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Distribution-Free Pricing 传播变为免费定价
Pub Date : 2019-10-26 DOI: 10.2139/SSRN.3090002
Hongqiao Chen, Ming Hu, G. Perakis
Problem definition: We study a monopolistic robust pricing problem in which the seller does not know the customers’ valuation distribution for a product but knows its mean and variance. Academic/practical relevance: This minimal requirement for information means that the pricing managers only need to be able to answer two questions: How much will your targeted customers pay on average? To measure your confidence in the previous answer, what is the standard deviation of customer valuations? Methodology: We focus on the maximin profit criterion and derive distribution-free upper and lower bounds on the profit function. Results: By maximizing the tight profit lower bound, we obtain the optimal robust price in closed form as well as its distribution-free, worst-case performance bound. We then extend the single-product result to study the robust pure bundle pricing problem where the seller only knows the mean and variance of each product, and we provide easily verifiable, distribution-free, sufficient conditions that guarantee the pure bundle to be more robustly profitable than à la carte (i.e., separate) sales. We further derive a distribution-free, worst-case performance guarantee for a heuristic scheme in which customers choose between buying either a single product or a pure bundle. Moreover, we generalize separate sales and pure bundling to a scheme called clustered bundling that imposes a price for each part (i.e., cluster) of a partition of all products and allows customers to choose one or multiple parts (i.e., clusters), and we provide various algorithms to compute clustered bundling heuristics. In parallel, most of our results hold for the minimax relative regret criterion as well. Managerial implications: The robust price for a single product is in closed form under the maximin profit or minimax relative regret criterion and hence, is easily computable. Its interpretation can be easily explained to pricing managers. We also provide efficient algorithms to compute various mixed bundling heuristics for the multiproduct problem.
问题定义:我们研究了一个垄断的鲁棒定价问题,其中卖方不知道顾客对产品的评价分布,但知道其均值和方差。学术/实践相关性:这种对信息的最低要求意味着定价经理只需要能够回答两个问题:你的目标客户平均会支付多少钱?要衡量你对前一个答案的信心,客户估值的标准差是多少?方法:重点研究利润最大化准则,推导出利润函数的无分布上下界。结果:通过最大化紧利润下界,我们得到了封闭形式的最优稳健价格及其无分配的最坏情况性能下界。然后,我们将单产品的结果推广到卖方只知道每个产品的均值和方差的鲁棒纯束定价问题,并提供了易于验证的、无分布的充分条件,保证纯束比单产品(即单独)销售更鲁棒盈利。我们进一步推导了一个启发式方案的无分布、最坏情况下的性能保证,其中客户在购买单个产品或纯捆绑产品之间进行选择。此外,我们将单独销售和纯捆绑推广到一个称为集群捆绑的方案,该方案为所有产品的一个分区的每个部分(即集群)施加价格,并允许客户选择一个或多个部分(即集群),我们提供了各种算法来计算集群捆绑启发式。同时,我们的大多数结果也适用于极大极小相对后悔准则。管理意义:单个产品的稳健价格在利润最大化或相对后悔最小最大化准则下是封闭形式,因此很容易计算。它的解释很容易向定价经理解释。我们还提供了计算多积问题的各种混合捆绑启发式的有效算法。
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引用次数: 21
Non-Linear Pricing and Conscious Consumption 非线性定价与有意识消费
Pub Date : 2019-10-08 DOI: 10.2139/ssrn.3465981
Nadia Burani, A. Mantovani
We consider a duopolistic market in which a green firm competes with a brown rival and each firm sells two quality-differentiated products. We study optimal non-linear contracts offered by the two firms when consumers: (i) Are privately informed about their willingness to pay for quality, and (ii) differ in their environmental consciousness. We characterize how consumers with different valuations for quality self-select into firms and show that the ranking of qualities, relative prices and profits all depend on the interplay between consumers’ valuations and firms’ cost heterogeneity. Interestingly, when consumers’ valuations for quality are relatively low, the brown firm does not offer a low-quality variety. This contrasts with the situation of full information, in which both firms commercialize a high- and a low-quality variety. Hence, the lack of information about consumers’ valuations may not only favor the green firm in terms of higher prices and profits, but also reduce the product range offered by the brown rival.
