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Increased availability of high-quality customer information has fueled interest in personalized pricing strategies, that is, strategies that predict an individual customer’s valuation for a product and then offer a price tailored to that customer. Although the appeal of personalized pricing is clear, it may also incur large costs in the forms of market research, investment in information technology and analytics expertise, and branding risks. In light of these trade-offs, our work studies the value of personalized pricing strategies over a simple single-price strategy. We first provide closed-form lower and upper bounds on the ratio between the profits of an idealized personalized pricing strategy (first-degree price discrimination) and a single-price strategy. Our bounds depend on simple statistics of the valuation distribution and shed light on the types of markets for which personalized pricing has little or significant potential value. Second, we consider a feature-based pricing model where customer valuations can be estimated from observed features. We show how to transform our aforementioned bounds into lower and upper bounds on the value of feature-based pricing over single pricing depending on the degree to which the features are informative for the valuation. Finally, we demonstrate how to obtain sharper bounds by incorporating additional information about the valuation distribution (moments or shape constraints) by solving tractable linear optimization problems. This paper was accepted by David Simchi-Levi, revenue management and market analytics. 

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.