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  1. Transactions on Economics and Computation (TEAC)
  2. ACM Transactions on Economics and Computation (TEAC) : Volume 4
  3. Issue 2, February 2016
  4. Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions
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ACM Transactions on Economics and Computation (TEAC) : Volume 5
ACM Transactions on Economics and Computation (TEAC) : Volume 4
Issue 4(Special Issue on EC'14), August 2016
Issue 3(Special Issue on EC'13), June 2016
Issue 2, February 2016
Mechanism Design with Strategic Mediators
Network Cost-Sharing without Anonymity
Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions
Price of Stability in Polynomial Congestion Games
Truthfulness and Stochastic Dominance with Monetary Transfers
Issue 1, December 2015
ACM Transactions on Economics and Computation (TEAC) : Volume 3
ACM Transactions on Economics and Computation (TEAC) : Volume 2
ACM Transactions on Economics and Computation (TEAC) : Volume 1

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Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions

Content Provider ACM Digital Library
Author Tang, Bo Kovács, Annamária Christodoulou, George Sgouritsa, Alkmini
Copyright Year 2016
Abstract We study the price of anarchy (PoA) of simultaneous first-price auctions (FPAs) for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian price of anarchy (BPoA) of these auctions are $\textit{e}/(\textit{e}$ ™ 1) [Syrgkanis and Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching lower bounds for both cases $\textit{even}$ for the case of full information and for mixed Nash equilibria via an explicit construction. We present an alternative proof of the upper bound of $\textit{e}/(\textit{e}$ ™ 1) for FPAs with fractionally subadditive valuations that reveals the worst-case price distribution, which is used as a building block for the matching lower bound construction. We generalize our results to a general class of item bidding auctions that we call bid-dependent auctions (including FPAs and all-pay auctions) where the winner is always the highest bidder and each bidder’s payment depends only on his own bid. Finally, we apply our techniques to discriminatory price multiunit auctions. We complement the results of de Keijzer et al. [2013] for the case of subadditive valuations by providing a matching lower bound of 2. For the case of submodular valuations, we provide a lower bound of 1.109. For the same class of valuations, we were able to reproduce the upper bound of $\textit{e}/(\textit{e}$ ™ 1) using our nonsmooth approach.
Starting Page 1
Ending Page 33
Page Count 33
File Format PDF
ISSN 21678375
e-ISSN 21678383
DOI 10.1145/2847520
Volume Number 4
Issue Number 2
Journal ACM Transactions on Economics and Computation (TEAC)
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2016-01-13
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Auctions Item bidding Price of anarchy
Content Type Text
Resource Type Article
Subject Economics and Econometrics Marketing Computational Mathematics Statistics and Probability Computer Science
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