我们考虑一个双寡头市场,其中一家绿色公司与一家棕色公司竞争,每家公司销售两种质量差异化的产品。我们研究了两家公司提供的最优非线性契约,当消费者:(i)私下了解他们为质量付费的意愿,(ii)他们的环境意识不同。我们描述了对质量有不同评价的消费者如何自我选择进入企业,并表明质量的排名、相对价格和利润都取决于消费者的评价和企业成本异质性之间的相互作用。有趣的是,当消费者对质量的评价相对较低时,棕色公司不会提供低质量的品种。这与充分信息的情况形成对比,在充分信息的情况下,两家公司都将高质量和低质量的品种商业化。因此,缺乏消费者评价信息不仅有利于绿色企业获得更高的价格和利润,而且也减少了棕色竞争对手提供的产品范围。
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引用次数: 1
Pricing in Service Systems with Rational Balking and Abandonment of Time-Sensitive Customers 具有时间敏感顾客理性回避和抛弃的服务系统定价
Pub Date : 2019-10-05 DOI: 10.2139/ssrn.3464899
Hossein Abouee Mehrizi, R. Konrad
The current literature on pricing in service systems with time-sensitive customers predominately ignores the rational abandonment of customers with mixed-risk attitudes. The goal of this paper is to address this gap. We consider an unobservable queueing system with a nonlinear waiting cost function, which is concave up to a certain point and then becomes convex, capturing the mixed-risk attitude of customers observed in empirical studies. We assume that customers are sensitive with respect to waiting time (delay) and strategic regarding their balking and abandonment decisions. We characterize the optimal pricing policy that maximizes the service provider's revenue. We show that the pricing policies studied in the literature, including the joint service and cancellation (entrance) fee policy, are suboptimal and cannot induce socially optimal behavior. We demonstrate that while the cancellation fee can regulate a customer's balking strategy, the service fee cannot effectively control a customer's abandonment decision. We then provide conditions under which the joint service and cancellation fee policy is optimal. We finally prove that the service provider should compensate customers for their waiting in order to efficiently control the abandonment of customers. We propose a pricing policy, which includes entrance, service, and wait time (delay) fees, that maximize the provider's revenue.
We derive the optimal fees and show that, under the proposed optimal pricing policy, customers pay service and cancellation fees while they are partially compensated for the time spent waiting for service.
目前关于具有时间敏感客户的服务系统定价的文献主要忽略了具有混合风险态度的客户的理性放弃。本文的目标是解决这一差距。我们考虑一个不可观察排队系统,该系统具有非线性等待成本函数,该函数在某一点上是凹的,然后变成凸的,捕捉了实证研究中观察到的顾客的混合风险态度。我们假设客户对等待时间(延迟)很敏感,对他们的犹豫和放弃决定很有策略。我们描述了使服务提供商收益最大化的最优定价策略。我们证明了文献中研究的定价政策,包括联合服务和取消(入场)费用政策,是次优的,不能诱导社会最优行为。研究表明,取消费用可以调节客户的退出策略,但服务费用不能有效控制客户的放弃决策。然后给出了联合服务和取消费用政策最优的条件。最后证明,为了有效地控制顾客的弃用行为,服务提供者应该对顾客的等待进行补偿。我们提出了一种定价策略,其中包括入口、服务和等待时间(延迟)费用,以使提供商的收入最大化。我们推导出最优收费,并证明在最优定价策略下,顾客支付服务费和取消费,而他们等待服务的时间得到部分补偿。
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引用次数: 1
Group Hug: Platform Competition with User-Groups 群体拥抱:与用户群体的平台竞争
Pub Date : 2019-09-30 DOI: 10.2139/ssrn.3468410
Sarit Markovich, Y. Yehezkel
We consider platform competition in the presence of small users and a usergroup. One platform enjoys a quality advantage and the other benefits from favorable beliefs. We study whether the group mitigates the users' coordination problem i.e., joining a low-quality platform because they believe that other users would do the same. We find that when the group is sufficiently large to facilitate coordination on the high-quality platform, the group may choose to join the low-quality one. When the group joins the more efficient platform it does not necessarily increase consumer surplus. Specifically, a non-group user benefits from a group with an intermediate size, and prefers a small group over a large group. The utility of a group user is also non-monotonic in the size of the group.
