Revenue Maximization Under Unknown Private Values with Nonobligatory Inspection

We consider the problem of selling k units of an item to n unit-demand buyers to maximize revenue, where the buyers’ values are independently distributed (not necessarily identical) according to publicly known distributions but unknown to the buyers themselves, with the option of allowing buyers to inspect the item at a cost. This problem can be interpreted as a revenue-maximizing variant of Weitzman’s Pandora’s problem with a nonobligatory inspection. We first fully characterize the optimal mechanism in selling to a single buyer subject to an upper bound on the allocation probability. Using this characterization, we then present an approximation mechanism that achieves $1-1/\sqrt{k+3}$ of the optimal revenue in expectation. Our mechanism is sequential and has a simple implementation that works in an online setting where buyers arrive in an arbitrary unknown order, yet achieving the aforementioned approximation with respect to the optimal offline mechanism.

Supplemental Material: The electronic companion is available at https://doi.org/10.1287/opre.2022.0024.