Download or read book Product Assortment and Price Competition Under Multinomial Logit Demand written by Omar Besbes and published by . This book was released on 2015 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: The role of assortment planning and pricing in shaping sales and profits of retailers is well documented and studied in monopolistic settings. However, such a role remains relatively unexplored in competitive environments. In this paper, we study equilibrium behavior of competing retailers in two settings: i.) when prices are exogenously fixed, and retailers compete in assortments only; and ii.) when retailers compete jointly in assortment and prices. For this, we model consumer choice using a multinomial Logit, and assume that each retailer selects products from a predefined set, and faces a display constraint. We show that when the sets of products available to retailers do not overlap, there always exists one equilibrium that pareto-dominates all others, and that such an outcome can be reached through an iterative process of best responses. A direct corollary of our results is that competition leads a firm to offer a broader set of products compared to when it is operating as a monopolist, and to broader offerings in the market compared to a centralized planner. When some products are available to all retailers, i.e., assortments might overlap, we show that display constraints drive equilibrium existence properties.

Download or read book Price Competition Under Mixed Multinomial Logit Demand Functions written by Margaret P. Pierson and published by . This book was released on 2014 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we postulate a general class of price competition models with mixed multinomial logit demand functions under affine cost functions. In these models, the market is partitioned into a finite set of market segments. We characterize the equilibrium behavior of this class of models in the case where each product in the market is sold by a separate, independent firm. We identify a simple and very broadly satisfied condition under which a pure Nash equilibrium exists and the set of Nash equilibria coincides with the solutions of the system of first-order-condition equations, a property of essential importance to empirical studies. This condition specifies that in every market segment, each firm captures less than 50% of the potential customer population when pricing at a specific level that, under the condition, is an upper bound for a rational price choice for the firm irrespective of the competitors' prices. We show that under a somewhat stronger, but still broadly satisfied, version of the above condition, a unique equilibrium exists. We complete the picture by establishing the existence of a Nash equilibrium, indeed a unique Nash equilibrium, for markets with an arbitrary degree of concentration, under sufficiently tight price bounds. We discuss how our results extend to a continuum of customer types. A discussion of the multiproduct case is included. The paper concludes with a discussion of implications for structural estimation methods.

Download or read book Price Competition Under Multinomial Logit Demand Functions with Random Coefficients written by Gad Allon and published by . This book was released on 2011 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we postulate a general class of price competition models with Mixed Multinomial Logit demand functions under affine cost functions. We first characterize the equilibrium behavior of this class of models in the case where each product in the market is sold by a separate, independent firm and customers share a common income level. We identify a simple and very broadly satisfied condition under which a Nash equilibrium exists while the set of Nash equilibria coincides with the solutions of the system of First Order Condition equations, a property of essential importance to empirical studies. This condition specifies that in every market segment, each firm captures less than 50% of the potential customer population when pricing at a level which, under the condition, can be shown to be an upper bound for a rational price choice for the firm irrespective of the prices chosen by its competitors. We show that under a somewhat stronger, but still broadly satisfied version of the above condition, a unique equilibrium exists. We complete the picture, establishing the existence of a Nash equilibrium, indeed a unique Nash equilibrium, for markets with an arbitrary degree of concentration; under sufficiently tight price bounds. We then discuss two extensions of our model: unequal customer income and a continuum of customer types. A discussion of the multi product case is included in the appendix. The paper concludes with a discussion of implications for structural estimation methods.

Download or read book Revealed Preference Tests for Price Competition in Multi product Differentiated Markets written by Yuta Yasui and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assumptions on competitive structure are often crucial for marginal cost estimation and counterfactual predictions. This paper introduces tests for price competition among multi-product firms are introduced. The tests are based on the firm's revealed preference (revealed profit function). In contrast to other approaches based on estimated demand functions such as conduct parameter estimation, the proposed tests do not require any instrumental variables even though the models can accommodate structural error terms. In this paper, I employ a demand structure introduced by Nocke and Schutz (2018), the discrete/continuous choice model, which nests the multinomial logit demand and CES demand functions. Any price and quantity data can be rationalized by price competition under a discrete/continuous choice model and increasing marginalcosts. Adding more assumptions on the demand function, such as logit, CES, or the co-evolving and log-concave property produces some falsifiable restrictions.