我们考虑的是存在小用户和用户群的平台竞争。一个平台享有质量优势,另一个则受益于良好的信念。我们研究群体是否缓解了用户的协调问题,即,因为他们相信其他用户也会这样做而加入一个低质量的平台。我们发现,当群体足够大,可以在高质量平台上进行协调时,群体可能会选择加入低质量平台。当这个群体加入效率更高的平台时,并不一定会增加消费者剩余。具体来说,非组用户从中等规模的组中受益,并且更喜欢小组而不是大组。组用户的效用在组的大小上也是非单调的。
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引用次数: 1
An Analysis of Allocation Phase Pricing and Clock Round Price Increases in the Canadian 600 MHz Auction 加拿大600 MHz拍卖中分配阶段定价和时钟轮价格上涨分析
Pub Date : 2019-09-20 DOI: 10.2139/ssrn.3463933
J. Bono, Allan T. Ingraham, Shreyas Ravi, William K. Schwartz, Christopher Sojourner
The 600 MHz auction conducted by Innovation, Science, and Economic Development (ISED) in Canada was a Combinatorial Clock Auction (CCA) that used a spectrum set-aside to prevent three large national wireless providers—specifically, Bell, Rogers, and Telus—from winning the entirety of the spectrum at auction. The product space was divided into 16 geographic areas, and seven 2x5 MHz block were available in each area. Within the context of the ISED consultation regarding auction design for the 3500 MHz tender, respondents have commented on certain aspects of the 600 MHz auction design as it relates to the set-aside and to price determination in the 600 MHz auction. The purpose of this paper is to provide interested parties with an accurate understanding of pricing in the Canadian 600 MHz auction of 2019. This paper does not take a position on any proposed design elements of the 3500 MHz auction in Canada. We find that set-aside eligible bidders in the 600 MHz auction did not significantly affect the base prices that Rogers or Telus paid for 600 MHz spectrum. In addition, an examination of clock round bidding behavior shows that open prices did not increase significantly due to bidding from set-aside eligible bidders.
由加拿大创新、科学和经济发展(ISED)进行的600 MHz拍卖是一种组合时钟拍卖(CCA),它使用预留的频谱来防止三家大型国家无线提供商——特别是贝尔、罗杰斯和telus——在拍卖中赢得整个频谱。产品空间被划分为16个地理区域,每个区域提供7个2x5 MHz块。在就3500兆赫招标的拍卖设计进行ISED咨询的背景下,受访者对600兆赫拍卖设计的某些方面发表了评论,因为它涉及600兆赫拍卖中的预留和价格确定。本文的目的是为感兴趣的各方提供对2019年加拿大600 MHz拍卖定价的准确理解。本文不对加拿大3500兆赫拍卖的任何拟议设计元素采取立场。我们发现,在600兆赫拍卖中预留合格投标人并没有显著影响罗杰斯或Telus为600兆赫频谱支付的基本价格。此外,对全天候投标行为的检查表明,由于预留合格投标人的投标,公开价格并未显着增加。
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引用次数: 0
Determinants of Channel Profitability: Retailers' Control over Product Selections as Contracting Leverage 渠道盈利能力的决定因素:零售商对产品选择的控制作为契约杠杆
Pub Date : 2019-09-12 DOI: 10.2139/ssrn.3625706
Sylvia Hristakeva
This study shows that retailers are likely to exploit their control over product selections as a negotiation tool.
