Privacy Preserving Auctions

Abstract: In many auction settings, the auctioneer must disclose the winner's identity and payment. We characterize the auction that minimizes the winner's privacy loss among those that maximize total surplus or seller revenue and are strategy-proof. Privacy loss is defined by what an outside observer learns from the disclosed price, measured as the mutual information between the price and the winner's valuation. When only interim individual rationality is required, the most privacy-preserving auction uses stochastic ex-post payments. Under ex-post individual rationality and a monotone hazard rate, privacy loss is minimized by the second-price auction with deterministic payments.