Efficiency of Non-Truthful Auctions in Auto-bidding with Budget Constraints
Pages 223 - 234
Abstract
We study the efficiency of non-truthful auctions for auto-bidders with both return on spend (ROS) and budget constraints. The efficiency of a mechanism is measured by the price of anarchy (PoA), which is the worst case ratio between the liquid welfare of any equilibrium and the optimal (possibly randomized) allocation. Our first main result is that the first-price auction (FPA) is optimal, among deterministic mechanisms, in this setting. Without any assumptions, the PoA of FPA is n which we prove is tight for any deterministic mechanism. However, under a mild assumption that a bidder's value for any query does not exceed their total budget, we show that the PoA is at most 2. This bound is also tight as it matches the optimal PoA without a budget constraint. We next analyze two randomized mechanisms: randomized FPA (rFPA) and "quasi-proportional'' FPA. We prove two results that highlight the efficacy of randomization in this setting. First, we show that the PoA of rFPA for two bidders is at most 1.8 without requiring any assumptions. This extends prior work which focused only on an ROS constraint. Second, we show that quasi-proportional FPA has a PoA of 2 for any number of bidders, without any assumptions. Both of these bypass lower bounds in the deterministic setting. Finally, we study the setting where bidders are assumed to bid uniformly. We show that uniform bidding can be detrimental for efficiency in deterministic mechanisms while being beneficial for randomized mechanisms, which is in stark contrast with the settings without budget constraints.
Supplemental Material
MP4 File
video presentation
- Download
- 975.34 MB
MP4 File
Supplemental video
- Download
- 27.55 MB
References
[1]
Gagan Aggarwal, Ashwinkumar Badanidiyuru, and Aranyak Mehta. 2019. Autobidding with constraints. In International Conference on Web and Internet Economics. Springer, 17--30.
[2]
Gagan Aggarwal, Andres Perlroth, and Junyao Zhao. 2023. Multi-Channel Auction Design in the Autobidding World. In Proceedings of the 24th ACM Conference on Economics and Computation.
[3]
Yeganeh Alimohammadi, Aranyak Mehta, and Andres Perlroth. 2023. Incentive Compatibility in the Auto-bidding World. arXiv preprint arXiv:2301.13414 (2023).
[4]
Yossi Azar, Michal Feldman, Nick Gravin, and Alan Roytman. 2017. Liquid price of anarchy. In International Symposium on Algorithmic Game Theory. Springer, 3--15.
[5]
Santiago Balseiro, Yuan Deng, Jieming Mao, Vahab Mirrokni, and Song Zuo. 2021a. Robust auction design in the auto-bidding world. Advances in Neural Information Processing Systems, Vol. 34 (2021), 17777--17788.
[6]
Santiago Balseiro, Yuan Deng, Jieming Mao, Vahab Mirrokni, and Song Zuo. 2022. Optimal mechanisms for value maximizers with budget constraints via target clipping. Available at SSRN (2022).
[7]
Santiago Balseiro, Christian Kroer, and Rachitesh Kumar. 2023. Contextual standard auctions with budgets: Revenue equivalence and efficiency guarantees. Management Science (2023).
[8]
Santiago R Balseiro, Yuan Deng, Jieming Mao, Vahab S Mirrokni, and Song Zuo. 2021b. The landscape of auto-bidding auctions: Value versus utility maximization. In Proceedings of the 22nd ACM Conference on Economics and Computation. 132--133.
[9]
Ioannis Caragiannis and Alexandros A Voudouris. 2018. The efficiency of resource allocation mechanisms for budget-constrained users. In Proceedings of the 2018 ACM Conference on Economics and Computation. 681--698.
[10]
Matteo Castiglioni, Andrea Celli, and Christian Kroer. 2023. Online Bidding in Repeated Non-Truthful Auctions under Budget and ROI Constraints. arXiv preprint arXiv:2302.01203 (2023).
[11]
Vincent Conitzer, Christian Kroer, Debmalya Panigrahi, Okke Schrijvers, Nicolas E Stier-Moses, Eric Sodomka, and Christopher A Wilkens. 2022. Pacing equilibrium in first price auction markets. Management Science, Vol. 68, 12 (2022), 8515--8535.
[12]
Yuan Deng, Negin Golrezaei, Patrick Jaillet, Jason Cheuk Nam Liang, and Vahab Mirrokni. 2022a. Fairness in the autobidding world with machine-learned advice. arXiv preprint arXiv:2209.04748 (2022).
[13]
Yuan Deng, Negin Golrezaei, Patrick Jaillet, Jason Cheuk Nam Liang, and Vahab Mirrokni. 2023 a. Multi-channel Autobidding with Budget and ROI Constraints. In Proceedings of the 40th International Conference on Machine Learning.
[14]
Yuan Deng, Jieming Mao, Vahab Mirrokni, Hanrui Zhang, and Song Zuo. 2022b. Efficiency of the first-price auction in the autobidding world. arXiv preprint arXiv:2208.10650 (2022).
[15]
Yuan Deng, Jieming Mao, Vahab Mirrokni, Hanrui Zhang, and Song Zuo. 2023 b. Autobidding Auctions in the Presence of User Costs. In Proceedings of the ACM Web Conference 2023. 3428--3435.
