Revenue Equivalence of Large Asymmetric Auctions

44 Pages Posted: 23 Dec 2016

See all articles by Gadi Fibich

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences

Arieh Gavious

Ono Academic College; Ben-Gurion University

Nir Gavish

Technion-Israel Institute of Technology - Faculty of Mathematics

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Date Written: December 22, 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/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 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(∈2/n 3) revenue equivalence to a broader class of asymmetric auctions.

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=2888775 or http://dx.doi.org/10.2139/ssrn.2888775

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Arieh Gavious

Ono Academic College ( email )

Kyriat Ono
Israel

Ben-Gurion University ( email )

Beer-Sheva 84105
Israel

Nir Gavish (Contact Author)

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

Haifa 32000
Israel
97248294181 (Phone)

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