这项研究表明,零售商可能会利用他们对产品选择的控制作为谈判工具。
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引用次数: 3
Rethinking the Efficiency of Price Discrimination 重新思考价格歧视的有效性
Pub Date : 2019-07-22 DOI: 10.2139/ssrn.3652696
Patrick Ward
Analysis of efficiency in legal fields from contracts to competition assumes that a consumer’s demand depends on the price the consumer faces, not on the prices a firm charges other customers. This project provides evidence to the contrary. It examines how the phenomenon impacts the analysis of personalized pricing, also known as perfect or first-degree price discrimination. Courts have long considered the practice efficient, and companies increasingly use big data to that end.

The paper reports the results of a sequence of experiments on a simple transaction: flatware purchases. When participants learned about a firm’s personalized-pricing mechanism, demand contracted by up to 24.8%. I model a company’s most profitable response to this behavior — namely, keeping consumers in the dark about personalization — and find that the ensuing demand-side inefficiency can dwarf that of uniform monopoly pricing.

Because personalized pricing has galvanized an industry of transparency-focused startups, I also model a company’s response when it cannot obscure its pricing mechanism. Its second-best strategy is to sell to a narrow range of high-value customers. Doing so excludes some lower-income or less-interested consumers from the market. This prompts a supply-side inefficiency that can also exceed that of uniform monopoly pricing.

Faithfully applying the consumer-welfare approach to these results suggests an expanded paradigm and new types of antitrust harms. Both strategies — opaqueness and exclusion — can lead to violations of the Sherman Act and facilitate showings of harm under the Robinson Patman Act. As such, this project supports policies aimed at the transparency of prices.
从合同到竞争等法律领域的效率分析假设,消费者的需求取决于消费者面临的价格,而不是企业向其他消费者收取的价格。这个项目提供了相反的证据。它考察了这种现象如何影响个性化定价分析,也被称为完全或一级价格歧视。长期以来,法院一直认为这种做法效率很高,企业也越来越多地为此使用大数据。本文报告了一个简单交易的一系列实验结果:购买餐具。当参与者了解到公司的个性化定价机制时,需求最多收缩了24.8%。我对一家公司对这种行为的最有利可图的反应——即让消费者对个性化一无所知——进行了建模,并发现随之而来的需求侧低效率可以使统一垄断定价相形见绌。由于个性化定价激励了一个以透明度为重点的初创企业的行业,我也对一家公司在无法模糊其定价机制时的反应进行了建模。它的次优策略是向一小部分高价值客户销售产品。这样做将一些低收入或不太感兴趣的消费者排除在市场之外。这导致了供给方面的低效率,这种低效率也可能超过统一垄断定价。忠实地将消费者福利方法应用于这些结果表明了一个扩展的范式和新的反垄断危害类型。这两种策略——不透明和排除——都可能导致违反《谢尔曼法》,并有助于根据《罗宾逊·帕特曼法》显示损害。因此,本项目支持旨在提高价格透明度的政策。
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引用次数: 0
Airport Regulation 机场监管
Pub Date : 2019-07-07 DOI: 10.2139/ssrn.3488237
Achim I. Czerny
Airport regulations can take the form of cost-based, incentive, single-till and dual-till regulations. The present chapter highlights that no regulatory regime can solve all pricing and investment problems involved in airport operations at once when airports control prices in the areas of aeronautical and non-aeronautical businesses. A closer control of airport aeronautical charges favors the use of incentive and single-till regulations. Cost-based and dual-till regulations provide an environment good for investments and service quality. The lesson is that policy makers have to choose whether they would like to maintain a tight control on airport prices possibly at the expense of service quality or achieve high levels of service quality possibly leading to high pricing levels.
