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 equilibrium of this auction. We then consider a sequence of auctions A r with n r bidders and k r objects. We show that price converges in probability to the true value of the object if and only if both k r → ∞ and n r - k r → ∞, i.e., both the number of objects and the number of bidders who do not receive an object go to infinity.