Selling to Intermediaries: Optimal Auction Design in a Common Value Model

38 Pages Posted: 15 Aug 2017

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

Date Written: August 11, 2017

Abstract

We characterize revenue maximizing auctions when the bidders are intermediaries who wish to resell the good. The bidders have differential information about their common resale opportunities: each bidder privately observes an independent draw of a resale opportunity, and the highest signal is a sufficient statistic for the value of winning the good. If the good must be sold, then the optimal mechanism is simply a posted price at which all bidders are willing to purchase the good, and all bidders are equally likely to be allocated the good, irrespective of their signals. If the seller can keep the good, then under the optimal mechanism, all bidders make the same expected payment and have the same expected probability of receiving the good, independent of the signal. Conditional on the good being sold, the allocation discriminates in favor of bidders with lower signals. In some cases, the optimal mechanism again reduces to a posted price. The model provides a foundation for posted prices in multi-agent screening problems.

Keywords: Optimal auction, Intermediaries, Posted price, Guaranteed demand auction, Common values, Revenue maximization, Revenue equivalence, First-price auction, Second-price auction, Resale, Maximum value game, Descending auction, Local incentive constraints, Global incentive constraints

JEL Classification: C72, D44, D82, D83

Suggested Citation

Bergemann, Dirk and Brooks, Benjamin A. and Morris, Stephen Edward, Selling to Intermediaries: Optimal Auction Design in a Common Value Model (August 11, 2017). Cowles Foundation Discussion Paper No. 2064R. Available at SSRN: https://ssrn.com/abstract=3018883 or http://dx.doi.org/10.2139/ssrn.3018883

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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