Download or read book Dynamic Pricing with Demand Learning and Reference Effects written by Arnoud den Boer and published by . This book was released on 2020 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a seller's dynamic pricing problem with demand learning and reference effects. We first study the case where customers are loss-averse: they have a reference price that can vary over time, and the demand reduction when the selling price exceeds the reference price dominates the demand increase when the selling price falls behind the reference price by the same amount. Thus, the expected demand as a function of price has a time-varying "kink" and is not differentiable everywhere. The seller neither knows the underlying demand function nor observes the time-varying reference prices. In this setting, we design and analyze a policy that (i) changes the selling price very slowly to control the evolution of the reference price, and (ii) gradually accumulates sales data to balance the tradeoff between learning and earning. We prove that, under a variety of reference-price updating mechanisms, our policy is asymptotically optimal; i.e., its T-period revenue loss relative to a clairvoyant who knows the demand function and the reference-price updating mechanism grows at the smallest possible rate in T. We also extend our analysis to the case of a fixed reference price, and show how reference effects increase the complexity of dynamic pricing with demand learning in this case. Moreover, we study the case where customers are gain-seeking and design asymptotically optimal policies for this case. Finally, we design and analyze an asymptotically optimal statistical test for detecting whether customers are loss-averse or gain-seeking.
Download or read book Online Learning and Pricing for Multiple Products with Reference Price Effects written by Sheng Ji and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the dynamic pricing problem of a monopolist seller who sells a set of mutually substitutable products over a finite time horizon. Customer demand is sensitive to the price of each individual product and the reference price which is formed from a comparison among the prices of all products. To maximize the total expected profit, the seller needs to determine the selling price of each product and also selects a reference product (to be displayed) that affects the consumer's reference price. However, the seller initially knows neither the demand function nor the customer's reference price, but can learn them from past observations on the fly. As such, the seller faces the classical trade-off between exploration (learning the demand function and reference price) and exploitation (using what has been learned thus far to maximize revenue). We propose a dynamic learning-and-pricing algorithm that integrates iterative least squares estimation and bandit control techniques in a seamless fashion. We show that the cumulative regret, i.e., the expected revenue loss caused by not using the optimal policy over $T$ periods, is upper bounded by $O((n^2+n) sqrt{T} log T)$, which is optimal up to a logarithmic factor in terms of the time horizon $T$ and polynomially scaling with the number of products $n$. We also establish the regret lower bound (for any learning policies) to be $ Omega(n^{1.5} sqrt{T})$. We then generalize our analysis to a more general demand model. Finally, our algorithm performs consistently well numerically, outperforming an exploration-exploitation benchmark. We also identify an interesting ``loss-leader'' phenomenon in our computational study.
Download or read book Dynamic Pricing and Demand Learning with Limited Price Experimentation written by Wang Chi Cheung and published by . This book was released on 2017 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a dynamic pricing problem where the demand function is not known a priori, price experimentation can be used as a demand learning tool. Existing literature usually assumes no constraint on price changes, but in practice sellers often face business constraints that prevent them from conducting extensive experimentation. We consider a dynamic pricing model where the demand function is unknown but belongs to a known finite set. The seller is allowed to make at most m price changes during T periods. The objective is to minimize the worst case regret, i.e., the expected total revenue loss compared to a clairvoyant who knows the demand distribution in advance. We demonstrate a pricing policy that incurs a regret of O(log^(m) T), or m iterations of the logarithm. Furthermore, we describe an implementation at Groupon, a large e-commerce marketplace for daily deals. The field study shows significant impact on revenue and bookings.
Download or read book Behavioral Consequences of Dynamic Pricing written by David Prakash and published by BoD – Books on Demand. This book was released on 2022-08-19 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Digital technologies are driving the application of dynamic pricing. Today, this pricing strategy is used not only for perishable products such as flights or hotel rooms, but for almost any product or service category. With dynamic pricing, retailers frequently adjust their prices over time to respond to factors such as demand, their supply and that of competitors, or the time of sale. Additionally, dynamic pricing allows retailers to take advantage of a large share of consumers' willingness to pay while avoiding losses from unsold products. Ultimately, this can lead to an increase in revenue and profit. However, the application of dynamic pricing comes with great challenges. In addition to the technological implementation, companies have to take into account that dynamic pricing can cause complex and unintended behavioral consequences on the consumer side. The key objective of this dissertation is to provide a deeper understanding of the impact of dynamic pricing on consumer behavior. To this end, this dissertation presents insights from four perspectives. First, how reference prices as a critical component in purchase decisions are operationalized. Second, how customers search for products priced dynamically, differentiated by business and private customers, as well as by different devices used for the search. Third, whether and how dynamic pricing influences the impact of internal reference prices on purchase decisions. Finally, this dissertation demonstrates that consumers perceive price changes as personalized in different purchase contexts, leading to reduced perceptions of fairness and undesirable behavioral consequences.
