Showing papers on "Dynamic pricing published in 2007"

Intertemporal Pricing with Strategic Customer Behavior

Abstract: This paper develops a model of dynamic pricing with endogenous intertemporal demand. In the model, there is a monopolist who sells a finite inventory over a finite time horizon. The seller adjusts prices dynamically to maximize revenue. Customers arrive continually over the duration of the selling season. At each point in time, customers may purchase the product at current prices, remain in the market at a cost to purchase later, or exit, and they wish to maximize individual utility. The customer population is heterogeneous along two dimensions: they may have different valuations for the product and different degrees of patience (waiting costs). We demonstrate that heterogeneity in both valuation and patience is important because they jointly determine the structure of optimal pricing policies. In particular, when high-value customers are proportionately less patient, markdown pricing policies are effective because the high-value customers would buy early at high prices while the low-value customers are willing to wait (i.e., they are not lost). On the other hand, when the high-value customers are more patient than the low-value customers, prices should increase over time to discourage inefficient waiting. Contrary to intuition, we find that strategic waiting by customers may sometimes benefit the seller: when low-value customers wait, they compete for availability with high-value customers and thus increase their willingness to pay. Our results also shed light on how the composition of the customer population affects optimal revenue, consumer surplus, and social welfare. Finally, we consider the long-run problem of selecting the optimal initial stocking quantity.

Dynamic Pricing Strategies with Reference Effects

Abstract: We consider the dynamic pricing problem of a monopolist firm in a market with repeated interactions, where demand is sensitive to the firm's pricing history. Consumers have memory and are prone to human decision-making biases and cognitive limitations. As the firm manipulates prices, consumers form a reference price that adjusts as an anchoring standard based on price perceptions. Purchase decisions are made by assessing prices as discounts or surcharges relative to the reference price in the spirit of prospect theory. We prove that optimal pricing policies induce a perception of monotonic prices, whereby consumers always perceive a discount, respectively surcharge, relative to their expectations. The effect is that of a skimming or penetration strategy. The firm's optimal pricing path is monotonic on the long run, but not necessarily at the introductory stage. If consumers are loss averse, we show that optimal prices converge to a constant steady-state price, characterized by a simple implicit equation; otherwise, the optimal policy cycles. The range of steady states is wider the more loss averse consumers are. Steady-state prices decrease with the strength of the reference effect and with customers' memory, all else equal. Offering lower prices to frequent customers may be suboptimal, however, if these are less sensitive to price changes than occasional buyers. If managers ignore such long-term implications of their pricing strategy, the model indicates that they will systematically price too low and lose revenue. Our results hold under very general reference dependent demand models.

Edgeworth Price Cycles, Cost-Based Pricing, and Sticky Pricing in Retail Gasoline Markets

Abstract: This paper examines dynamic pricing behavior in Canadian retail gasoline markets. I find three distinct pricing patterns: cost-based pricing, sticky pricing, and sharp asymmetric retail price cycles that resemble the Edgeworth cycles of Maskin and Tirole (1988). I use a Markov-switching regression to estimate the prevalence of the regimes and the structural characteristics of the cycles themselves. I find cycles are more prevalent when there are more small firms and are accelerated and amplified with very many small firms. In markets with few small firms, sticky pricing dominates. The findings are consistent with the theory of Edgeworth cycles.

Dynamic pricing in the airline industry

Abstract: Dynamic price discrimination adjusts prices based on the option value of future sales, which varies with time and units available. This paper surveys the theoretical literature on dynamic price discrimination, and confronts the theories with new data from airline pricing behavior. Correspondence to: R. Preston McAfee, 100 Baxter Hall, California Institute of Technology, Pasadena, CA 91125, preston@mcafee.cc.

