research-article

Nash Convergence of Mean-Based Learning Algorithms in First Price Auctions

Authors:

Weiqiang ZhengAuthors Info & Claims

WWW '22: Proceedings of the ACM Web Conference 2022

Pages 141 - 150

https://doi.org/10.1145/3485447.3512059

Published: 25 April 2022 Publication History

Abstract

Understanding the convergence properties of learning dynamics in repeated auctions is a timely and important question in the area of learning in auctions, with numerous applications in, e.g., online advertising markets. This work focuses on repeated first price auctions where bidders with fixed values for the item learn to bid using mean-based algorithms – a large class of online learning algorithms that include popular no-regret algorithms such as Multiplicative Weights Update and Follow the Perturbed Leader. We completely characterize the learning dynamics of mean-based algorithms, in terms of convergence to a Nash equilibrium of the auction, in two senses: (1) time-average: the fraction of rounds where bidders play a Nash equilibrium approaches 1 in the limit; (2) last-iterate: the mixed strategy profile of bidders approaches a Nash equilibrium in the limit. Specifically, the results depend on the number of bidders with the highest value: Our discovery opens up new possibilities in the study of convergence dynamics of learning algorithms.

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Cited By

Fikioris GTardos ELeyton-Brown KSamuelson LHartline J(2023)Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted AuctionsProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597772(678-698)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597772
Cai LWeinberg SWildenhain EZhang S(2023)Selling to Multiple No-Regret BuyersWeb and Internet Economics10.1007/978-3-031-48974-7_7(113-129)Online publication date: 4-Dec-2023
https://dl.acm.org/doi/10.1007/978-3-031-48974-7_7

Index Terms

Nash Convergence of Mean-Based Learning Algorithms in First Price Auctions
1. Applied computing
2. Theory of computation
  1. Design and analysis of algorithms
  2. Theory and algorithms for application domains

Index terms have been assigned to the content through auto-classification.

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Published In

cover image ACM Conferences

WWW '22: Proceedings of the ACM Web Conference 2022

April 2022

3764 pages

ISBN:9781450390965

DOI:10.1145/3485447

Editors:
Frédérique Laforest
INSA Lyon, France
,
Raphaël Troncy
EURECOM, France
,
Elena Simperl
King’s College London, UK
,
Deepak Agarwal
Pinterest, USA
,
Aristides Gionis
KTH Royal Institute of Technology, Sweden
,
Ivan Herman
W3C / retired
,
Lionel Médini
Université Lyon 1, France

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Published: 25 April 2022

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WWW '22: The ACM Web Conference 2022

April 25 - 29, 2022

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Cited By

Fikioris GTardos ELeyton-Brown KSamuelson LHartline J(2023)Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted AuctionsProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597772(678-698)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597772
Cai LWeinberg SWildenhain EZhang S(2023)Selling to Multiple No-Regret BuyersWeb and Internet Economics10.1007/978-3-031-48974-7_7(113-129)Online publication date: 4-Dec-2023
https://dl.acm.org/doi/10.1007/978-3-031-48974-7_7

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