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Distributionally robust mechanism design

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Title: Distributionally robust mechanism design
Authors: Koçyiğit, Ç
Iyengar, G
Kuhn, D
Wiesemann, W
Item Type: Working Paper
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.
Issue Date: 22-Jul-2018
URI: http://hdl.handle.net/10044/1/65427
DOI: https://dx.doi.org/10.2139/ssrn.2956273
Publisher: SSRN
Copyright Statement: © 2018 The Author(s).
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/M028240/1
Keywords: 08 Information And Computing Sciences
15 Commerce, Management, Tourism And Services
Operations Research
Publication Status: Published
Appears in Collections:Imperial College Business School