机场管制可以采取成本为基础、激励、单税和双税管制的形式。本章强调,当机场控制航空和非航空业务领域的价格时,任何管制制度都不能立即解决涉及机场业务的所有定价和投资问题。对机场航空收费的更严格控制有利于使用激励和单一收费规定。以成本为基础的双重收费制为投资和服务质量提供了良好的环境。从中得到的教训是,政策制定者必须做出选择,是继续严格控制机场价格(可能以牺牲服务质量为代价),还是实现高水平的服务质量(可能导致高价格水平)。
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引用次数: 3
Priority Service Pricing with Heterogeneous Customers: Impact of Delay Cost Distribution 异构客户优先服务定价:延迟成本分布的影响
Pub Date : 2019-05-28 DOI: 10.2139/ssrn.3084534
P. Cao, Yaolei Wang, Jingui Xie
This is the peer reviewed version of the following article: Cao, P., Wang, Y. and Xie, J. (2019), Priority Service Pricing with Heterogeneous Customers: Impact of Delay Cost Distribution. Prod Oper Manag, 28: 2854-2876., which has been published in final form at https://doi.org/10.1111/poms.13086. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
本文为以下文章的同行评议版本:曹鹏,王勇,谢杰(2019),具有异质客户的优先服务定价:延迟成本分配的影响。管理学报,28:2854-2876。,最终版本已在https://doi.org/10.1111/poms.13086上发表。根据威利自存档版本使用条款和条件,本文可用于非商业目的。
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引用次数: 14
Oil and Pump Prices: Is There Any Asymmetry in the Greek Oil Downstream Sector? 石油和泵价格:希腊石油下游行业是否存在不对称?
Pub Date : 2019-05-06 DOI: 10.2139/ssrn.3444840
Zacharias G. Bragoudakis, Stavros Degiannakis, G. Filis
The aim of this study is to assess whether fuel prices in Greece respond asymmetrically to changes in the global oil prices. To do so, we depart from the current practice in the literature that focuses on fuel prices. Rather, we consider the mark-up of both the refineries and retailers. Even more, unlike the bulk of the existing literature, we take into consideration the whole supply chain, i.e. both the refineries and the retail fuel sector. Hence, we first assess whether the refineries’ mark-up responds asymmetrically to the global oil prices and subsequently whether the retailers’ mark-up shows an asymmetric behaviour relatively to changes in the refineries’ fuel prices. Our findings show that the Greek fuel retailers do not change their mark-up behaviour based on changes of the refined fuel price. By contrast, the asymmetric behaviour is evident in the refineries mark-up relatively to changes in the global oil prices, which is then passed through to the retailers and consumers. Finally, we convincingly show that weekly and monthly data mask any such asymmetric relationship. Thus, we maintain that unless the appropriate data frequency, fuel price transformations and the whole supply chain are considered, misleading findings could be revealed.
本研究的目的是评估希腊的燃料价格是否对全球石油价格的变化做出不对称的反应。为了做到这一点,我们偏离了目前关注燃料价格的文献中的做法。相反,我们考虑的是炼油厂和零售商的加价。更重要的是,与现有文献的大部分不同,我们考虑了整个供应链,即炼油厂和零售燃料部门。因此,我们首先评估炼油厂的加价是否对全球油价做出不对称的反应,然后评估零售商的加价是否对炼油厂燃料价格的变化表现出不对称的行为。我们的研究结果表明,希腊燃料零售商不会根据成品油价格的变化改变他们的加价行为。相比之下,这种不对称行为在炼油厂相对于全球油价变化的加价中表现得很明显,而全球油价的变化随后会传递给零售商和消费者。最后,我们令人信服地表明,周数据和月数据掩盖了任何这种不对称关系。因此,我们认为,除非考虑适当的数据频率、燃料价格转换和整个供应链,否则可能会发现误导性的结果。
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引用次数: 13
期刊
ERN: Pricing (Topic)
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