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On the efficiency of equilibria in generalized second price auctions

Published: 05 June 2011 Publication History

Abstract

In sponsored search auctions, advertisers compete for a number of available advertisement slots of different quality. The auctioneer decides the allocation of advertisers to slots using bids provided by them. Since the advertisers may act strategically and submit their bids in order to maximize their individual objectives, such an auction naturally defines a strategic game among the advertisers. In order to quantify the efficiency of outcomes in generalized second price auctions, we study the corresponding games and present new bounds on their price of anarchy, improving the recent results of Paes Leme and Tardos [16] and Lucier and Paes Leme [13]. For the full information setting, we prove a surprisingly low upper bound of 1.282 on the price of anarchy over pure Nash equilibria. Given the existing lower bounds, this bound denotes that the number of advertisers has almost no impact on the price of anarchy. The proof exploits the equilibrium conditions developed in [16] and follows by a detailed reasoning about the structure of equilibria and a novel relation of the price of anarchy to the objective value of a compact mathematical program. For more general equilibrium classes (i.e., mixed Nash, correlated, and coarse correlated equilibria), we present an upper bound of 2.310 on the price of anarchy. We also consider the setting where advertisers have incomplete information about their competitors and prove a price of anarchy upper bound of 3.037 over Bayes-Nash equilibria. In order to obtain the last two bounds, we adapt techniques of Lucier and Paes Leme [13] and significantly extend them with new arguments.

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      cover image ACM Conferences
      EC '11: Proceedings of the 12th ACM conference on Electronic commerce
      June 2011
      384 pages
      ISBN:9781450302616
      DOI:10.1145/1993574
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      Published: 05 June 2011

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      Author Tags

      1. auctions
      2. equilibria
      3. generalized second price
      4. price of anarchy

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      EC '11: ACM Conference on Electronic Commerce
      June 5 - 9, 2011
      California, San Jose, USA

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      • (2023)Private Data Manipulation in Sponsored Search AuctionsCAAI Artificial Intelligence Research10.26599/AIR.2023.9150024(9150024)Online publication date: Dec-2023
      • (2023)Breaking the traditional: a survey of algorithmic mechanism design applied to economic and complex environmentsNeural Computing and Applications10.1007/s00521-023-08647-135:22(16193-16222)Online publication date: 20-May-2023
      • (2022)Simple mechanisms for welfare maximization in rich advertising auctionsProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602320(28280-28292)Online publication date: 28-Nov-2022
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      • (2019)Learning Theory and Algorithms for Revenue Maximization in Sponsored Search2019 International Conference on Data Mining Workshops (ICDMW)10.1109/ICDMW.2019.00069(434-440)Online publication date: Nov-2019
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