skip to main content

Title: The Power of Opaque Products in Pricing
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 more » 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. « less
Award ID(s):
Publication Date:
Journal Name:
Management Science
Page Range or eLocation-ID:
4686 to 4702
Sponsoring Org:
National Science Foundation
More Like this
  1. 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 positivemore »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.« less
  2. We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and the customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Because all the utility parameters of the MNL model are unknown, the seller needs to simultaneously learn customers’ choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or, equivalently, to minimize the expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products [Formula: see text]. The optimal regret of the dynamic assortment planning problem under the most basic and popular choice model—the MNL model—is still open. By carefully analyzing a revenue potential function, we develop a trisection-based policy combined with adaptive confidence bound construction, which achieves an item-independent regret bound of [Formula: see text], where [Formula: see text] is the length of selling horizon. We further establish the matching lower bound result to show the optimality of our policy. There aremore »two major advantages of the proposed policy. First, the regret of all our policies has no dependence on [Formula: see text]. Second, our policies are almost assumption-free: there is no assumption on mean utility nor any “separability” condition on the expected revenues for different assortments. We also extend our trisection search algorithm to capacitated MNL models and obtain the optimal regret [Formula: see text] (up to logrithmic factors) without any assumption on the mean utility parameters of items.« less
  3. Large fractions of online advertisements are sold via repeated second-price auctions. In these auctions, the reserve price is the main tool for the auctioneer to boost revenues. In this work, we investigate the following question: how can the auctioneer optimize reserve prices by learning from the previous bids while accounting for the long-term incentives and strategic behavior of the bidders? To this end, we consider a seller who repeatedly sells ex ante identical items via a second-price auction. Buyers’ valuations for each item are drawn independently and identically from a distribution F that is unknown to the seller. We find that if the seller attempts to dynamically update a common reserve price based on the bidding history, this creates an incentive for buyers to shade their bids, which can hurt revenue. When there is more than one buyer, incentive compatibility can be restored by using personalized reserve prices, where the personal reserve price for each buyer is set using the historical bids of other buyers. Such a mechanism asymptotically achieves the expected revenue obtained under the static Myerson optimal auction for F. Further, if valuation distributions differ across bidders, the loss relative to the Myerson benchmark is only quadratic inmore »the size of such differences. We extend our results to a contextual setting where the valuations of the buyers depend on observed features of the items. When up-front fees are permitted, we show how the seller can determine such payments based on the bids of others to obtain an approximately incentive-compatible mechanism that extracts nearly all the surplus.« less
  4. We consider dynamic assortment problems with reusable products, in which each arriving customer chooses a product within an offered assortment, uses the product for a random duration of time, and returns the product back to the firm to be used by other customers. The goal is to find a policy for deciding on the assortment to offer to each customer so that the total expected revenue over a finite selling horizon is maximized. The dynamic-programming formulation of this problem requires a high-dimensional state variable that keeps track of the on-hand product inventories, as well as the products that are currently in use. We present a tractable approach to compute a policy that is guaranteed to obtain at least 50% of the optimal total expected revenue. This policy is based on constructing linear approximations to the optimal value functions. When the usage duration is infinite or follows a negative binomial distribution, we also show how to efficiently perform rollout on a simple static policy. Performing rollout corresponds to using separable and nonlinear value function approximations. The resulting policy is also guaranteed to obtain at least 50% of the optimal total expected revenue. The special case of our model with infinite usagemore »durations captures the case where the customers purchase the products outright without returning them at all. Under infinite usage durations, we give a variant of our rollout approach whose total expected revenue differs from the optimal by a factor that approaches 1 with rate cubic-root of Cmin, where Cmin is the smallest inventory of a product. We provide computational experiments based on simulated data for dynamic assortment management, as well as real parking transaction data for the city of Seattle. Our computational experiments demonstrate that the practical performance of our policies is substantially better than their performance guarantees and that performing rollout yields noticeable improvements.« less
  5. This paper studies a dynamic pricing problem under model misspecification. To characterize model misspecification, we adopt the ε-contamination model—the most fundamental model in robust statistics and machine learning. In particular, for a selling horizon of length T, the online ε-contamination model assumes that demands are realized according to a typical unknown demand function only for [Formula: see text] periods. For the rest of [Formula: see text] periods, an outlier purchase can happen with arbitrary demand functions. The challenges brought by the presence of outlier customers are mainly due to the fact that arrivals of outliers and their exhibited demand behaviors are completely arbitrary, therefore calling for robust estimation and exploration strategies that can handle any outlier arrival and demand patterns. We first consider unconstrained dynamic pricing without any inventory constraint. In this case, we adopt the Follow-the-Regularized-Leader algorithm to hedge against outlier purchase behavior. Then, we introduce inventory constraints. When the inventory is insufficient, we study a robust bisection-search algorithm to identify the clearance price—that is, the price at which the initial inventory is expected to clear at the end of T periods. Finally, we study the general dynamic pricing case, where a retailer has no clue whether the inventorymore »is sufficient or not. In this case, we design a meta-algorithm that combines the previous two policies. All algorithms are fully adaptive, without requiring prior knowledge of the outlier proportion parameter ε. Simulation study shows that our policy outperforms existing policies in the literature.« less