Optimal Auction Design with Common Values: An Informationally-Robust Approach

Abstract

A profit-maximizing Seller has a single unit of a good to sell. The bidders have a pure common value that is drawn from a distribution that is commonly known. The Seller does not know the bidders' beliefs about the value and thinks that the information structure is chosen adversarially by Nature to minimize profit. We construct what we term a strong maxmin solution to this joint mechanism design and information design problem, which consists of a mechanism, an information structure, and an equilibrium, with the property that neither the Seller nor Nature can move profit in their preferred direction, even if the deviator can select the new equilibrium. We show the mechanism and information structure solve a family of maxmin mechanism design and minmax information design problems, respectively, regardless of how an equilibrium is selected. The maxmin auction has a relatively simple structure, in which bids are one-dimensional, the aggregate supply depends only on the aggregate bid, and individual allocations are proportional to bids. Transfers solve a system of differential equations that align the Seller's profit with the bidders' local incentives. We report a number of additional properties of the maxmin mechanisms, including what happens as the number of bidders grows large and robustness with respect to the prior on the value.

Keywords: Mechanism design, information design, optimal auctions, profit maximiza- tion, common value, information structure, maxmin, Bayes correlated equilibrium, direct mechanism

JEL Classification: C72, D44, D82, D83