Optimal auction design with common values: an informationally robust approach

Abstract

A Seller can sell a single unit of a good to a group of bidders. The good is costly to produce, and the bidders have a pure common value that may be higher or lower than the production cost. The value is drawn from a prior distribution that is commonly known. The Seller does not know the bidders' beliefs about the value and values each auction mechanism according to the lowest expected profit across all Bayes Nash equilibria and across all common-prior type spaces that are consistent with the given known value distribution. We characterize and construct optimal auctions for such a Seller. The optimal auctions we construct have a simple structure, in which bidders make one-dimensional bids, the total allocation is a function of the aggregate bid, and individual allocations are proportional to bids. We report a number of further results on optimal auction design with common values and maxmin auction design.