Relative Entropy, Exponential Utility, and Robust Dynamic Pricing

Abstract: In the area of dynamic revenue management, optimal pricing policies are typically computed on the basis of an underlying demand rate model. From the perspective of applications, this approach implicitly assumes that the model is an accurate representation of the real-world demand process and that the parameters characterizing this model can be accurately calibrated using data. In many situations, neither of these conditions are satisfied. Indeed, models are usually simplified for the purpose of tractability and may be difficult to calibrate because of a lack of data. Moreover, pricing policies that are computed under the assumption that the model is correct may perform badly when this is not the case. This paper presents an approach to single-product dynamic revenue management that accounts for errors in the underlying model at the optimization stage. Uncertainty in the demand rate model is represented using the notion of relative entropy, and a tractable reformulation of the “robust pricing problem” is obtained using results concerning the change of probability measure for point processes. The optimal pricing policy is obtained through a version of the so-called Isaacs' equation for stochastic differential games, and the structural properties of the optimal solution are obtained through an analysis of this equation. In particular, (i) closed-form solutions for the special case of an exponential nominal demand rate model, (ii) general conditions for the exchange of the “max” and the “min” in the differential game, and (iii) the equivalence between the robust pricing problem and that of single-product revenue management with an exponential utility function without model uncertainty, are established through the analysis of this equation.

An Economic Framework for Spectrum Allocation and Service Pricing with Competitive Wireless Service Providers

Abstract: In the future, we can expect to see more dynamic service offerings and profiles, as users move from long-term service provider agreements to more opportunistic service models. Moreover, when the radio spectrum is itself traded in a market- based scenario, wireless service providers (WSPs) will likely require new strategies to deploy services, define service profiles, and price them. Currently, there is little understanding on how such a dynamic trading system will operate so as to make the system feasible under economic terms. From an economic point of view, we analyze two main components of this overall trading system: (i) spectrum allocation to WSPs and (ii) interaction of end users with the WSPs. For this two-tier trading system, we present a winner determining sealed-bid knapsack auction mechanism that dynamically allocates spectrum to the WSPs based on their bids. We propose a dynamic pricing strategy based on game theory to capture the conflict of interest between WSPs and end users, both of whom try to maximize their respective net utilities. We show that even in such a greedy and non-cooperative behavioral game model, it is in the best interest of the WSPs to adhere to a price threshold which is a consequence of a price equilibrium in an oligopoly situation. Through simulation results, we show that the proposed auction entices the WSPs to participate in the auction, makes optimal use of the common spectrum pool, and avoids collusion among WSPs. Moreover, numerical results demonstrate how pricing can be used as an effective tool for providing incentives to the WSPs to upgrade their network resources and offer better services.

Pricing for Utility-Driven Resource Management and Allocation in Clusters

Abstract: Users perceive varying levels of utility for each different job completed by the cluster. Therefore, there is a need for existing cluster resource management systems (RMS) to provide a means for the user to express its perceived utility during job submission. The cluster RMS can then obtain and consider these user-centric needs such as Quality-of-Service requirements in order to achieve utility-driven resource management and allocation. We advocate the use of computational economy for this purpose. In this paper, we describe an architectural framework for a utility-driven cluster RMS. We present a user-level job submission specification for soliciting user-centric information that is used by the cluster RMS for making better resource allocation decisions. In addition, we propose a dynamic pricing function that the cluster owner can use to determine the level of sharing within a cluster. Finally, we define two user-centric performance evaluation metrics: Job QoS Satisfaction and Cluster Profitability for measuring the effectiveness of the proposed pricing function in realizing utility-driven resource management and allocation.

Demand Management and Inventory Control for Substitutable Products

Abstract: This paper studies dynamic inventory and pricing decisions for a set of substitutable products over a flnite planning horizon. We present a general stochastic, price-dependent demand model that unifles many commonly used demand models in the literature. Unsatisfled demands are backlogged. There are linear purchasing, inventory-holding, and backordering costs. The objective is to maximize the total expected discounted proflt. The original formulation is not jointly concave in the decision variables and is therefore intractable. One key observation here is that the problem becomes jointly concave if we work with the inverse of the price vector { the market share vector. We characterize the optimal policy and develop algorithms to compute it. We establish conditions under which the optimal policy demonstrates certain monotonicity property, which, in turn, can greatly enhance computation. We also analyze the myopic policy and its optimality, and present a numerical study to illustrate the interplay of the pricing and inventory decisions.