[16]
Yuan Deng, Jieming Mao, Vahab Mirrokni, and Song Zuo. 2021. Towards efficient auctions in an auto-bidding world. In Proceedings of the Web Conference 2021. 3965--3973.
[17]
Yuan Deng, Vahab Mirrokni, and Hanrui Zhang. 2022c. Posted Pricing and Dynamic Prior-independent Mechanisms with Value Maximizers. Advances in Neural Information Processing Systems, Vol. 35 (2022), 24158--24169.
[18]
Yuan Deng and Hanrui Zhang. 2021. Prior-independent dynamic auctions for a value-maximizing buyer. Advances in Neural Information Processing Systems, Vol. 34 (2021), 13847--13858.
[19]
Shahar Dobzinski and Renato Paes Leme. 2014. Efficiency guarantees in auctions with budgets. In Automata, Languages, and Programming: 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8--11, 2014, Proceedings, Part I 41. Springer, 392--404.
[20]
Zhe Feng, Swati Padmanabhan, and Di Wang. 2023. Online Bidding Algorithms for Return-on-Spend Constrained Advertisers. In Proceedings of the ACM Web Conference 2023. 3550--3560.
[21]
Giannis Fikioris and Éva Tardos. 2023. Liquid welfare guarantees for no-regret learning in sequential budgeted auctions. In Proceedings of the 24th ACM Conference on Economics and Computation. 678--698.
[22]
Jason Gaitonde, Yingkai Li, Bar Light, Brendan Lucier, and Aleksandrs Slivkins. 2022. Budget pacing in repeated auctions: Regret and efficiency without convergence. arXiv preprint arXiv:2205.08674 (2022).
[23]
Negin Golrezaei, Ilan Lobel, and Renato Paes Leme. 2021. Auction design for roi-constrained buyers. In Proceedings of the Web Conference 2021. 3941--3952.
[24]
Christopher Liaw, Aranyak Mehta, and Andres Perlroth. 2023. Efficiency of non-truthful auctions under auto-bidding. In Proceedings of the ACM Web Conference 2023. 3561--3571.
[25]
Brendan Lucier, Sarath Pattathil, Aleksandrs Slivkins, and Mengxiao Zhang. 2023. Autobidders with Budget and ROI Constraints: Efficiency, Regret, and Pacing Dynamics. arXiv preprint arXiv:2301.13306 (2023).
[26]
Aranyak Mehta. 2022. Auction design in an auto-bidding setting: Randomization improves efficiency beyond VCG. In Proceedings of the ACM Web Conference 2022. 173--181.
[27]
Vahab Mirrokni, S Muthukrishnan, and Uri Nadav. 2010. Quasi-proportional mechanisms: Prior-free revenue maximization. In Latin American Symposium on Theoretical Informatics. Springer, 565--576.
[28]
Bonan Ni, Xun Wang, Qi Zhang, Pingzhong Tang, Zhourong Chen, Tianjiu Yin, Liangni Lu, Xiaobing Liu, Kewu Sun, and Zhe Ma. 2023. Ad Auction Design with Coupon-Dependent Conversion Rate in the Auto-bidding World. In Proceedings of the ACM Web Conference 2023. 3417--3427.
[29]
Andres Perlroth and Aranyak Mehta. 2023. Auctions without commitment in the auto-bidding world. In Proceedings of the ACM Web Conference 2023. 3478--3488. io
Index Terms
- Efficiency of Non-Truthful Auctions in Auto-bidding with Budget Constraints
Recommendations
Efficiency of Non-Truthful Auctions in Auto-bidding: The Power of Randomization
WWW '23: Proceedings of the ACM Web Conference 2023Auto-bidding is now widely adopted as an interface between advertisers and internet advertising as it allows advertisers to specify high-level goals, such as maximizing value subject to a value-per-spend constraint. Prior research has mainly focused on ...
Auctions without commitment in the auto-bidding world
WWW '23: Proceedings of the ACM Web Conference 2023Advertisers in online ad auctions are increasingly using auto-bidding mechanisms to bid into auctions instead of directly bidding their value manually. One of the prominent auto-bidding formats is that of target cost-per-acquisition (tCPA) which ...
Simple Auctions with Simple Strategies
EC '15: Proceedings of the Sixteenth ACM Conference on Economics and ComputationWe introduce single-bid auctions as a new format for combinatorial auctions. In single-bid auctions, each bidder submits a single real-valued bid for the right to buy items at a fixed price. Contrary to other simple auction formats, such as simultaneous ...
Comments
Information & Contributors
Information
Published In
May 2024
4826 pages
ISBN:9798400701719
DOI:10.1145/3589334
- General Chairs:
- Tat-Seng Chua,
- Chong-Wah Ngo,
- Proceedings Chair:
- Roy Ka-Wei Lee,
- Program Chairs:
- Ravi Kumar,
- Hady W. Lauw
Copyright © 2024 Owner/Author.
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 13 May 2024
Check for updates
Author Tags
Qualifiers
- Research-article
Conference
WWW '24
Sponsor:
Acceptance Rates
Overall Acceptance Rate 1,899 of 8,196 submissions, 23%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 213Total Downloads
- Downloads (Last 12 months)213
- Downloads (Last 6 weeks)54
Reflects downloads up to 22 Dec 2024
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in