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 (1 - α)-th quantile of the "average" of the marginal distributions if a fraction α 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).