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             Department of Systems Engineering and Engineering Management
                     The Chinese University of Hong Kong

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Date: Friday, May 14, 2021, 16:30 to 17:30

Title: Distributionally Robust Auction Design

Speaker: Professor Çağıl Koçyiğit, University of Luxembourg

Abstract:

Auctions are routinely used in economic transactions that are characterized by demand uncertainty, ranging from the sale of financial instruments (e.g., U.S. Treasury bills), antiques, collectibles and commodities (e.g., radio spectra, electricity and carbon emissions) to livestock and holidays.  We study the 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.

Biography:

Çağıl Koçyiğit is an assistant professor at the Luxembourg Centre for Logistics and Supply Chain Management, University of Luxembourg. Her research focuses on optimization under uncertainty with applications in economics and mechanism design. Prior to joining the University of Luxembourg, she received a Ph.D. in Management of Technology from École Polytechnique Fédérale de Lausanne in 2020 and has been awarded the Kilian Schindler Excellence Award for her thesis. She holds a B.Sc. degree and an M.Sc. degree in Industrial Engineering from Bilkent University.