Optimal Dynamic Pricing Strategies for High-Occupancy/Toll Lanes

Abstract: This paper proposes a self-learning approach for determining pricing strategies for high-occupancy/toll lane operations. The approach learns recursively motorists’ willingness to pay by mining the loop detector data, and specifies toll rates to maximize the freeway’s throughput while ensuring a superior free-flow travel service to the users of the toll lanes. In determination of the tolls, a multi-lane hybrid traffic flow model is used to explicitly consider the impacts of the lane-changing behaviors before the entry points of the toll lanes. Simulation experiments are conducted to demonstrate and validate the proposed approach, and provide insights on when to convert high-occupancy lanes to toll lanes.

Bounded Rationality in Pricing under State-Dependent Demand: Do Firms Look Ahead, and if So, How Far?:

Abstract: The authors propose an empirical procedure to investigate the pricing behavior of manufacturers and retailers in the presence of state-dependent demand. Rather than assuming that firms are perfectl...

Dynamic Pricing Models for Digital Content

Abstract: Dynamic pricing models which facilitate efficient distribution of digital content online. Particular implementations of the invention dynamically base pricing for digital content on relatively current, aggregated information regarding Internet user behavior and preferences, such as search query and/or page hit logs. Some implementations of the present invention are directed to pricing digital content based on the inherent properties of digital content and the mechanics of how electronic files are typically distributed on the Internet.

Dynamic Pricing and Advertising for Web Content Providers

Abstract: The accumulated evidence indicates that pure revenue models, such as free-access models and pure subscription fee based models, are not sufficient to support the survival of online information sellers. Hence, hybrid models based on a combination of subscription fees and advertising revenues are replacing the pure revenue models. In response to increasing interest in hybrid models, we study the problem of dynamic pricing of web content on a site where revenue is generated from subscription fee as well as advertisements. We use the optimal control theory to solve the problem and obtain the subscription fee and the advertisement level over time. We first consider the case when the subscription fee can vary over time, but the advertisement level stays the same. Then we extend it by optimizing both the subscription fee and the advertisement level dynamically. We also present several analytical and numerical results that provide important managerial insights.

Digital online exchange for pricing items to exhaust inventory by an expiration time

Abstract: A dynamic pricing system for pricing items for sale by a seller which items are available in a limited quantity comprises a pricing server and various types of data stored in memory. The pricing server includes memory, a processor and a clock. One type of data stored in memory is indicative of the initial quantity of an item available in a limited quantity. Another type of data stored in memory is indicative of the current remaining quantity of the item available in a limited quantity. Yet another type of data stored in memory is indicative of an expiration time at which it is desired that all of the item available in a limited quantity be sold. The processor is configured to price the item available in a limited quantity so as to deplete the inventory of the item available in a limited quantity by the expiration date based in part by accessing the memory to retrieve the data indicative of the initial quantity, the current remaining quantity and the expiration time and accessing the clock.

How to Reap Higher Profits With Dynamic Princing

Abstract: Dynamic pricing, in which prices respond to supply and demand pressures in real time or near-real time, has long been used by airlines and hotels. Now dynamic pricing is making inroads in many different sectors including apparel, automobiles, consumer electronics, personal services, telecommunications and second- hand goods. These companies are making use of new findings on dynamic pricing and of increases in data-processing power to raise their average realized prices, thereby increasing revenues and profits. There are two mechanisms for dynamic pricing: posted prices that customers can see; and price-discovery mechanisms, in which customers determine prices through their own actions. These two mechanisms are employed in seven different forms: yield management (commonly used by airlines), demandbased pricing, three types of auctions, group buying and negotiations. The article describes eight situations for using the various forms of dynamic pricing. An important constraint in employing dynamic pricing is consumers? Latitude of Price Acceptance, which varies for different products and situations and which can be discovered through observation, surveys or analysis of demand elasticities. Customer participation in the pricing process decreases the chances of a consumer backlash. Customers also tend to embrace dynamic pricing in the following situations: where the price reflects intensity of demand for the product, there is communication between the seller and the consumer, and the price difference is explained by a difference in perceived value across channels through which the transaction occurred. The more the seller understands the buying cycles and habits of the customer, the more he is able to manage price margins to the rhythm of the customer?s shopping, to segment customers and to develop price discrimination.

