Ex-post full surplus extraction, straightforwardly

Abstract

Consider an estimate of the common value of an auctioned asset that is symmetric in the bidders' types. Such an estimate can be represented solely in terms of the order statistics of those types. This representation forms the basis for a pricing rule yielding truthful bidding as an equilibrium, whether bidders' types are a¢ liated or independent. We highlight the link between the estimator and full surplus extraction, providing a necessary and su¢ cient condition for ex-post full surplus extraction, including the possibility of independent types. The results o¤er sharp insights into the strengths and limits of simple auctions by identifying the source of informational rents in such environments.Harstad acknowledges hospitable accommodation by the Fuqua School of Business, Duke University, and the Olin School of Business, Washington University in St. Louis, during parts of this research. We are grateful for comments and suggestions from Richard McLean and Jeroen Swinkels.

Information Variability Impacts in Auctions

“…An example with sizable deviations from symmetric type distributions illustrates. Let types be drawn from uniform distributions: 5,6] and the mean-preserving spreads 4,7]. The more dispersed environment exhibits a greater expected profit, E X (1) − X (2) = 0.45 < E Z (1) − Z (2) = 0.83, and a greater expected revenue, E X (2) = 5.21 < E Z (2) = 5.34.…”

“…If the density function h is continuously differentiable and log-concave on [a, b], then the distribution H has IFR. 7 For completeness, for U ∼ H, define U (n+1) = inf{t : U (t) > 0}; this step assumes X (n+1) and Z (n+1) are finite, which is harmless for present purposes. Theorem 3.…”

Endogenous Competition Alters the Structure of Optimal Auctions

“…29 That revenue is higher when the realized number of bidders is higher does not imply that a seller prefers to take steps to increase the expected number of bidders.…”