Asymptotic prices in uniform-price multi-unit auctions

This paper considers a uniform-price auction in which each of n symmetric bidders can place, say, M bids. Each bidder has privately known, decreasing marginal values from an arbitrary M -dimensional distribution. We provide a quantile-type description of the asymptotic price that appropriately generalizes the characterization of the unit-demand asymptotic price. Specifically, the limiting price equals the <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$ (1-\alpha )$</EquationSource> </InlineEquation>-th quantile of the “average” of the marginal distributions if a fraction <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\alpha $</EquationSource> </InlineEquation> of the demand is met asymptotically. The result also implies that the expected price in the limit as n becomes large depends only on the aggregate of the marginal distributions of each bidder’s marginal values (and not on the correlation between the marginal values). Copyright Springer-Verlag Berlin/Heidelberg 2005