Download or read book Price Discounts and Personalized Product Assortment Under Multinomial Logit Choice Model written by Qingwei Jin and published by . This book was released on 2020 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: With increasing availability of consumer data and rapid advancement and applications of technologies, online retailers are gaining better knowledge of shopping behavior and preferences of their customers. Thus more and more retailers are providing customized product assortment to better match the needs of customers and generate more sales. In this paper, we study a two-stage revenue management model where a retailer decides non-customized price discounts at stage one due to fairness consideration and customized product assortment at stage two (upon the arrival of customers) under the multinomial logit choice model. We employ a robust approach for the joint discounts and customized assortment optimization problem to handle data uncertainty for estimating customer preferences and distribution of different customer segments. We analyze the structural properties of the problems and propose efficient computational methods to solve the problems with/without cardinality constraint on the assortment. In certain cases, our algorithm converges at a superlinear rate. When there is a cardinality constraint on the assortment, we find the retailer should offer deeper discounts as the constraint becomes more restrictive. We also provide some discussion on the value of our robust solution and the extension when the customer discount sensitivity function is also uncertain. Finally, our extensive numerical study shows that the solutions under the robust approach perform very well compared to the one assuming accurate information and has robustness when there is uncertainty.

Download or read book Multi Product Price and Assortment Competition written by Awi Federgruen and published by . This book was released on 2014 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: We address a generic price competition model in an industry with an arbitrary number of competitors, each offering all or a subset of a given line of N products. The products are substitutes in the sense that the demand volume of each product weakly increases whenever the price of another product increases. The cost structure is linear, with arbitrary cost rates.Our demand model is the unique regular extension of a set of demand functions that are affine in a limited polyhedral subset of the price space. A set of demand functions is regular if it satisfies the following conditions: under any given price vector, when some product is priced out of the market, i.e., has zero demand, any increase of its price has no impact on the demand volumes. Depending on the set of prices selected by the competing firms, a different product assortment is offered on the market.We characterize the equilibrium prices, product assortment and sales volumes in the price competition model, under this demand model. Under minimal conditions, we show that a pure Nash equilibrium always exists; while multiple price equilibria may arise, they are equivalent in the sense of generating an identical product assortment and sales volumes.

Download or read book Revenue Management and Pricing Analytics written by Guillermo Gallego and published by Springer. This book was released on 2019-08-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: “There is no strategic investment that has a higher return than investing in good pricing, and the text by Gallego and Topaloghu provides the best technical treatment of pricing strategy and tactics available.” Preston McAfee, the J. Stanley Johnson Professor, California Institute of Technology and Chief Economist and Corp VP, Microsoft. “The book by Gallego and Topaloglu provides a fresh, up-to-date and in depth treatment of revenue management and pricing. It fills an important gap as it covers not only traditional revenue management topics also new and important topics such as revenue management under customer choice as well as pricing under competition and online learning. The book can be used for different audiences that range from advanced undergraduate students to masters and PhD students. It provides an in-depth treatment covering recent state of the art topics in an interesting and innovative way. I highly recommend it." Professor Georgia Perakis, the William F. Pounds Professor of Operations Research and Operations Management at the Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts. “This book is an important and timely addition to the pricing analytics literature by two authors who have made major contributions to the field. It covers traditional revenue management as well as assortment optimization and dynamic pricing. The comprehensive treatment of choice models in each application is particularly welcome. It is mathematically rigorous but accessible to students at the advanced undergraduate or graduate levels with a rich set of exercises at the end of each chapter. This book is highly recommended for Masters or PhD level courses on the topic and is a necessity for researchers with an interest in the field.” Robert L. Phillips, Director of Pricing Research at Amazon “At last, a serious and comprehensive treatment of modern revenue management and assortment optimization integrated with choice modeling. In this book, Gallego and Topaloglu provide the underlying model derivations together with a wide range of applications and examples; all of these facets will better equip students for handling real-world problems. For mathematically inclined researchers and practitioners, it will doubtless prove to be thought-provoking and an invaluable reference.” Richard Ratliff, Research Scientist at Sabre “This book, written by two of the leading researchers in the area, brings together in one place most of the recent research on revenue management and pricing analytics. New industries (ride sharing, cloud computing, restaurants) and new developments in the airline and hotel industries make this book very timely and relevant, and will serve as a critical reference for researchers.” Professor Kalyan Talluri, the Munjal Chair in Global Business and Operations, Imperial College, London, UK.

