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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: Journal Article
Abstract: We study a mechanism design problem where an indivisible good is auctioned to multiple bidders, for eachof whom it has a private value that is unknown to the seller and the other bidders. The agents perceive theensemble of all bidder values as a random vector governed by an ambiguous probability distribution, whichbelongs to a commonly known ambiguity set. The seller aims to design a revenue maximizing mechanism thatis not only immunized against the ambiguity of the bidder values but also against the uncertainty about thebidders’ attitude towards ambiguity. We argue that the seller achieves this goal by maximizing the worst-caseexpected revenue across all value distributions in the ambiguity set and by positing that the bidders haveKnightian preferences. For ambiguity sets containing all distributions supported on a hypercube, we showthat the Vickrey auction is the unique mechanism that is optimal, efficient and Pareto robustly optimal. Ifthe bidders’ values are additionally known to be independent, then the revenue of the (unknown) optimalmechanism does not exceed that of a second price auction with only one additional bidder. For ambiguitysets under which the bidders’ values are dependent and characterized through moment bounds, on the otherhand, we provide a new class of randomized mechanisms, the highest-bidder-lotteries, whose revenues cannotbe matched by any second price auction with a constant number of additional bidders. Moreover, we showthat the optimal highest-bidder-lottery is a 2-approximation of the (unknown) optimal mechanism, whereasthe best second price auction fails to provide any constant-factor approximation guarantee.
Issue Date: 1-Jan-2020
Date of Acceptance: 18-Sep-2018
URI: http://hdl.handle.net/10044/1/69307
DOI: 10.1287/mnsc.2018.3219
ISSN: 0025-1909
Publisher: INFORMS
Start Page: 159
End Page: 189
Journal / Book Title: Management Science
Volume: 66
Issue: 1
Copyright Statement: © 2019 INFORMS
Keywords: Social Sciences
Science & Technology
Operations Research & Management Science
Business & Economics
mechanism design
distributionally robust optimization
ambiguity aversion
Knightian preferences
Operations Research
08 Information and Computing Sciences
15 Commerce, Management, Tourism and Services
Publication Status: Published
Online Publication Date: 2019-10-24
Appears in Collections:Imperial College Business School