Information Aggregation in Common Value Auctions

Abstract

A key question in information economics and finance is whether prices aggregate information in a competitive environment. That is, when agents are endowed with private information, does competition lead in the limit to prices which would occur if all information were public?. This paper examines the asymptotic properties of prices in common value auctions when the number of bidders becomes large. The main idea in this paper is to separate the issue of information aggregation from the issue of revenue efficiency. We also distinguish between the amount of information prices contain, and the degree to which prices approximate the asset’s value. Using this approach we get a simple characterization of the limiting distribution of prices. We are not only able to answer whether prices converge to the asset’s value, but also get an explicit form for the limiting distribution. Prices converge to the expected value of the asset conditional on the information possessed by what we call the “pivotal bidder.” This provides insights on how the auction format and the information structure influence the limiting behavior of prices. It shows that the limiting distribution of prices can be derived from the statistical properties of certain order statistics. This lets us abstract from the specific equilibrium bidding strategies. For example, we show that while the first and second price auction have different equilibrium strategies they share a similar limiting distribution of prices. These auctions yield different limiting distributions from auctions such as the English auction or kn auction. Our