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 Duopoly Price Competition with Reference Effects Under Logit Demand written by Mengzi Amy Guo and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a duopoly price competition with each firm selling one substitute product to strategic consumers, who assess their willingness to pay based on the reference price and make purchase decisions through the MNL model. The influence of reference price on consumer demand, known as the reference effect, can be potentially asymmetric, which incurs the non-smoothness in revenue functions. In the one-shot game, we show the existence, uniqueness, and structure of Nash equilibrium (NE) in loss-neutral and loss-averse scenarios (our proof also extends to the oligopoly setting). By contrast, in the gain-seeking scenario, the NE exists but may not be unique, where we provide a sufficient condition for the occurrence of multiple equilibria. Additionally, our one-shot game can be naturally extended to a repeated game with consecutive periods linked by reference price updates. We derive theoretical insights on the long-run market dynamics in this multi-period competitive framework under two practical pricing policies. Notably, the market stability (i.e., convergence behavior) hinges on the presence of a gain-seeking product. In the absence of gain-seeking products, we prove the convergence of price and reference price paths to the stationary Nash equilibrium (SNE) when firms possess full rationality and adopt the equilibrium pricing policy. We further characterize the structure of SNE and show that it is unique if and only if both products are loss-neutral. Meanwhile, when firms only exhibit bounded rationality and adhere to the best-response pricing policy, we draw the same conclusion in a special case where consumers have short-term memories. Conversely, when any gain-seeking product is introduced, the SNE ceases to exist, implying that the market never stabilizes in the long run under either equilibrium or best-response pricing policy.

Download or read book Capacitated Assortment and Price Optimization Under the Multinomial Logit Model written by Ruxian Wang and published by . This book was released on 2014 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an assortment and price optimization problem where a retailer chooses an assortment of competing products and determines their prices to maximize the total expected profit subject to a capacity constraint. Customers' purchase behavior follows the multinomial logit choice model with general utility functions. This paper simplifies it to a problem of finding a unique fixed point of a single-dimensional function and visualizes the assortment optimization process. An efficient algorithm to find the optimal assortment and prices is provided.

Download or read book Tractable Multi product Pricing Under Discrete Choice Models written by Philipp Wilhelm Keller and published by . This book was released on 2013 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a retailer offering an assortment of differentiated substitutable products to price-sensitive customers. Prices are chosen to maximize profit, subject to inventory/ capacity constraints, as well as more general constraints. The profit is not even a quasi-concave function of the prices under the basic multinomial logit (MNL) demand model. Linear constraints can induce a non-convex feasible region. Nevertheless, we show how to efficiently solve the pricing problem under three important, more general families of demand models. Generalized attraction (GA) models broaden the range of nonlinear responses to changes in price. We propose a reformulation of the pricing problem over demands (instead of prices) which is convex. We show that the constrained problem under MNL models can be solved in a polynomial number of Newton iterations. In experiments, our reformulation is solved in seconds rather than days by commercial software. For nested-logit (NL) demand models, we show that the profit is concave in the demands (market shares) when all the price-sensitivity parameters are sufficiently close. The closed-form expressions for the Hessian of the profit that we derive can be used with general-purpose nonlinear solvers. For the special (unconstrained) case already considered in the literature, we devise an algorithm that requires no assumptions on the problem parameters. The class of generalized extreme value (GEV) models includes the NL as well as the cross-nested logit (CNL) model. There is generally no closed form expression for the profit in terms of the demands. We nevertheless how the gradient and Hessian can be computed for use with general-purpose solvers. We show that the objective of a transformed problem is nearly concave when all the price sensitivities are close. For the unconstrained case, we develop a simple and surprisingly efficient first-order method. Our experiments suggest that it always finds a global optimum, for any model parameters. We apply the method to mixed logit (MMNL) models, by showing that they can be approximated with CNL models. With an appropriate sequence of parameter scalings, we conjecture that the solution found is also globally optimal.

