S. Viswanathan
Duke University, Durham, NC 27708
James J.D. Wang
Duke University, Durham, NC 27708
ABSTRACT
This paper highlights the tension between two important goals in many auction design problems: Allocational efficiency of the auction mechanism, and revenue maximization by the seller. In an auction environment with a stochastic supply of divisible asset, we characterize the symmetric strategy equilibria for three alternative auction formats: the Vickrey auction, the uniform-price auction, and the discriminatory ("pay your bid") auction. Our analysis is distinguished from Wilson's seminal work on share auctions by the presence of supply noise, i.e., the exact quantity being auctioned is unknown in our auction models. We show that the Vickrey auction has a unique dominant-strategy linear equilibrium that is independent of the distribution of supply noise. Unique, linear strategy equilibria are also obtained for the uniform-price and discriminatory auctions (in the latter case, we assume that the distribution of the supply noise is uniform).
We compare the seller's expected revenues among the three auction formats for a class of equilibria where the bidders have different valuations and linearly declining marginal valuation curves. The revenue comparison shows that the Vickrey format dominates the uniform-price auction unless there is sufficient heterogeneity in bidder valuations. However, when the valuations are heterogenous of the supply noise is low or the number of bidders is small, the discriminatory auction yields the seller a higher expected revenue. Our analysis suggests that while Vickrey auctions are allocationally efficient, they are often revenue dominated by discriminatory auctions. This implies that the tension between allocational efficiency and revenue maximization by the seller persists under a Vickrey auction format.