Efficiency and information aggregation in large uniform-price auctions

We prove that the equilibria of a large interdependent-value, uniform-price auction model where bidders have arbitrary preferences for multiple units can be approximated by a nonatomic exchange economy. We show that the uniform-price auction is approximately efficient with a large number of participants and asymptotically aggregates idiosyncratic bidder information into the market price. More generally our analysis framework provides conditions justifying the use of nonatomic limit model approximations to analyze the large-market behavior of game-theoretic models. We demonstrate continuity requirements on the economic primitives sufficient for the equilibrium strategies of the two models to converge as the number of participants in the finite game approaches infinity. ∗I would like to thank Ilya Segal, Paul Milgrom, Doug Bernheim, Jon Levin, C. Lanier Benkard, Larry Blume, Eric Budish, David Easley, Matthew Jackson, Ramesh Johari, Philip Reny, Robert Wilson, Marcello Miccoli, Juuso Toikka, Alex Hirsch, Carlos Lever, Edward Augenblick, Isabelle Sin, John Lazarev, and Bumin Yenmez for invaluable discussions regarding this topic. In additional, valuable comments were received during seminars at Stanford, the Stanford Graduate School of Business, Yale School of Management, Kellogg MEDS, Boston University, the University of Rochester, Cornell University, the Ohio State University, and the INFORMS Conference. I gratefully acknowledge the support of the Jacob K. Javits Fellowship program and the Bradley Research Fellowship. An earlier version was written under the title ”The Simple Behavior of Large Mechanisms.”