Download or read book Supermodularity and Complementarity written by Donald M. Topkis and published by Princeton University Press. This book was released on 2011-02-11 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The economics literature is replete with examples of monotone comparative statics; that is, scenarios where optimal decisions or equilibria in a parameterized collection of models vary monotonically with the parameter. Most of these examples are manifestations of complementarity, with a common explicit or implicit theoretical basis in properties of a super-modular function on a lattice. Supermodular functions yield a characterization for complementarity and extend the notion of complementarity to a general setting that is a natural mathematical context for studying complementarity and monotone comparative statics. Concepts and results related to supermodularity and monotone comparative statics constitute a new and important formal step in the long line of economics literature on complementarity. This monograph links complementarity to powerful concepts and results involving supermodular functions on lattices and focuses on analyses and issues related to monotone comparative statics. Don Topkis, who is known for his seminal contributions to this area, here presents a self-contained and up-to-date view of this field, including many new results, to scholars interested in economic theory and its applications as well as to those in related disciplines. The emphasis is on methodology. The book systematically develops a comprehensive, integrated theory pertaining to supermodularity, complementarity, and monotone comparative statics. It then applies that theory in the analysis of many diverse economic models formulated as decision problems, noncooperative games, and cooperative games.
Download or read book Multi Product Dynamic Pricing with Reference Effects Under Logit Demand written by Mengzi Amy Guo and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an infinite-horizon multi-product dynamic pricing problem with reference effects in a monopolistic setting, where the reference price is an exponentially weighted average of historical prices. In each period, the demand follows the multinomial logit (MNL) model, where the utility depends on both the current price and the reference price, and consumers can have product-differentiated sensitivities to the price and the reference price. We conduct thorough analyses of the myopic pricing policy, including its solution, long-run convergence behavior, and performance guarantee compared to the long-term discounted revenue of the optimal pricing policy. Furthermore, we establish the structural properties of the optimal pricing policy. When consumers are loss-neutral towards all products, we explicitly characterize the optimal pricing policy if it converges to a steady state, and based on our characterization we show that the steady state price can be computed efficiently by a binary search. Interestingly, we find that such a convergence behavior of the optimal pricing policy heavily relies on the upper bound of the admissible price range, and a low price upper bound facilitates the policy to converge. In contrast, when consumers are gain-seeking towards all products, we prove that the optimal pricing policy admits no steady state regardless of the price range. Nevertheless, if consumers are only gain-seeking towards certain but not all products, the optimal pricing policy can potentially be convergent. In addition, our numerical experiments show that loss-aversion over all products does not rule out price fluctuations. This finding is at odds with the classic belief on loss-averse consumers and hence, highlights the significance of accounting for cross-product effects through the MNL demand.
Download or read book Mathematical and Computational Models for Congestion Charging written by Siriphong Lawphongpanich and published by Springer Science & Business Media. This book was released on 2006-06-05 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigorous treatments of issues related to congestion pricing are described in this book. It examines recent advances in areas such as mathematical and computational models for predicting traffic congestion, determining when, where, and how much to levy tolls, and analyzing the impact on transportation systems. The book follows recent schemes judged to be successful in London, Singapore, Norway, as well as a number of projects in the United States.
Download or read book Dynamic Pricing Implications of Uncertainity about Demand written by Eric Gordon Wruck and published by . This book was released on 1989 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Surprising Sufficiency of Linear Models for Dynamic Pricing with Demand Learning written by Omar Besbes and published by . This book was released on 2014 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a multi-period single product pricing problem with an unknown demand curve. The seller's objective is to adjust prices in each period so as to maximize cumulative expected revenues over a given finite time horizon; in doing so, the seller needs to resolve the tension between learning the unknown demand curve and maximizing earned revenues. The main question that we investigate is the following: how large of a revenue loss is incurred if the seller uses a simple parametric model which differs significantly (i.e., is misspecified) relative to the underlying demand curve. This "price of misspecification'' is expected to be significant if the parametric model is overly restrictive. Somewhat surprisingly, we show (under reasonably general conditions) that this may not be the case.