Practice Prize Report---An Assortmentwide Decision-Support System for Dynamic Pricing and Promotion Planning in DIY Retailing

Abstract: The main objective of this report is to describe a decision-support system for dynamic retail pricing and promotion planning. Our weekly demand model incorporates price, reference price effects, seasonality, article availability information, features, and discounts. Building on previous research, we quantify demand interdependencies and integrate the resulting profit-lifting effects into the optimal pricing model. The methodology was developed and implemented at bauMax, an Austrian do-it-yourself retailer. Along with the practical requirements, an objective function was employed that can be used as a vehicle for implementing a retailer's strategy. Eight pricing rounds with thousands of different stock-keeping units have each served as a testing ground for our approach. Based on various benchmarking methods, a positive impact on profit was reported. The currently implemented marketing decision-support system increased gross profit on average by 8.1 and sales by 2.1%.

Detecting and Forecasting Economic Regimes in Multi-Agent Automated Exchanges

Abstract: We show how an autonomous agent can use observable market conditions to characterize the microeconomic situation of the market and predict future market trends. The agent can use this information to make both tactical decisions, such as pricing, and strategic decisions, such as product mix and production planning. We develop methods to learn dominant market conditions, such as over-supply or scarcity, from historical data using Gaussian mixture models to construct price density functions. We discuss how this model can be combined with real-time observable information to identify the current dominant market condition and to forecast market changes over a planning horizon. We forecast market changes via both a Markov correction-prediction process and an exponential smoother. Empirical analysis shows that the exponential smoother yields more accurate predictions for the current and the next day (supporting tactical decisions), while the Markov correction-prediction process is better for longer term predictions (supporting strategic decisions). Our approach offers more flexibility than traditional regression based approaches, since it does not assume a fixed functional relationship between dependent and independent variables. We validate our methods by presenting experimental results in a case study, the Trading Agent Competition for Supply Chain Management.

Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk

Abstract: We introduce, in continuous time, an axiomatic approach to assign to any financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity) of the ask (resp. bid) price. Time consistency is a crucial property for dynamic pricing. Generalizing the result of Jouini and Kallal, we prove that the No Free Lunch condition for a time consistent dynamic pricing procedure (TCPP) is equivalent to the existence of an equivalent probability measure $R$ that transforms a process between the bid process and the ask process of any financial instrument into a martingale. Furthermore we prove that the ask price process associated with any financial instrument is then a $R$-supermartingale process which has a cadlag modification. Finally we show that time consistent dynamic pricing allows both to extend the dynamics of some reference assets and to be consistent with any observed bid ask spreads that one wants to take into account. It then provides new bounds reducing the bid ask spreads for the other financial instruments.

Variable Ticket Pricing in Major League Baseball

Abstract: Sport teams have historically been reluctant to change ticket prices during the season. Recently, however, numerous sport organizations have implemented variable ticket pricing in an effort to maximize revenues. In Major League Baseball, variable pricing results in ticket price increases or decreases depending on factors such as quality of the opponent, day of the week, month of the year, and for special events such as opening day, Memorial Day and Independence Day (July 4). Using censored regression and elasticity analysis, this paper demonstrates that variable pricing would have yielded approximately $590,000 per year in additional ticket revenue for each Major League team in 1996, ceteris paribus. Accounting for capacity constraints, this amounts to only about a 2.8% increase above what occurs when prices are not varied. For the 1996 season, the largest revenue gain would have been the Cleveland Indians, who would have generated an extra $1.4 million in revenue. The largest percentage revenue gain would have been the San Francisco Giants. The Giants would have seen an estimated 6.7% increase in revenue had they used optimal variable pricing.

Price Guarantees in Dynamic Pricing and Revenue Management

Abstract: We present a new model for revenue management of product sales that incorporates both dynamic pricing and a price guarantee. The guarantee provides customers with compensation if, prior to a fixed future date, the price of the product drops below a level specified at the time of purchase. We consider the problem of simultaneously determining optimal dynamic price and guarantee policies for items from a fixed stock when demand depends both on the price and on the parameters of the price guarantee. The model can be used for pricing any items with limited availability over a fixed time horizon. We formulate this model as a discrete-time optimal control problem, prove the existence of its optimal solution, explore some of the structural properties of the solution, present lower-bounding heuristics for solving the problem, and report numerical results.

