Rates of information aggregation in common value auctions

We study the rates at which transaction prices aggregate information in common value auctions under the different information structures in Wilson (Rev. Econ. Stud. 44 (1977) 511) and Pesendorfer and Swinkels (Econometrica 65 (1997) 1247). We consider uniform-price auctions in which k identical objects of unknown value are auctioned to n bidders, where both n and k are allowed to diverge to infinity, and k/n converges to a number in [0,1). The Wilson assumptions lead to information aggregation at a rate proportional to n/√k , but the price aggregates information at a rate proportional to n/√k in the PS setting. We also consider English auctions, and investigate whether the extra information revealed in equilibrium improves convergence rates in these auctions.

[1]  Robert B. Wilson.  A Bidding Model of Perfect Competition , 1977 .

[2]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[3]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[4]  A. Wald.  Note on the Consistency of the Maximum Likelihood Estimate , 1949 .

[5]  L. de Haan,et al.  Limit Distributions for Order Statistics. II , 1978 .

[6]  K. DonaldW..  Generalized Method of Moments Estimation When a Parameter Is on a Boundary , 1999 .

[7]  D. Zizzo,et al.  Rational Expectations , 2006 .

[8]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[9]  Paul R. Milgrom,et al.  Good News and Bad News: Representation Theorems and Applications , 1981 .

[10]  Paul R. Milgrom,et al.  A Convergence Theorem for Competitive Bidding with Differential Information , 1979 .

[11]  R. Z. Khasʹminskiĭ,et al.  Statistical estimation : asymptotic theory , 1981 .

[12]  Victor Chernozhukov,et al.  Conditional Extremes and Near-Extremes , 2000 .

[13]  Paul R. Milgrom,et al.  Rational Expectations, Information Acquisition, and Competitive Bidding , 1981 .

[14]  Ilan Kremer.  Information Aggregation in Common Value Auctions , 2002 .

[15]  W. Whitt.  Uniform conditional stochastic order , 1980 .

[16]  Jeroen M. Swinkels,et al.  The Loser's Curse and Information Aggregation in Common Value Auctions , 1997 .

[17]  Ruqu Wang.  Common-value auctions with discrete private information , 1991 .