Distributionally Robust Auction Design
Çağıl Koçyiğit
Risk Analytics and Optimization at École Polytechnique Fédérale de Lausanne (EPFL)
Dec 20, 1:40 p.m.
EA-409
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.
Çağıl Koçyiğit is a PhD candidate in Risk Analytics and Optimization at École Polytechnique Fédérale de Lausanne (EPFL), working with Daniel Kuhn. Her research revolves around optimization under uncertainty and the application of optimization in economics with a special focus on mechanism design and pricing. Before joining EPFL, she received a B.Sc. and an M.Sc. in Industrial Engineering from Bilkent University, where her senior design project won the INFORMS Undergraduate Operations Research Prize 2013.
