Optimal Auction Design: Uncertainty, Robustness, and Revenue Maximization

Recent literature on robust mechanism design focuses on detail-free mechanisms to address issues on the restrictive common knowledge assumption. However, most of the existing studies focus on the implementability of an allocation mechanism in a more robust setting, whereas very little is known regarding how these formulations differ from the revenue perspective in the context of optimal mechanism design. In this paper, we revisit the optimal auction design problem and propose a robust formulation based on an uncertainty set that characterizes the conservativeness of the bidders’ beliefs, with two special cases being the Bayesian and Ex post formulations. Using the network approach, we identify the necessary and sufficient conditions under which the expected revenues achieved by different formulations are identical. Furthermore, we show that there is no discrepancy between any pair of formulations in the single-object auction even if the bidders’ types are discrete. Nevertheless, in a multiple-object auction, the auctioneer’s expected revenue may strictly decrease as the bidders’ beliefs become more uncertain.