Sequential Mechanisms with Ex Post Individual Rationality

• Published in: Operations research 2023-01, Vol.71 (1), p.245-258
• Main Authors: Ashlagi, Itai, Daskalakis, Constantinos, Haghpanah, Nima
• Format: Article
• Language: English
• Subjects: Algorithms; ex post individual rationality; Market Analytics and Revenue Management; multiproduct monopolist; Operations research; Prices; Rationality; sequential mechanisms
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.2022.2332

Online multiproduct sellers increasingly use interactive selling strategies to customize their offers to individual buyers. For example, a seller may adjust the prices of products dynamically based on user interaction and offer discounts for buying bundles of products. What selling strategy should such a seller use to maximize profit? In “Sequential Mechanisms with ex Post Individual Rationality,” I. Ashlagi, C. Daskalakis, and N. Haghpanah provide a recursive characterization of the optimal selling strategy. This characterization is used to identify conditions under which the ability to bundle products is less profitable for the seller than the ability to adjust prices dynamically. We study optimal mechanisms for selling multiple products to a buyer who learns her values for those products sequentially. A mechanism may use static prices or adjust them over time, and it may sell the products separately or as bundles. We study mechanisms that provide the buyer a nonnegative ex post utility. We show that there exists an optimal mechanism that determines the allocation of each product as soon as the buyer learns her value for that product. This observation allows us to solve for optimal mechanisms recursively. We use this recursive characterization to show that static mechanisms are suboptimal if the buyer first learns her values for products that are ex ante less valuable. Under this condition, the ability to bundle products is less profitable than the ability to adjust prices dynamically. Funding: This work was supported by ONR [Grant N00014-12-1-0999] and NSF Awards CCF-0953960 (CAREER), CCF-1551875 and SES-1254768. Part of this work was done while the authors were visiting the Simons Institute for Theory of Computing. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2332 .