Revenue Equivalence of Large Asymmetric Auctions

Abstract

The paper analyzes the revenue of auctions with asymmetric bidders with a large, but finite number of players. We explicitly calculate the seller’s expected revenue in large asymmetric first-price, second-price, and optimal auctions to O(1/n 3) accuracy, where n is the number of players. These calculations show that the revenue differences among these three auction mechanisms scale as ∈2/n 3, where e is the level of asymmetry (heterogeneity) among the distributions of bidders’ valuations. This novel scaling law shows that bidders’ asymmetry already has a negligible effect on revenue ranking of auctions with several (e.g., n = 6) bidders. In contrast, previous results studied only the limiting case n → ∞. We also show that bidders’ asymmetry always reduces the expected revenue in large auctions, but not necessarily in small ones. Finally, we extend the asymptotic O(∈2/n 3) revenue equivalence to a broader class of asymmetric auctions.