Sequential Mechanisms with Ex Post Individual Rationality

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.