Countering the Winner’s Curse: Optimal Auction Design in a Common Value Model

38 Pages Posted: 26 Nov 2018

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 2 versions of this paper

Date Written: November 16, 2018

Abstract

We characterize revenue maximizing mechanisms in a common value environment where the value of the object is equal to the highest of bidders’ independent signals. The optimal mechanism exhibits either neutral selection, wherein the object is randomly allocated at a price that all bidders are willing to pay, or advantageous selection, wherein the object is allocated with higher probability to bidders with lower signals. If neutral selection is optimal, then the object is sold with probability one by a deterministic posted price. If advantageous selection is optimal, the object is sold with probability less than one at a random price. By contrast, standard auctions that allocate to the bidder with the highest signal (e.g., the first-price, second-price or English auctions) deliver lower revenue because of the adverse selection generated by the allocation rule: if a bidder wins the good, then he revises his expectation of its value downward.

We further show that the posted price mechanism is optimal among those mechanisms that always allocate the good. A sufficient condition for the posted price to be optimal among all mechanisms is that there is at least one potential bidder who is omitted from the auction. Our qualitative results extend to more general common value environments where adverse selection is high.

Keywords: Optimal auction, Common values, Maximum game, Posted price, Revenue equivalence, Adverse selection, Neutral selection, Advantageous selection

JEL Classification: C72, D44, D82, D83

Suggested Citation

Bergemann, Dirk and Brooks, Benjamin A. and Morris, Stephen Edward, Countering the Winner’s Curse: Optimal Auction Design in a Common Value Model (November 16, 2018). Cowles Foundation Discussion Paper No. 2147. Available at SSRN: https://ssrn.com/abstract=3287049 or http://dx.doi.org/10.2139/ssrn.3287049

Dirk Bergemann (Contact Author)

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

28 Hillhouse Ave
New Haven, CT 06520-8268
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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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