We study robustly optimal mechanisms for selling multiple items. The seller maximizes revenue against a worst-case distribution of a buyer’s valuations within a set of distributions, called an “ambiguity” set. We identify the exact forms of robustly optimal selling mechanisms and the worst-case distributions when the ambiguity set satisfies various moment conditions on the values of subsets of goods. The analysis reveals general properties of the ambiguity set that justifies categorical bundling, which includes separate sales and pure bundling as special cases.

We develop a methodology for analyzing the revenue and efficiency performance of auctions when buyers have private information about their willingness to pay and ability to pay. We then apply the framework to scenarios involving standard auction mechanisms. In the simplest case, where bidders face absolute spending limits, first-price auctions yield higher expected revenue and social surplus than second-price auctions. The revenue dominance of first-price auctions over second-price auctions carries over to the case where bidders have access to credit. These rankings are explained by differences in the extent to which financial constraints bind in different auction formats.

Procuring an innovation involves motivating a research effort to generate a new idea and then implementing that idea efficiently. If research efforts are unverifiable and implementation costs are private information, a trade-off arises between the two objectives. The optimal mechanism resolves the trade-off via two instruments: a cash prize and a follow-on contract. It primarily uses the latter, by favouring the innovator at the implementation stage when the value of the innovation is above a certain threshold and handicapping the innovator when the value of the innovation is below that threshold. A cash prize is employed as a supplementary incentive only when the value of innovation is sufficiently high. These features are consistent with current practices in the procurement of innovation and the management of unsolicited proposals.