More Like this

1. The Power of Opaque Products in Pricing

   https://doi.org/10.1287/mnsc.2020.3750  

   Elmachtoub, Adam N.; Hamilton, Michael L. (August 2021, Management Science)

   null (Ed.)

   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. 

   more » « less
2. Static Pricing for Multi-unit Prophet Inequalities

   https://doi.org/10.1287/opre.2023.0031  

   Chawla, Shuchi; Devanur, Nikhil; Lykouris, Thodoris (November 2023, Operations Research)

   Characterizing the Efficiency of Static Pricing Schemes as a Function of the Supply The problem of selling a supply of k units to a stream of customers constitutes one of the cornerstones in revenue management. Static pricing schemes (that output the same price to all customers) are commonly used because of their simplicity and their many desirable properties; they are anonymous, nonadaptive, and order oblivious. Although the efficiency of those schemes should improve as the supply k increases, prior work has only focused either on algorithms that aim for a constant approximation that is independent of k or on the setting where k becomes really large. In contrast, this paper characterizes the efficiency of static pricing schemes as a function of the supply. Our approach stems from identifying a “sweet spot” between selling enough items and obtaining enough utility from customers with high valuations. Subsequent work shows that our pricing scheme is the optimal static pricing for every value of k. 

   more » « less
3. A Simple and Approximately Optimal Mechanism for a Buyer with Complements

   https://doi.org/10.1287/opre.2020.2039  

   Eden, Alon; Feldman, Michal; Friedler, Ophir; Talgam-Cohen, Inbal; Weinberg, S. Matthew (January 2021, Operations Research)

   We consider a revenue-maximizing seller with m heterogeneous items and a single buyer whose valuation for the items may exhibit both substitutes and complements. We show that the better of selling the items separately and bundling them together— guarantees a [Formula: see text]-fraction of the optimal revenue, where d is a measure of the degree of complementarity; it extends prior work showing that the same simple mechanism achieves a constant-factor approximation when buyer valuations are subadditive (the most general class of complement-free valuations). Our proof is enabled by a recent duality framework, which we use to obtain a bound on the optimal revenue in the generalized setting. Our technical contributions are domain specific to handle the intricacies of settings with complements. One key modeling contribution is a tractable notion of “degree of complementarity” that admits meaningful results and insights—we demonstrate that previous definitions fall short in this regard. 

   more » « less
4. Learning Revenue-Maximizing Auctions With Differentiable Matching

   Curry, Michael J.; Lyi, Uro; Goldstein, Tom; Dickerson, John P. (January 2022, Proceedings of The 25th International Conference on Artificial Intelligence and Statistics)

   We propose a new architecture to approximately learn incentive compatible, revenue-maximizing auctions from sampled valuations. Our architecture uses the Sinkhorn algorithm to perform a differentiable bipartite matching which allows the network to learn strategyproof revenue-maximizing mechanisms in settings not learnable by the previous RegretNet architecture. In particular, our architecture is able to learn mechanisms in settings without free disposal where each bidder must be allocated exactly some number of items. In experiments, we show our approach successfully recovers multiple known optimal mechanisms and high-revenue, low-regret mechanisms in larger settings where the optimal mechanism is unknown. 

   more » « less
5. Pricing ordered items

   https://doi.org/10.1145/3519935.3520065  

   Chawla, Shuchi; Rezvan, Rojin; Teng, Yifeng; Tzamos, Christos (June 2022, Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing)

   We study the revenue guarantees and approximability of item pricing. Recent work shows that with n heterogeneous items, item-pricing guarantees an O(logn) approximation to the optimal revenue achievable by any (buy-many) mechanism, even when buyers have arbitrarily combinatorial valuations. However, finding good item prices is challenging – it is known that even under unit-demand valuations, it is NP-hard to find item prices that approximate the revenue of the optimal item pricing better than O(√n). Our work provides a more fine-grained analysis of the revenue guarantees and computational complexity in terms of the number of item “categories” which may be significantly fewer than n. We assume the items are partitioned in k categories so that items within a category are totally-ordered and a buyer’s value for a bundle depends only on the best item contained from every category. We show that item-pricing guarantees an O(logk) approximation to the optimal (buy-many) revenue and provide a PTAS for computing the optimal item-pricing when k is constant. We also provide a matching lower bound showing that the problem is (strongly) NP-hard even when k=1. Our results naturally extend to the case where items are only partially ordered, in which case the revenue guarantees and computational complexity depend on the width of the partial ordering, i.e. the largest set for which no two items are comparable. 

   more » « less