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。     

Capacity Allocation and Pricing Strategies for New Wireless Services

Indoor cell phone users often suffer poor connectivity. One promising solution to this issue, femtocell technology, has been rapidly developed and deployed over the past few years. One of the biggest challenges facing femtocell deployment is the lack of a clear business model. This study investigates the economic incentive for cellular operators (also called macrocell operators) to enable femtocell service by leasing spectrum resources to independent femtocell operators. We model the interactions between a macrocell operator, a femtocell operator, and end‐users as a three‐stage dynamic game, and derive the equilibrium pricing and capacity allocation decisions. We show that when spectrum resources are very limited, the macrocell operator has more incentive to lease spectrum to the femtocell operator, as femtocell services can help cover more users and improve the utilization efficiency of the limited spectrum resource. However, when the total spectrum resource is large, femtocell service offers significant competition to macrocell service and, as a result, the macrocell operator has less incentive to enable femtocell service. We also show the impact of the additional operational costs and limited coverage of femtocell service on equilibrium decisions, consumer surplus, and social welfare.     

无外部市场条件下中间产品转移价格的博弈分析与决策

本文首先用反例证明了文^[1]中在各分厂成本函数和最终产品需求函数已知的条件下,给出的中间产品最优转移价格的两个计算公式并不总是成立的,给出了这两个计算公式成立的充要条件,并分析了公司关于中间产品转移价格决策的动态一致性问题。接着,利用完全信息动态博弈对中间产品转移价格的确定问题做了进一步的分析研究。最后,针对文^[1]中给出的中间产品最优转移价格的两个计算公式不成立的情况,讨论了中间产品转移价格的确定问题。     

On the Unimodality of the Profit Function of the Pricing Newsvendor

In this note, we study the price‐setting newsvendor problem. We use three conditions, the log‐convexity of the coefficient of variation, the log‐concavity of the deterministic profit function, and the log‐convexity of the random noise's expectation conditional on having leftover inventory to establish the log‐concavity of the retailer's expected profit function. This new result is complementary to existing results and removes some assumptions in the pricing and inventory coordination literature. It also addresses the conjecture made by Petruzzi and Dada (1999), and can be applied in the pricing game.     

Dynamic Pricing in the Presence of Myopic and Strategic Consumers: Theory and Experiment

We investigate retailers’ dynamic pricing decisions in a stylized two‐period setting with possible supply constraints and demand from both myopic and strategic consumers. We present an analytical model and then test its predictions in a behavioral experiment in which human subjects played the role of pricing managers. We find that the fraction of strategic consumers in the market systematically moderates the optimal pricing structure. When this fraction exceeds a certain threshold, the retailer offers relatively small late season markdowns to discourage strategic consumers from waiting and to incentivize them to buy during the early season; otherwise, the retailer offers relatively large markdowns to divert all strategic consumers to the late season, where the majority of revenue is made. Our model analyses suggest that the latter policy is optimal under fairly broad conditions. Our experiment shows that after some significant learning, aggregate behavior is able to approximate the key qualitative predictions from our model analysis, with one notable deviation: in the presence of a mixture of myopic and strategic consumers, subjects act somewhat myopically – they underprice and oversell in the main selling season, which significantly limits their ability to generate revenue in the markdown season.     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.     

Keyword Auctions,Unit‐Price Contracts,and the Role of Commitment

Motivated by the enormous growth of keyword advertising, this paper explores the design of performance‐based unit‐price contract auctions, in which bidders bid their unit prices and the winner is chosen based on both their bids and performance levels. The previous literature on unit‐price contract auctions usually considers a static case where bidders' performance levels are fixed. This paper studies a dynamic setting in which bidders with a low performance level can improve their performance at a certain cost. We examine the effect of the performance‐based allocation on overall bidder performance, auction efficiency, and the auctioneer's revenue, and derive the revenue‐maximizing and efficient policies accordingly. Moreover, the possible upgrade in bidders' performance level gives the auctioneer an incentive to modify the auction rules over time, as is confirmed by the practice of Yahoo! and Google. We thus compare the auctioneer's revenue‐maximizing policies when she is fully committed to the auction rule and when she is not, and show that the auctioneer should give less preferential treatment to low‐performance bidders when she is fully committed.     

