Distributionally Robust Mechanism Design

55 Pages Posted: 21 Apr 2017 Last revised: 22 Jul 2018

See all articles by Çağıl Koçyiğit

Çağıl Koçyiğit

Ecole Polytechnique Fédérale de Lausanne

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Daniel Kuhn

École polytechnique fédérale de Lausanne

Wolfram Wiesemann

Imperial College Business School

Date Written: April 20, 2017

Abstract

We study a mechanism design problem where an indivisible good is auctioned to multiple bidders, for each of whom it has a private value that is unknown to the seller and the other bidders. The agents perceive the ensemble of all bidder values as a random vector governed by an ambiguous probability distribution, which belongs to a commonly known ambiguity set. The seller aims to design a revenue maximizing mechanism that is not only immunized against the ambiguity of the bidder values but also against the uncertainty about the bidders' attitude towards ambiguity. We argue that the seller achieves this goal by maximizing the worst-case expected revenue across all value distributions in the ambiguity set and by positing that the bidders have Knightian preferences. For ambiguity sets containing all distributions supported on a hypercube, we show that the Vickrey auction is the unique mechanism that is optimal, efficient and Pareto robustly optimal. If the bidders' values are additionally known to be independent, then the revenue of the (unknown) optimal mechanism does not exceed that of a second price auction with only one additional bidder. For ambiguity sets under which the bidders' values are dependent and characterized through moment bounds, on the other hand, we provide a new class of randomized mechanisms, the highest-bidder-lotteries, whose revenues cannot be matched by any second price auction with a constant number of additional bidders. Moreover, we show that the optimal highest-bidder-lottery is a 2-approximation of the (unknown) optimal mechanism, whereas the best second price auction fails to provide any constant-factor approximation guarantee.

Keywords: auction, mechanism design, distributionally robust optimization, ambiguity aversion, Knightian preferences

JEL Classification: C61, D82, D44

Suggested Citation

Kocyigit, Cagil and Iyengar, Garud and Kuhn, Daniel and Wiesemann, Wolfram, Distributionally Robust Mechanism Design (April 20, 2017). Available at SSRN: https://ssrn.com/abstract=2956273 or http://dx.doi.org/10.2139/ssrn.2956273

Cagil Kocyigit (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Station 5
Odyssea 1.04
1015 Lausanne, CH-1015
Switzerland

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States
+1 212-854-4594 (Phone)
+1 212-854-8103 (Fax)

Daniel Kuhn

École polytechnique fédérale de Lausanne ( email )

EPFL CDM MTEI RAO
Station 5
Lausanne, Vaud CH-1015
Switzerland

HOME PAGE: http://rao.epfl.ch

Wolfram Wiesemann

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

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