Revenue Equivalence of Large Asymmetric Auctions (original) (raw)

SSRN Electronic Journal, 2016

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/<i>n</i> ³) accuracy, where <i>n</i> is the number of players. These calculations show that the revenue differences among these three auction mechanisms scale as ∈²/<i>n</i> ³, where ε 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., <i>n</i> = 6) bidders. In contrast, previous results studied only the limiting case <i>n</i> → ∞. 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/<i>n</i> ³) revenue equivalence to a broader class of asymmetric auctions.

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