Auctions, actions, and the failure of information aggregation

We study a market in which k identical and indivisible objects are allocated using a uniform-price auction where n > k bidders each demand one object. Before the auction, each bidder receives an informative but imperfect signal about the state of the world. The good that is auctioned is a common-value object for the bidders, and a bidder's valuation for the object is determined jointly by the state of the world and an action that he chooses after winning the object but before he observes the state. We show that there are equilibria in which the auction price is completely uninformative about the state of the world and aggregates no information even in an arbitrarily large auction. In the equilibrium that we construct, because prices do not aggregate information, agents have strict incentives to acquire costly information before they participate in the market. Also, market statistics other than price, such as the amount of rationing and bid distributions contain extra information about the state. Our findings sharply contrast with past work which shows that in large auctions where there is no ex-post action, the auction price aggregates information.