Efficiency of Large Private Value Auctions

We consider discriminatory and uniform price auctions for multiple identical units of a good. Players have private values, possibly asymmetrically distributed and for multiple units. Our setting allows for aggregate uncertainty about demand and supply. In this setting, equlibria generally will be inefficient. Despite this, we show that such auctions become arbitrarily close to efficient if they are "large," and use this to derive an asymptotic characterization of revenue and bidding behavior.