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Revenue Equivalence of Large Asymmetric Auctions

43 Pages Posted: 28 Jul 2017  

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences

Arieh Gavious

Ben-Gurion University of the Negev

Nir Gavish

Technion-Israel Institute of Technology - Faculty of Mathematics

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Date Written: December 22, 2016

Abstract

The paper analyzes the seller's expected revenue in auctions with a large number of asymmetric players. We explicitly calculate the 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 ε2/n3, 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., 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(ε2/n3) revenue equivalence to a broader class of asymmetric auctions.

Keywords: Auction theory, revenue equivalence, first-price auction, second-price auction, optimal auctions, asymptotic methods

JEL Classification: C72, D44, D82, C65

Suggested Citation

Fibich, Gadi and Gavious, Arieh and Gavish, Nir, Revenue Equivalence of Large Asymmetric Auctions (December 22, 2016). Available at SSRN: https://ssrn.com/abstract=2888765

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Arieh Gavious

Ben-Gurion University of the Negev ( email )

POB 653
Beer Sheva, 8410501
Israel

Nir Gavish (Contact Author)

Technion-Israel Institute of Technology - Faculty of Mathematics ( email )

Haifa 32000
Israel
97248294181 (Phone)

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