Dynamic Price Competition with Capacity Constraints and a Strategic Buyer

Dynamic Price Competition with Capacity Constraints and a Strategic Buyer
Author: James J. Anton
Publisher:
Total Pages: 0
Release: 2014
Genre:
ISBN:

We analyze a simple dynamic durable good model. Two incumbent sellers and potential entrants choose their capacities at the start of the game. We solve for equilibrium capacity choices and the (necessarily mixed) pricing strategies. In equilibrium, the buyer splits the order with positive probability to preserve competition, making it possible that a high and low price seller both have sales. Sellers command a rent above the value of unmet demand by the other seller. A buyer benefits from either a commitment not to make future purchases or by hiring an agent to always buy from the lowest priced seller.

Dynamic Pricing Under Demand Uncertainty in the Presence of Strategic Consumers

Dynamic Pricing Under Demand Uncertainty in the Presence of Strategic Consumers
Author: Yinhan Meng
Publisher:
Total Pages: 96
Release: 2011
Genre:
ISBN:

We study the effect of strategic consumer behavior on pricing, inventory decisions, and inventory release policies of a monopoly retailer selling a single product over two periods facing uncertain demand. We consider the following three-stage two-period dynamic pricing game. In the first stage the retailer sets his inventory level and inventory release policy; in the second stage the retailer faces uncertain demand that consists of both myopic and strategic consumers. The former type of consumers purchase the good if their valuations exceed the posted price, while the latter type of consumers consider future realizations of prices, and hence their future surplus, before deciding when to purchase the good; in the third stage, the retailer releases its remaining inventory according to the release policy chosen in the first stage. Game theory is employed to model strategic decisions in this setting. Each of the strategies available to the players in this setting (the consumers and the retailer) are solved backward to yield the subgame perfect Nash equilibrium, which allows us to derive the equilibrium pricing policies. This work provides three primary contributions to the fields of dynamic pricing and revenue management. First, if, in the third stage, inventory is released to clear the market, then the presence of strategic consumers may be beneficial for the retailer. Second, we find the optimal inventory release strategy when retailers have capacity limitation. Lastly, we numerically demonstrate the retailer's optimal decisions of both inventory level and the inventory release strategy. We find that market clearance mechanism and intermediate supply strategy may emerge as the retailers optimal choice.

Dynamic Pricing Strategies in the Presence of Demand Shifts

Dynamic Pricing Strategies in the Presence of Demand Shifts
Author: Omar Besbes
Publisher:
Total Pages: 33
Release: 2016
Genre:
ISBN:

Many factors introduce the prospect of changes in the demand environment that a firm faces, with the specifics of such changes not necessarily known in advance. If and when realized, such changes affect the delicate balance between demand and supply and thus current prices should account for these future possibilities. We study the dynamic pricing problem of a retailer facing the prospect of a change in the demand function during a finite selling season with no inventory replenishment opportunity. In particular, the time of the change and the postchange demand function are unknown upfront, and we focus on the fundamental trade-off between collecting revenues from current demand and doing so for postchange demand, with the capacity constraint introducing the main tension. We develop a formulation that allows for isolating the role of dynamic pricing in balancing inventory consumption throughout the horizon. We establish that, in many settings, optimal pricing policies follow a monotone path up to the change in demand. We show how one may compare upfront the attractiveness of pre- and postchange demand conditions and how such a comparison depends on the problem primitives. We further analyze the impact of the model inputs on the optimal policy and its structure, ranging from the impact of model parameter changes to the impact of different representations of uncertainty about future demand.

Dynamic Pricing of Experience Goods in Markets with Demand Uncertainty

Dynamic Pricing of Experience Goods in Markets with Demand Uncertainty
Author: Yu-Hung Chen
Publisher:
Total Pages: 38
Release: 2018
Genre:
ISBN:

This paper studies a firm's optimal dynamic pricing strategies for its new experience goods inmarkets where the distribution of consumers' valuations is ex ante unknown. We examine whetherand how the firm facing information asymmetry and demand uncertainty can signal its high qualityand learn market demand through its pricing strategy. First, we find that a high-quality firm cancredibly reveal its true quality in the early period with either a skimming-pricing strategy or apenetration-pricing strategy under different conditions. Second, though a high-quality firm canbenefit more from learning market demand than a low-quality firm, the high-quality firm may inequilibrium adopt a penetration-pricing strategy to forgo the benefit of learning demand in orderto separate from the low-quality firm, who would adopt a skimming strategy to learn marketdemand. Third, although consumers have higher willing-to-pay for a high-quality product, thehigh-quality firm may in equilibrium charge a lower initial price than the low-quality firm. Fourth,interestingly, the high-quality firm may earn higher profits when its initial price is made underdemand uncertainty than under no uncertainty. Lastly, with perfect social learning (i.e., in the laterperiod, all consumers can learn the firm's quality from earlier customers), the high-quality firmcan in equilibrium signal its quality and learn market demand by adopting a skimming strategy.

