gallego and van Ryzin is specialized to the case of constant elasticity of demand. A closed form is developed, which has an even simpler form than that arising with exponential demand and which possesses an excellent approximation. In this environment, monopoly is efficient, which means that all the behavior usually attributed to monopoly pricing is actually a consequence of efficient pricing and would arise even in a perfectly competitive environment. If the initial supply is not too large, consumers have no incentive to delay their purchases to get a lower price at the average inventory prevailing at any time.     

A Nonatomic‐Game Approach to Dynamic Pricing under Competition

We study a revenue management problem involving competing firms. We assume the presence of a continuum of infinitesimal firms where no individual firm has any discernable influence over the evolution of the overall market condition. Under this nonatomic‐game approach, the unanimous adoption of an equilibrium pricing policy by all firms will yield a market‐condition process that in turn will elicit the said policy as one of the best individual responses. For both deterministic‐ and stochastic‐demand cases, we show the existence of equilibrium pricing policies that exhibit well‐behaving monotone trends. Our computational study reveals many useful insights, including the fact that only a reasonable number of firms are needed for our approach to produce near‐rational pricing policies.     

竞争环境下基于顾客策略行为的易逝品动态定价研究

在两个提供相同易逝品的零售商折线竞争下,从顾客策略行为出发,研究竞争环境下两零售商的动态定价策略。首先建立供大于求的情况下两零售商动态定价模型,给出了均衡价格满足的条件,并探讨了在一些特殊情况下均衡价格的特性。然后将这一模型扩展到供小于求的情形,探讨模型的求解方法。算例分析了在折线竞争模式下零售商在面对顾客策略行为时,如何动态的决定价格。同时发现,在供大于求的情况下,顾客策略行为导致零售商的收益降低;在供小于求的情况下,一定程度的顾客策略行为可以使零售商获得更高的期望收益。     

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.     

Recent Developments in Dynamic Pricing Research: Multiple Products,Competition, and Limited Demand Information

Dynamic pricing enables a firm to increase revenue by better matching supply with demand, responding to shifting demand patterns, and achieving customer segmentation. In the last 20 years, numerous success stories of dynamic pricing applications have motivated a rapidly growing research interest in a variety of dynamic pricing problems in the academic literature. A large class of problems that arise in various revenue management applications involve selling a given amount of inventory over a finite time horizon without inventory replenishment. In this study, we identify most recent trends in dynamic pricing research involving such problems. We review existing research on three new classes of problems that have attracted a rapidly growing interest in the last several years, namely, problems with multiple products, problems with competition, and problems with limited demand information. We also identify a number of possible directions for future research.     

Pricing,Allocation, and Overbooking in Dynamic Service Network Competition When Demand Is Uncertain

We study the problem of combined pricing, resource allocation, and overbooking by service providers involved in dynamic noncooperative oligopolistic competition on a network that represents the relationships of the providers to one another and to their customers when service demand is uncertain. We propose, analyze, and compute solutions for a model that is more general than other models reported in the revenue management literature to date. In particular, previous models typically consider only three or four of five key revenue management features that we have purposely built into our model: (1) pricing, (2) resource allocation, (3) dynamic competition, (4) an explicit network, and (5) uncertain demand. Illustrative realizations of the abstract problem we study are those of airline revenue management and service provision by companies facing resource constraints. Under fairly general regularity conditions, we prove existence and uniqueness of a pure strategy Nash equilibrium for dynamic oligopolistic service network competition described by our model. We also show, for an appropriate notion of regularity, that competition leads to the underpricing of network services, a finding numerically illustrated by an example of intermediate size. Our proposed algorithm can be implemented using well‐known off‐the‐shelf commercial software.     

基于需求转移的易逝性产品最优动态定价策略

本文针对易逝性产品中新产品对老产品需求的转移作用,应用收入管理方法得出老产品的最优动态定价策略,并应用最大凹向包络理论给出了简化算法的方法.数值算例表明在存在需求转移的情况下,应更早的提供较低的价格.最后作者给出了包含生产和定价的综合模型.     

Ordering,Pricing, and Lead‐Time Quotation Under Lead‐Time and Demand Uncertainty

In this article, we study the newsvendor problem with endogenous setting of price and quoted lead‐time. This problem can be observed in situations where a firm orders semi‐finished product prior to the selling season and customizes the product in response to customer orders during the selling season. The total demand during the selling season and the lead‐time required for customization are uncertain. The demand for the product depends not only on the selling price but also on the quoted lead‐time. To set the quoted lead‐time, the firm has to carefully balance the benefit of increasing demand as the quoted lead‐time is reduced against the cost of increased tardiness. Our model enables the firm to determine the optimal selling price, quoted lead‐time, and order quantity simultaneously, and provides a new set of insights to managers.     

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。     

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.     

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。     

收益的定价管理在网络空间租赁中的应用

将收益管理技术引入网络空间租赁领域,通过对网络空间特点的分析,得出影响供应商定价的5种因素:软硬件配置及基础设施建设、服务、租赁空间的大小、租赁时间和技术进步,并通过相关数据说明这些因素对供应商定价产生的影响。将收益管理与网络租赁产品价格设计联系起来,简要阐述了网络产品价格设计的全过程,并针对当前价格设计中存在的问题,提出了几种有效的解决方法。     

成套产品定价方法研究

在给出成套产品定价的概念的基础上,通过一个简单的算例来说明成套产品定价方法的思想,给出了纯成套产品定价方法的总收益大于产品单卖时的总收益的条件,并给出了混合成套产品定价时最优成套出售的套数k^#存在的区间。     