Download or read book Dynamic Pricing Implications of Uncertainty about Demand written by Eric Gordon Wruck and published by . This book was released on 1989 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Pricing with Reference Price Effects written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Pricing with Demand Learning Under Competition written by Carine Anne Marie Simon and published by . This book was released on 2007 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: (cont.) Finally, we consider closed-loop strategies in a duopoly market when demand is stochastic. Unlike open-loop policies (such policies are computed once and for all at the beginning of the time horizon), closed loop policies are computed at each time period, so that the firm can take advantage of having observed the past random disturbances in the market. In a closed-loop setting, subgame perfect equilibrium is the relevant notion of equilibrium. We investigate the existence and uniqueness of a subgame perfect equilibrium strategy, as well as approximations of the problem in order to be able to compute such policies more efficiently.
Download or read book Robust Dynamic Pricing with Demand Learning in the Presence of Outlier Customers written by Chen, Xi and published by . This book was released on 2020 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the dynamic pricing problem under model mis-specifi cation settings. To characterize the model mis-specification, we extend the "eps-contamination model | the most fundamental model in robust statistics and machine learning, to the online setting. In particular, for a selling horizon of length T, the online "eps-contamination model assumes that the demands are realized according to a typical unknown demand function only for (1-eps)T periods. For the rest of eps T periods, an outlier purchase can happen with arbitrary demand functions. Under this model, we develop new robust dynamic pricing policies to hedge against outlier purchase behavior. For the dynamic pricing problem, there are two critical prices, the revenue-maximizing price and inventory clearance price, and the optimal price is the larger price. The challenge is that the seller has no information about which price is larger, and the revenues near these two prices behave entirely differently. To address this challenge, we propose robust online policies for both cases when the optimal price is the revenue-maximizing price and when the optimal price is the clearance price, and then develop a meta algorithm that combines these two cases. Our algorithm is a fully adaptive policy that does not require any prior knowledge of the outlier proportion parameter ". Our simulation study shows that our policy outperforms existing policies in the literature.
Download or read book An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation written by Maxime Cohen and published by . This book was released on 2020 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a multi-period, multi-item dynamic pricing problem faced by a retailer. The objective is to maximize the total profit by choosing prices, while satisfying several business rules. The strength of our work lies in our graphical model reformulation, which allows us to use ideas from combinatorial optimization. We do not make any assumptions on the structure of the demand function. The complexity of our method depends linearly on the number of time periods but is exponential in the memory of the model (number of past prices that affect current demand) and in the number of items. We prove that the profit maximization problem is NP-hard by showing an approximation preserving reduction from the weighted Max-3-SAT problem. We next introduce the discrete reference price model which is a discretized version of the reference price model, accounting for an exponentially smoothed contribution of all past prices. We show that our problem can be solved efficiently under this model. We then approximate common demand functions using the discrete reference price model. To handle cross-item effects among multiple items, we propose to use a virtual reference price that assigns a reference price for each category of items (as opposed to a reference price for each item). To enhance the tractability of our approach, we cluster items into blocks and show how to adapt our method to include business constraints across blocks. Finally, we apply our solution approach using demand models calibrated with supermarket data and validate its practical performance.
Download or read book Pricing and Revenue Optimization written by Robert Phillips and published by Stanford University Press. This book was released on 2005-08-05 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].
Download or read book Intertemporal Price Discrimination Via Reference Price Effects written by Zizhuo Wang and published by . This book was released on 2015 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the dynamic pricing problem a monopolistic seller faces when customers arrive in heterogeneous time periods and their purchase decisions are affected by reference prices formed from their past purchase experiences. We illustrate that a new form of price discrimination opportunity exists in such situations, where the seller's optimal pricing strategy is a cyclic one, even when the customers are loss-neutral and their demand functions are identical. This result differs from those in prior studies where the optimal price paths are shown to be asymptotically constant when customer arrival times are homogeneous or when there are no reference price effects, thus is unique due to the interaction between the heterogeneous arrivals and the reference price effects. We also provide the length of the cycle when the demand function is linear. In this era where customer information becomes easier accessible, our results suggest the seller consider this new dimension of price discrimination in conjunction with the old ones, in order to take advantage of the full power of customer data.
Download or read book Pricing and Equilibrium written by Erich Schneider and published by . This book was released on 1952 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