Pricing and Revenue Optimization

Pricing and Revenue Optimization
Author: Robert Phillips
Publisher: Stanford University Press
Total Pages: 470
Release: 2005-08-05
Genre: Business & Economics
ISBN: 0804781648

This is the first comprehensive introduction to the concepts, theories, and applications of pricing and revenue optimization. From the initial success of "yield management" in the commercial airline industry down to more recent successes of markdown management and dynamic pricing, the application of mathematical analysis to optimize pricing has become increasingly important across many different industries. But, since pricing and revenue optimization has involved the use of sophisticated mathematical techniques, the topic has remained largely inaccessible to students and the typical manager. With methods proven in the MBA courses taught by the author at Columbia and Stanford Business Schools, this book presents the basic concepts of pricing and revenue optimization in a form accessible to MBA students, MS students, and advanced undergraduates. In addition, managers will find the practical approach to the issue of pricing and revenue optimization invaluable. Solutions to the end-of-chapter exercises are available to instructors who are using this book in their courses. For access to the solutions manual, please contact [email protected].

Dynamic Pricing with Demand Model Uncertainty

Dynamic Pricing with Demand Model Uncertainty
Author: Mr. Nuri Bora Keskin
Publisher:
Total Pages:
Release: 2012
Genre:
ISBN:

Pricing decisions often involve a tradeoff between learning about customer behavior to increase long-term revenues, and earning short-term revenues. In this thesis we examine that tradeoff. Whenever a firm is not certain about how its customers will respond to price changes, there is an opportunity to use price as a tool for learning about a demand curve. Most firms try to solve the tradeoff between learning and earning by managing these two goals separately. A common practice is to first estimate the parameters of the demand curve, and then choose the optimal price, assuming the parameter estimates are accurate. In this thesis we show that this conventional approach is far from being optimal, running the risk of incomplete learning--a negative statistical outcome in which the decision maker stops learning prematurely. We also propose several remedies to avoid the incomplete learning problem, and guard against poor performance. In Chapter 1, we model a learn-and-earn problem using a theoretical framework in which a seller has a prior belief about the demand curve for its product, and updates his belief upon observing customer responses to successive sales attempts. We assume that the seller's prior is a binary distribution, i.e. one of two demand curves is known to apply, although our analysis can be extended to any finite prior. In this setting, we first analyze the myopic Bayesian policy (MBP), which is a stylized representative of the estimate-and-then-optimize policies described above. Our analysis makes three contributions to the literature: first, we show that under the MBP the seller's beliefs can get stuck at a confounding value, leading to poor revenue performance. This result elucidates incomplete learning as a consequence of myopic pricing. Our second contribution is the development of a constrained variant of the MBP as a way to tweak the MBP in the binary-prior setting. By forbidding prices that are not sufficiently informative, constrained MBP (CMBP) avoids the incomplete learning problem entirely, and moreover, its expected performance gap relative to a clairvoyant who iv knows the underlying demand curve is bounded by a constant independent of the sales horizon. Finally, we generalize the CMBP family to obtain more flexible pricing policies that are suitable in case the seller has an arbitrary prior on model parameters. The incomplete learning result and the pricing policies we design have a practical significance. Because firms have no means to check whether they are suffering from incomplete learning, the myopic policies used in practice need to be modified with some kind of forced price experimentation, and our policies provide guidelines on how price experimentation can be employed to prevent incomplete learning. In Chapter 2, we consider several research questions: for example, when a seller has been charging an incumbent price for a very long time, how can he make use of the information contained in that incumbent price? Or, when a seller offers multiple products with substitutable demand, can he safely employ an independent price experimentation strategy for each product? More importantly, what if the particular pricing policies in literature are not feasible in a given business setting? To handles such cases, can we derive general principles that identify the essential ingredient of successful price experimentation policies? We address these questions using a fairly general dynamic pricing model, where a monopolist sells a set of products over a given time horizon. The expected demand for products is given by a linear curve, the parameters of which are not known by the seller. The seller's goal is to learn the parameters of the demand curve as he keeps trying to earn revenues. This chapter makes four main contributions to the learning-and-earning literature. First, we formulate an incumbent-price problem, where the seller starts out knowing one point on its demand curve, and show that the value of information contained in the incumbent price is substantial. Second, unlike previous studies that focus on a particular form of price experimentation, we derive general sufficient conditions for accumulating information in a near-optimal manner. We believe that practitioners can use these conditions as guidelines to design successful pricing policies in various settings. Third, we develop a unifying theme to obtain performance bounds in operations management problems with model uncertainty. We employ (i) the concept of Fisher information to derive natural lower bounds on regret, and (ii) martingale theory to analyze the estimation errors and generate well-performing policies. Finally, we analyze the pricing of multiple products with substitutable demand. Our analysis shows that multi-product pricing is not a straightforward repetition of single-product pricing. Learning in a high dimensional price space essentially requires sufficient "variation" in the directions of successive price vectors, which brings forth the idea of orthogonal pricing. In Chapter 3, we extend our analysis to the case where information can become obsolete. The particular dynamic pricing problem we consider includes a seller who tries to simultaneously learn about a time-varying demand curve, and earn sales revenues. We conduct a simulation study to evaluate the revenue performance of several pricing policies in this setting. Our results suggest that policies designed for static demand settings do not perform well in time-varying demand settings. Moreover, if the demand environment is not very noisy and the changes are not very frequent, a simple modification of the estimate-and-then-optimize approach, which is based on a moving time window, performs reasonably well in changing demand environments.