Optimal Auction Design With Common Values: An Informationally-Robust Approach

78 Pages Posted: 10 Mar 2018 Last revised: 14 Oct 2021

See all articles by Benjamin Brooks

Benjamin Brooks

University of Chicago - Department of Economics

Songzi Du

University of California, San Diego (UCSD) - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: Nov 11, 2020

Abstract

A profit-maximizing Seller has a single unit of a good to sell. The bidders have a pure common value that is drawn from a distribution that is commonly known. The Seller does not know the bidders' beliefs about the value and thinks that beliefs are designed adversarially by Nature to minimize profit. We construct a strong maxmin solution to this joint mechanism design and information design problem, consisting of a mechanism, an information structure, and an equilibrium, such that neither the Seller nor Nature can move profit in their preferred direction, even if the deviator can select the new equilibrium. The mechanism and information structure solve a family of maxmin mechanism design and minmax information design problems, regardless of how an equilibrium is selected. The maxmin mechanism takes the form of a proportional auction: each bidder submits a one-dimensional bid, the aggregate allocation and aggregate payment depend on the aggregate bid, and individual allocations and payments are proportional to bids. We report a number of additional properties of the maxmin mechanisms, including what happens as the number of bidders grows large and robustness with respect to the prior over the value.

Keywords: Mechanism design, information design, optimal auctions, profit maximization, common value, information structure, maxmin, Bayes correlated equilibrium, direct mechanism

JEL Classification: C72, D44, D82, D83

Suggested Citation

Brooks, Benjamin and Du, Songzi, Optimal Auction Design With Common Values: An Informationally-Robust Approach (Nov 11, 2020). Econometrica, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3137227 or http://dx.doi.org/10.2139/ssrn.3137227

Benjamin Brooks

University of Chicago - Department of Economics ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Songzi Du (Contact Author)

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States

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