Download or read book Multi Product Price Optimization and Competition Under the Nested Logit Model with Product Differentiated Price Sensitivities written by Guillermo Gallego and published by . This book was released on 2014 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study firms that sell multiple substitutable products and customers whose purchase behavior follows a Nested Logit model, of which the Multinomial Logit model is a special case. Customers make purchasing decision sequentially under the Nested Logit model: they first select a nest of products and subsequently purchase one within the selected nest. We consider the multi-product pricing problem under the general Nested Logit model with product-differentiated price sensitivities and arbitrary nest coefficients. We show that the adjusted markup, defined as price minus cost minus the reciprocal of price sensitivity, is constant for all products within a nest at optimality. This reduces the problem's dimension to a single variable per nest. We also show that the adjusted nest-level markup is nest-invariant for all the nests, which further reduces the problem to maximizing a single-variable unimodal function under mild conditions. We also use this result to simplify the oligopolistic multi-product price competition and characterize the Nash equilibrium. We also consider more general attraction functions that include the linear utility and the multiplicative competitive interaction models as special cases, and show that similar techniques can be used to significantly simplify the corresponding pricing problems.

Download or read book Planning Production and Inventories in the Extended Enterprise written by Karl G. Kempf and published by Springer Science & Business Media. This book was released on 2011-01-12 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: In two volumes, Planning Production and Inventories in the Extended Enterprise: A State of the Art Handbook examines production planning across the extended enterprise against a backdrop of important gaps between theory and practice. The early chapters describe the multifaceted nature of production planning problems and reveal many of the core complexities. The middle chapters describe recent research on theoretical techniques to manage these complexities. Accounts of production planning system currently in use in various industries are included in the later chapters. Throughout the two volumes there are suggestions on promising directions for future work focused on closing the gaps.

Download or read book Consumer Driven Demand and Operations Management Models written by Serguei Netessine and published by Springer Science & Business Media. This book was released on 2009-06-02 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book is by top scholars in supply chain management, revenue management, and e-commerce, all of which are grounded in information technologies and consumer demand research. The book looks at new selling techniques designed to reach the consumer.

Download or read book Assortment and Price Optimization Under an Endogenous Context Dependent Multinomial Logit Model written by Yicheng Bai and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by empirical evidence that the utility of each product depends on the assortment of products offered along with it, we propose an endogenous context-dependent multinomial logit model (Context-MNL) under which the utility of each product depends on both the product's intrinsic value and the deviation of the intrinsic value from the expected maximum utility among all the products in the offered assortment. Under the Context-MNL model, an assortment provides a context in which customers evaluate the utility of each product. Our model generalizes the standard multinomial logit model and allows the utility of each product to depend on the offered assortment. The model is parsimonious, requires only one parameter more than the standard multinomial logit model, captures the assortment-dependent effect endogenously, and does~not require the decision-maker to determine in advance the relevant attributes of the assortment that might affect the product utility. The Context-MNL model also admits tractable maximum likelihood estimation and is operationally tractable, with efficient solution methods for solving assortment and price optimization problems. Our numerical study, which is based on data from Expedia, shows that compared to the standard multinomial logit model, the Context-MNL model substantially improves out-of-sample goodness of fit and prediction accuracy.

Download or read book Assortment and Price Optimization Under MNL Model with Price Range Effect written by Stefanus Jasin and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study the assortment and price optimization problems under Multinomial Logit (MNL) model with price range effect, where the utility of a product is affected by the relative position of its price with respect to the highest and the lowest prices in the offer set. This model is motivated by the so-called Range Theory popularized in the behavioral economics and psychology literature. It addresses the limitation of a single-point interpretation of reference price, which ignores the impact of all other distributional information. We investigate the pure assortment problem, the pure pricing problem, and the joint assortment and pricing problem under the MNL model with price range effect. For each model, we first identify the structure of the optimal policy, and then we propose tractable algorithms that either output the optimal solution in polynomial time or admit an Fully Polynomial-Time Approximation Scheme (FPTAS).

Download or read book Assortment of Optimization and Pricing Problems Under Multi stage Multinomial Logit Models written by Yuhang Ma and published by . This book was released on 2019 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: In most E-commerce scenarios such as hotel booking and online shopping, products are not offered to customers simultaneously. Instead, they are divided into different webpages and presented to customers sequentially. In this thesis, we focus on solving a common problem faced by online retailers: when products are revealed to customers sequentially, which products should the retailers display at each stage and what prices should the retailers charge for each product so that the expected revenue can be maximized? To solve those problems, we generalize the classical multinomial logit model to capture the customer's choice behavior under the sequential setting and present efficient algorithms for different generalized choice models and different operational constraints.