基于逆周期缓冲机制的或有可转债研究

基于逆周期缓冲机制的双触发器或有可转债(简记为CoCoCb)为债券发行银行提供资本再重组机会。当经济与金融系统性风险累积到较高的水平,CoCoCb可以按照事先约定的折扣率回售,或者被转换为等价值的普通或有可转债(CoCo)。当债券发行银行陷入财务困境时,CoCo转换为股权以吸收银行的损失,并维持银行正常运营。CoCoCb的回售机制允许银行在经济与金融危机爆发前债务减记,即CoCoCb嵌入了逆周期缓冲机制;债转股机制使得CoCoCb具有很强的损失吸收能力。基于Black-Scholes期权定价模型、Jarrow-Turnbull简约化定价模型和无违约风险假设,利用复制方法求解零息票CoCoCb定价解析式。实证分析表明:信贷与GDP的缺口(Gap)值达到峰值事件服从泊松过程。选取适当的回售比率能保证CoCoCb兼具逆周期缓冲与损失吸收能力。     

基于转换点生存概率的或有可转债定价研究

首先利用二叉树模型及风险中性定价原理,给出了离散时间下或有可转债(Contingent Convertible Bonds,简称Co Cos)的估值方法;然后通过刻画Co Cos在各转换点的生存概率,扩展构建了一个连续时间下的Co Cos定价模型;最后以瑞信集团发行的或有可转债"BCN"为例,进行定价计算及敏感性分析。结果表明银行资产及资产波动率对Co Cos价值有显著的正向影响。另外,为弥补现有研究不足,本文以权益比率为触发器,避免了银行权益与Co Cos价值间的多重均衡问题,并通过建立权益比率与核心一级资本充足率的线性模型,使定价模型可推广适用于以资本充足率为触发器的债券。     

或有可转换债券的定价和公司资本结构

假设公司收益流服从算术布朗运动,考虑包含或有可转换债券(CCB) 的公司资本结构问题,计算公司证券均衡价格,分析公司破产概率、公司收益风险与公司资本结构之间的数量关系． 结果表明: CCB 不但显著降低破产概率,减小管理者“资产替代”动机,而且吸收公司大部分风险,大幅提升公司总价值; CCB 的收益率差价明显高于普通债券; 公司收益流与市场正(负) 相关程度越高,公司总价值越小(大) ．     

考虑需求端和产出端不确定性的服务平台定价和商业模式研究

同时考虑平台需求端和供给端不确定性,分析此时服务平台的产品定价、最优激励、商业模式和效率损失传导。通过将委托代理理论和平台理论结合的方法进行分析,研究表明:(1)需求端和产出端的不确定性越高,平台对消费端的定价越低;随着需求端自网络外部性增强,需求端不确定对消费端的影响减弱;随需求端交叉网络外部性增强,需求端不确定对消费端的定价影响增强。(2)需求或产出不确定性越大,分成报酬占总报酬比例越低,平台商业模式更接近于雇佣或自营模式;反之接近纯平台模式。(3)产出端不确定性带来的效率损失在平台两端之间传导。当服务端存在不确定性,服务端报酬和需求端定价同时上升,服务提供端的报酬升高幅度大于需求端产品价格升高幅度。同时,平台将部分效率损失内化,平台承担的效率损失与需求端交叉网络外部性成正比。     

考虑旅客跨区间流转的机票多预定区间折扣优化模型研究

多预定区间差异化折扣逐渐成为机票收益管理的重要分支。本文提出了一种新的收益管理模型：基于顾客跨区间流转的收益管理模型,并给出了二分法迭代求解方法。假设各个预订时间区间的潜在需求可以通过大数据手段进行预测,首先结合旅客的价格敏感和潜在需求跨时间段流转的特性分析了各区间的需求函数,然后结合需求函数构建了多预定区间折扣优化模型。由于该模型属于动态的收益管理模型,因此构建了一种动态求解方法——二分迭代法。最后,依据航空公司的实际情况设计了两个仿真实验。实验计算结果不仅验证了新模型和算法的有效性,而且得出一些比较有用的结论：（1）票价与提前购票时间不存在单调的线性关系;（2）预订区间远离离港日折扣逐渐变大,靠近离港日的折扣会逐渐减少,但是包含离港日的预订区间的折扣又会变大;（3）流转率越高则折扣越少;（4）价格敏感系数越高折扣越高;（5）流转率通过改变价格敏感系数而影响折扣的大小。本文给出的折扣优化决策模型符合旅游产品多预定区间折扣决策的实践,可以为机票、酒店、景区等多种旅游产品的票价决策提供有益参考。     

Joint Pricing and Contingent Free-Shipping Decisions in B2C Transactions

We consider an online retailer's joint pricing and contingent free-shipping (CFS) decisions in both monopoly and duopoly structures, which is an important marketing-operations interface problem. We begin by investigating the impacts of a retailer's decisions on consumers' purchase behaviors, and show that the CFS strategy is useful to acquire the consumers with large order sizes. Then, we compute the probability of repeated purchases, and construct an expected profit function for an online retailer in the monopolistic setting. We find that the fixed shipping fees may have the largest impact on the retailer's profit among all shipping-related parameters, and the retailer can benefit more from homogeneous markets than from heterogeneous ones. Next, we consider the competition between two retailers in the duopoly structure, and analytically show that, if two retailers have identical fixed and variable shipping fees, then their equilibrium decisions are equal. In order to numerically find a Nash equilibrium for two retailers, we develop a simulation approach using Arena and OptQuest. Our simulation-based examples suggest that, as a result of the competition, the two retailers should decrease their profit margins but increase their CFS cutoff levels if they have the same fixed and also the same variable shipping fees.