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Problem definition: We seek to provide an interpretable framework for segmenting users in a population for personalized decision making. Methodology/results: We propose a general methodology, market segmentation trees (MSTs), for learning market segmentations explicitly driven by identifying differences in user response patterns. To demonstrate the versatility of our methodology, we design two new specialized MST algorithms: (i) choice model trees (CMTs), which can be used to predict a user’s choice amongst multiple options, and (ii) isotonic regression trees (IRTs), which can be used to solve the bid landscape forecasting problem. We provide a theoretical analysis of the asymptotic running times of our algorithmic methods, which validates their computational tractability on large data sets. We also provide a customizable, open-source code base for training MSTs in Python that uses several strategies for scalability, including parallel processing and warm starts. Finally, we assess the practical performance of MSTs on several synthetic and real-world data sets, showing that our method reliably finds market segmentations that accurately model response behavior. Managerial implications: The standard approach to conduct market segmentation for personalized decision making is to first perform market segmentation by clustering users according to similarities in their contextual features and then fit a “response model” to each segment to model how users respond to decisions. However, this approach may not be ideal if the contextual features prominent in distinguishing clusters are not key drivers of response behavior. Our approach addresses this issue by integrating market segmentation and response modeling, which consistently leads to improvements in response prediction accuracy, thereby aiding personalization. We find that such an integrated approach can be computationally tractable and effective even on large-scale data sets. Moreover, MSTs are interpretable because the market segments can easily be described by a decision tree and often require only a fraction of the number of market segments generated by traditional approaches. Disclaimer: This work was done prior to Ryan McNellis joining Amazon. Funding: This work was supported by the National Science Foundation [Grants CMMI-1763000 and CMMI-1944428]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.1195 . 

Price discrimination strategies, which offer different prices to customers based on differences in their valuations, have become common practice. Although it allows sellers to increase their profits, it also raises several concerns in terms of fairness (e.g., by charging higher prices (or denying access) to protected minorities in case they have higher (or lower) valuations than the general population). This topic has received extensive attention from media, industry, and regulatory agencies. In this paper, we consider the problem of setting prices for different groups under fairness constraints. We first propose four definitions: fairness in price, demand, consumer surplus, and no-purchase valuation. We prove that satisfying more than one of these fairness constraints is impossible even under simple settings. We then analyze the pricing strategy of a profit-maximizing seller and the impact of imposing fairness on the seller’s profit, consumer surplus, and social welfare. Under a linear demand model, we find that imposing a small amount of price fairness increases social welfare, whereas too much price fairness may result in a lower welfare relative to imposing no fairness. On the other hand, imposing fairness in demand or consumer surplus always decreases social welfare. Finally, no-purchase valuation fairness always increases social welfare. We observe similar patterns under several extensions and for other common demand models numerically. Our results and insights provide a first step in understanding the impact of imposing fairness in the context of discriminatory pricing. This paper was accepted by Jayashankar Swaminathan, operations management. Funding: A. N. Elmachtoub was supported by the Division of Civil, Mechanical and Manufacturing Innovation [Grants 1763000 and 1944428]. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2022.4317 . 

We consider a fundamental pricing model in which a fixed number of units of a reusable resource are used to serve customers. Customers arrive to the system according to a stochastic process and, upon arrival, decide whether to purchase the service, depending on their willingness to pay and the current price. The service time during which the resource is used by the customer is stochastic, and the firm may incur a service cost. This model represents various markets for reusable resources, such as cloud computing, shared vehicles, rotable parts, and hotel rooms. In the present paper, we analyze this pricing problem when the firm attempts to maximize a weighted combination of three central metrics: profit, market share, and service level. Under Poisson arrivals, exponential service times, and standard assumptions on the willingness-to-pay distribution, we establish a series of results that characterize the performance of static pricing in such environments. In particular, although an optimal policy is fully dynamic in such a context, we prove that a static pricing policy simultaneously guarantees 78.9% of the profit, market share, and service level from the optimal policy. Notably, this result holds for any service rate and number of units the firm operates. Our proof technique relies on a judicious construction of a static price that is derived directly from the optimal dynamic pricing policy. In the special case in which there are two units and the induced demand is linear, we also prove that the static policy guarantees 95.5% of the profit from the optimal policy. Our numerical findings on a large test bed of instances suggest that the latter result is quite indicative of the profit obtained by the static pricing policy across all parameters. 

We study the power of selling opaque products, that is, products where a feature (such as color) is hidden from the customer until after purchase. Opaque products, which are sold with a price discount, have emerged as a powerful vehicle to increase revenue for many online retailers and service providers that offer horizontally differentiated items. In the opaque selling models we consider, all of the items are sold at a single common price alongside opaque products that may correspond to various subsets of the items. We consider two types of customers, risk-neutral ones, who assume they will receive a truly random item of the opaque product, and pessimistic ones, who assume they will receive their least favorite item of the opaque product. We benchmark opaque selling against two common selling strategies: discriminatory pricing, where one explicitly charges different prices for each item, and single pricing, where a single price is charged for all the items. We give a sharp characterization of when opaque selling outperforms discriminatory pricing; namely, this result holds for situations where all customers are pessimistic or the item valuations are supported on two points. In the latter case, we also show that opaque selling with just one opaque product guarantees at least 71.9% of the revenue from discriminatory pricing. We then provide upper bounds on the potential revenue increase from opaque selling strategies over single pricing and describe cases where the increase can be significantly more than that of discriminatory pricing. Finally, we provide pricing algorithms and conduct an extensive numerical study to assess the power of opaque selling for a variety valuation distributions and model extensions. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. 

In the online video game industry, a significant portion of the revenue is generated from microtransactions, where a small amount of real-world currency is exchanged for virtual items to be used in the game. One popular way to conduct microtransactions is via a loot box, which is a random allocation of virtual items whose contents are not revealed until after purchase. In this work, we consider how to optimally price and design loot boxes from the perspective of a revenue-maximizing video game company and analyze customer surplus under such selling strategies. Our paper provides the first formal treatment of loot boxes, with the aim to provide customers, companies, and regulatory bodies with insights into this popular selling strategy. We consider two types of loot boxes: a traditional one where customers can receive (unwanted) duplicates and a unique one where customers are guaranteed to never receive duplicates. We show that as the number of virtual items grows large, the unique box strategy is asymptotically optimal among all possible strategies, whereas the traditional box strategy only garners 36.7% of the optimal revenue. On the other hand, the unique box strategy leaves almost zero customer surplus, whereas the traditional box strategy leaves positive surplus. Further, when designing traditional and unique loot boxes, we show it is asymptotically optimal to allocate the items uniformly, even when the item valuation distributions are heterogeneous. We also show that, when the seller purposely misrepresents the allocation probabilities, their revenue may increase significantly, and thus, strict regulation is needed. Finally, we show that, even if the seller allows customers to salvage unwanted items, then the customer surplus can only increase by at most 1.4%. This paper was accepted by Victor Martinez-de-Albeniz, operations management.