TY - UNPB

T1 - Revenue Equivalence of Large Asymmetric Auctions

AU - Fibich, Gadi

AU - Gavious, Arieh

AU - Gavish, Nir

PY - 2016/12/23

Y1 - 2016/12/23

N2 - 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/n3) accu- racy, 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.

AB - 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/n3) accu- racy, 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.

U2 - 10.2139/ssrn.2888775

DO - 10.2139/ssrn.2888775

M3 - Preprint

BT - Revenue Equivalence of Large Asymmetric Auctions

PB - SSRN

ER -