On the Near-Optimality of Second Price Mechanisms for a Class of Asymmetric Auctions, Games and Economic Behavior
Consider a setting with n sellers having i.i.d. costs with log-concave density f from cumulative F , and a buyer who puts a premium i on procuring from seller i. We show how for any given Δ1,..., Δn, a a simple second price bonus auction can be chosen which comes surprisingly close to giving the auctioneer the same surplus as an optimal mechanism. The bonuses depend only on the magnitude and monotonicity of the slope of virtual costs given F. We show that these in turn depend only on fairly coarse information about F. We explore how this result generalizes to asymmetrically distributed costs.
Jeroen Swinkels, Vladimir N. Mares
Swinkels, Jeroen, and Vladimir N. Mares. 2011. On the Near-Optimality of Second Price Mechanisms for a Class of Asymmetric Auctions. Games and Economic Behavior. 72(1): 218-241.