The Loser's Curse and Information Aggregation in Common Value Auctions

We consider an auction in which k identical objects of unknown value are auctioned off to n bidders. The k highest bidders get an object and pay the k+1st bid. Bidders receive a signal that provides information about the value of the object. We characterize the unique symmetric equilibirum of this auction. We then consider a sequence of auctions Ar with nr bidders and kr objects. We show that price converges in probability to the true value of the object if and only if both kr-->infinity and nr--kr-->infinity, i.e., the number of objects and the number of bidders who do not receive an object in equilibrium go to infinty.