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research article

Distributionally Robust Mechanism Design

Kocyigit, Cagil  
•
Iyengar, Garud
•
Kuhn, Daniel  
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2020
Management Science

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 rectangle, we show that the optimal mechanism is a second price auction that is both efficient and displays a powerful Pareto dominance property. 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.

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Type
research article
DOI
10.1287/mnsc.2018.3219
Author(s)
Kocyigit, Cagil  
Iyengar, Garud
Kuhn, Daniel  
Wiesemann, Wolfram
Date Issued

2020

Published in
Management Science
Volume

66

Issue

1

Start page

159

End page

189

Subjects

Auction

•

Mechanism design

•

Distributionally robust optimization

•

Ambiguity aversion

•

Knightian preferences

Note

Available from Optimization Online

URL

URL

http://www.optimization-online.org/DB_HTML/2017/04/5968.html
Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
RAO  
Available on Infoscience
April 20, 2017
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/136548
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