The Loser's Curse and Information Aggregation in Common Value Auctions, Econometrica
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 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 → ∞ and nr - kr → ∞, i.e., both the number of objects and the number of bidders who do not receive an object go to infinity.
Jeroen Swinkels, Wolfgang Pesendorfer
Swinkels, Jeroen, and Wolfgang Pesendorfer. 1997. The Loser's Curse and Information Aggregation in Common Value Auctions. Econometrica. 65: 1247-1282.