隐匿价值、社群学习与知识付费动态定价

互联网知识付费中,知识产品价值对供需双方皆具有“隐匿性”。而网络社群作为产品体验信息的重要来源,在知识价值“显现化”过程中发挥着关键作用。基于此,本文将社群交互因素纳入知识付费两期动态定价博弈模型,深入探讨社群学习机制对最优定价策略的影响。模型分析发现：①最优社群价格存在上限阈值,以确保营造良好社群学习氛围。②最优市场价格依赖于知识成本、消费者参与收益和知识价值后验信念,与知识价值之间呈现“非线性”关系。③知识产品一般应采取渗透式定价方式,而消费者耐心程度、社群活跃度与社群交互效率对均衡价格具有重要影响。进一步福利分析表明,互联网社群学习情境将提升提供者收益。本文揭示了互联网知识交易定价的深层逻辑：社群学习引致的“策略效应”和“信息效应”重塑了消费者行为模式,进而倒逼提供者采取适应性动态定价机制。     

具有网络外部性的双寡头市场的动态定价策略

本文通过将消费者对网络大小的预期引入消费者的效用函数,刻画了消费者预期如何影响市场潜量。然后,通过微分对策,分析了在垄断竞争的市场结构中的厂商如何在考虑到消费者对今后的预期时,如何动态的决定自己的价格和相应的策略。结果表明,随着消费者对网络增长预期的增大,将导致更大的网络规模和更低的初始价格。寡头的利润受消费者对其产量的预期的影响。     

A Model of Consumer Inertia with Applications to Dynamic Pricing

This paper introduces a decision model of consumer inertia. Consumers exhibit inertia when they have an inherent bias to delay purchases. Inertia may induce consumers to wait even when it is optimal to buy immediately. We embed our decision model within a dynamic pricing context. There is a firm that sells a fixed capacity over two time periods to an uncertain number of both rational and inertial consumers. We find that consumer inertia has both positive and negative effects on profits: it decreases demand (in period one) but intensifies competition among consumers for the product (in period two). We show that our model of inertia is consistent with well‐established behavioral regularities, such as loss aversion and probability weighting in the sense of prospect theory, and hyperbolic time preferences. We offer practical recommendations for firms to influence the level of consumer inertia. These include offering returns policies (to mitigate potential consumer losses), providing decision aids (to avoid perception errors), and offering flexible payment options (to lower transaction costs).     

Endogenous Completeness of Diffusion Driven Equilibrium Markets

We study the existence of dynamic equilibria with endogenously complete markets in continuous‐time, heterogenous agents economies driven by diffusion processes. Our main results show that under appropriate conditions on the transition density of the state variables, market completeness can be deduced from the primitives of the economy. In particular, we prove that a sufficient condition for market completeness is that the volatility of dividends be invertible and provide higher order conditions that apply when this condition fails as is the case in the presence of fixed income securities. In contrast to previous research, our formulation does not require that securities pay terminal dividends, and thus allows for both finite and infinite horizon economies.     

Supply Chain Coordination in the Presence of Gray Markets and Strategic Consumers

The practice of diverting genuine products to unauthorized gray markets continues to challenge companies in various industries and creates intense competition for authorized channels. Recent industry surveys report that the abuse of channel incentives is a primary reason for the growth of gray market activities. Therefore, it is crucial that companies take the presence of gray markets into consideration when they design contracts to distribute products through authorized retailers. This issue has received little attention in the extensive literature on contracting and supply chain coordination. In this study, we analyze the impacts of gray markets on two classic contracts, wholesale price and quantity discount, in a supply chain with one manufacturer and one retailer when the retailer has the opportunity to sell to a domestic gray market. Our analysis provides interesting and counterintuitive results. First, a classic quantity‐discount contract that normally coordinates the supply chain can perform so poorly in the presence of a gray market that the supply chain would be better off using a wholesale price contract instead. Second, the presence of gray market can also degrade the performance of the wholesale price contract; therefore, a more sophisticated contract is needed for coordinating the supply chain. We show that contracts that solely depend on retailer's order quantity cannot coordinate the supply chain, and provide the conditions for coordinating the supply chain with price‐dependent quantity discount contracts. We also provide comparative statics and show that when there is a gray market, coordinating the supply chain enhances total consumer welfare.     

Dynamic Pricing in e‐Services under Demand Uncertainty

High volatility of the e‐services market, due to increasing competition, low life cycle of products, and easy availability of information about competing service offerings to customers, makes the demand for service offerings quite uncertain. Revenue management in such markets calls for real‐time techniques to learn the demand and its dependence on both the price and the service level associated with the service offering. We assume firms reply on exploratory approaches for demand estimation, in which firms experiment with different service offerings in order to simultaneously learn the demand while doing business. Such exploration and learning process can be costly without supervision. As reported by Rothschild (Journal of Economic Theory, 9 185‐202, 1974), traditional Bayesian dynamic control approaches may conclude with suboptimal offerings. We propose a novel demand learning approach that is guaranteed to converge to the optimal offering. The approach combines simulated annealing algorithm with Bayesian learning. We further present intelligent techniques that adaptively reduce the effort of exploration on suboptimal service offerings so as to improve the long‐run average profit.     

