First Price Auctions with General Information Structures: Implications for Bidding and Revenue

102 Pages Posted: 12 Aug 2015

See all articles by Dirk Bergemann

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics; Yale University - Cowles Foundation

Benjamin A. Brooks

Princeton University - Department of Economics

Stephen Morris

Princeton University - Department of Economics

Multiple version iconThere are 7 versions of this paper

Date Written: August 11, 2015

Abstract

This paper explores the consequences of information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over valuations, we characterize the set of possible outcomes that can arise in a Bayesian equilibrium for some information structure. In particular, we characterize maximum and minimum revenue across all information structures when bidders may not know their own values, and maximum revenue when they do know their values. Revenue is maximized when buyers know who has the highest valuation, but the highest valuation buyer has partial information about others' values. Revenue is minimized when buyers are uncertain about whether they will win or lose and incentive constraints are binding for all upward bid deviations.

We provide further analytic results on possible welfare outcomes and report computational methods which work when we do not have analytic solutions. Many of our results generalize to asymmetric value distributions. We apply these results to study how entry fees and reserve prices impact the welfare bounds.

Keywords: First price auction, Information structure, Bayes correlated equilibrium, Private values, Interdependent values, Common values, Revenue, surplus, Welfare bounds, Reserve price, Entry fee

JEL Classification: C72, D44, D82, D83

Suggested Citation

Bergemann, Dirk and Brooks, Benjamin A. and Morris, Stephen Edward, First Price Auctions with General Information Structures: Implications for Bidding and Revenue (August 11, 2015). Cowles Foundation Discussion Paper No. 2018. Available at SSRN: https://ssrn.com/abstract=2642372 or http://dx.doi.org/10.2139/ssrn.2642372

Dirk Bergemann (Contact Author)

Yale University - Cowles Foundation - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3592 (Phone)
203-432-2128 (Fax)

HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Benjamin A. Brooks

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

Stephen Edward Morris

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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