Bayesian strategies for dynamic pricing in e‐commerce

Abstract: E-commerce platforms afford retailers unprecedented visibility into customer purchase behavior and provide an environment in which prices can be updated quickly and cheaply in response to changing market conditions. This study investigates dynamic pricing strategies for maximizing revenue in an Internet retail channel by actively learning customers' demand response to price. A general methodology is proposed for dynamically pricing information goods, as well as other nonperishable products for which inventory levels are not an essential consideration in pricing. A Bayesian model of demand uncertainty involving the Dirichlet distribution or a mixture of such distributions as a prior captures a wide range of beliefs about customer demand. We provide both analytic formulas and efficient approximation methods for updating these prior distributions after sales data have been observed. We then investigate several strategies for sequential pricing based on index functions that consider both the potential revenue and the information value of selecting prices. These strategies require a manageable amount of computation, are robust to many types of prior misspecification, and yield high revenues compared to static pricing and passive learning approaches. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007

A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders

Abstract: In this paper, we present a continuous time optimal control model for studying a dynamic pricing and inventory con- trol problem for a make-to-stock manufacturing system. We consider a multiproduct capacitated, dynamic setting. We introduce a demand-based model where the demand is a linear function of the price, the inventory cost is linear, the production cost is an increasing strictly convex function of the production rate, and all coefficients are time-dependent. A key part of the model is that no backorders are allowed. We introduce and study an algorithm that computes the optimal production and pricing policy as a function of the time on a finite time horizon, and discuss some insights. Our results illustrate the role of capacity and the effects of the dynamic nature of demand in the model. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 54: 767-795, 2007

Designing Markets: Why Competitive Bidding and Auctions in Government Often Fail To Deliver

Abstract: Governments continue to embrace the market-like mechanisms of auctions and bidding. This essay considers how governments (as bid-takers) and firms and nonprofits (as bidders) strategically interact in the design and implementation of these systems. I assess with regard to the uniqueness of bidding in government four principles on the role of: credible commitments, rational collusion, the setting of reserve prices, and heterogeneity among bidders. I also address recent calls for expanding the use of dynamic pricing in government.

Variable Ticket Pricing in Major League Baseball

Abstract: Sport teams have historically been reluctant to change ticket prices during the season. Recently, however, numerous sport organizations have implemented variable ticket pricing in an effort to maximize revenues. In Major League Baseball, variable pricing results in ticket price increases or decreases depending on factors such as quality of the opponent, day of the week, month of the year, and for special events such as opening day, Memorial Day and Independence Day (July 4). Using censored regression and elasticity analysis, this paper demonstrates that variable pricing would have yielded approximately $590,000 per year in additional ticket revenue for each Major League team in 1996, ceteris paribus. Accounting for capacity constraints, this amounts to only about a 2.8% increase above what occurs when prices are not varied. For the 1996 season, the largest revenue gain would have been the Cleveland Indians, who would have generated an extra $1.4 million in revenue. The largest percentage revenue gain would have been the San Francisco Giants. The Giants would have seen an estimated 6.7% increase in revenue had they used optimal variable pricing.

Method and system for dynamic pricing

Abstract: A computer system and method for dynamic pricing is described. The system includes at least one dynamic calculator, which performs calculations based upon conditional rules.

Dynamic pricing of seasonal goods with spot and forward purchase demands

Abstract: This paper deals with the problem of jointly determining the order size and dynamic prices for a perishable inventory system over a finite time planning horizon when firms simultaneously provide customers with a prompt delivery option and a delivery schedule option. Customers are segmented into two types, namely spot purchase customers and the forward purchase customers. Demands for both types of customers are assumed to be time and price dependent. The decision-maker of the inventory system is assumed to apply pricing policies to stimulate demand to improve revenues under the condition that customers with forward purchases may cancel their orders. A mathematical model is developed to find the optimal number of price settings, the optimal dynamic prices and the order quantity. A solution procedure is found to determine the optimal decisions.