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。     

考虑商誉的双渠道供应链动态定价与联合减排策略

考虑由一个制造商和一个零售商组成的双渠道供应链,将产品商誉和减排量作为状态变量构建微分博弈模型。文章首先讨论了不同渠道结构下供应链成员的最优均衡策略,随后探讨了广告合作-减排成本分担契约对供应链协调性的影响,最后通过算例对模型进行了分析。研究发现,产品商誉轨迹随时间变化呈现多变性,而减排量轨迹则具有单调性。与单渠道相比,双渠道下零售商的广告努力和利润下降,而制造商的减排努力和利润增大,只有当传统渠道市场占有率较高且制造商竞争较小时,制造商单渠道的利润才高于双渠道,此时制造商将不会开设网络渠道。广告合作-减排成本分担契约可以实现制造商、零售商和整个供应链系统利润的帕累托改善,且消费者低碳偏好和品牌偏好越高,制造商和零售商越有动力达成合作。     

Static and Dynamic Pricing of Excess Capacity in a Make‐to‐Order Environment

We consider a make‐to‐order manufacturer that serves two customer classes: core customers who pay a fixed negotiated price, and “fill‐in” customers who make submittal decisions based on the current price set by the firm. Using a Markovian queueing model, we determine how much the firm can gain by explicitly accounting for the status of its production facility in making pricing decisions. Specifically, we examine three pricing policies: (1) static, state‐independent pricing, (2) constant pricing up to a cutoff state, and (3) general state‐dependent pricing. We determine properties of each policy, and illustrate numerically the financial gains that the firm can achieve by following each policy as compared with simpler policies. Our main result is that constant pricing up to a cutoff state can dramatically outperform a state‐independent policy, while at the same time achieving most of the increase in revenue achievable from general state‐dependent pricing. Thus, we find that constant pricing up to a cutoff state presents an attractive tradeoff between ease of implementation and revenue gain. When the costs of policy design and implementation are taken into account, this simple heuristic may actually out‐perform general state‐dependent pricing in some settings.     

基于晶格场理论和动态规划的国债期货定价研究

通过用一个二维量子场取代传统金融上的布朗运动,构建了可有效纳入国债远期利率在到期时间和日历时间两个维度上的不完全相关性的量子场理论模型,并离散化二维量子场,得到国债远期利率的晶格场理论模型,同时结合动态规划方法,将国债期货的所有交易交割规则纳入一个模型进行建模,实现在统一的模型框架下对国债期货及其内嵌的择时期权和质量期权进行定价。研究结果亦表明,所构建的国债期货定价模型的定价效果均显著优于传统的主流两因子HJM模型,且与真实市场结算价的贴合性均很强,特别地,在临近交割月份,其定价误差均降至0.05%以内。而各国债期货合约的质量期权价值都在其对应的国债期货面值的2%至6%之间,其择时期权价值大部分时间都在0附近徘徊,但随交割月份临近,择时期权价值开始迅速上升,最大时约为期货合约面值的0.6%。     

考虑消费者网购体验滞后的产品定价研究

随着电子商务技术的发展,网络购物越来越便利。与此同时,网络购物带来的产品体验滞后也导致了消费者对产品的认知不确定性。而这种不确定性正在成为消费者策略性退货行为的主要原因,如消费者同时购买多件具有横向差异的产品,在收到货物后经亲身体验后保留一件而将其他产品退货。本文通过构建Hotelling模型,探讨了企业在考虑此种影响情况下的最优定价策略,分析得出：当消费者的退货成本增加时,企业最优定价也随之增加;消费者对产品的先验效用差异化越小,企业的最优定价也越低。同时发现,若某种产品无消费者单独购买,企业的最优定价会随消费者偏好的增加而增加;而当两种产品均有消费者单独购买且消费者退货成本较大时,企业的最优定价不但不会随消费者偏好的增加而提高,反而会随消费者偏好增加而减少。此外,本文给出了消费者策略性退货行为存在的临界条件,当消费者的退货成本高于这一临界条件时消费者的策略退货行为将消失。     

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick‐response supplier and a regular supplier that both suffer random disruptions, and faces price‐sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick‐response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base‐stock type and the optimal pricing policy is a list‐price policy with markdowns.     

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。