Bayesian Calibrated Click-Through Auctions

Authors Junjie Chen, Minming Li, Haifeng Xu, Song Zuo



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Author Details

Junjie Chen
  • City University of Hong Kong, Hong Kong, China
Minming Li
  • City University of Hong Kong, Hong Kong, China
Haifeng Xu
  • University of Chicago, IL, USA
Song Zuo
  • Google Research, New York, NY, USA

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Junjie Chen, Minming Li, Haifeng Xu, and Song Zuo. Bayesian Calibrated Click-Through Auctions. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.44

Abstract

We study information design in click-through auctions, in which the bidders/advertisers bid for winning an opportunity to show their ads but only pay for realized clicks. The payment may or may not happen, and its probability is called the click-through rate (CTR). This auction format is widely used in the industry of online advertising. Bidders have private values, whereas the seller has private information about each bidder’s CTRs. We are interested in the seller’s problem of partially revealing CTR information to maximize revenue. Information design in click-through auctions turns out to be intriguingly different from almost all previous studies in this space since any revealed information about CTRs will never affect bidders' bidding behaviors - they will always bid their true value per click - but only affect the auction’s allocation and payment rule. In some sense, this makes information design effectively a constrained mechanism design problem. Our first result is an FPTAS to compute an approximately optimal mechanism under a constant number of bidders. The design of this algorithm leverages Bayesian bidder values which help to "smooth" the seller’s revenue function and lead to better tractability. The design of this FPTAS is complex and primarily algorithmic. Our second main result pursues the design of "simple" mechanisms that are approximately optimal yet more practical. We primarily focus on the two-bidder situation, which is already notoriously challenging as demonstrated in recent works. When bidders' CTR distribution is symmetric, we develop a simple prior-free signaling scheme, whose construction relies on a parameter termed optimal signal ratio. The constructed scheme provably obtains a good approximation as long as the maximum and minimum of bidders' value density functions do not differ much.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
Keywords
  • information design
  • ad auctions
  • online advertising
  • mechanism design

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References

  1. Itai Arieli and Yakov Babichenko. Private bayesian persuasion. Journal of Economic Theory, 182:185-217, 2019. Google Scholar
  2. Moshe Babaioff, Robert Kleinberg, and Renato Paes Leme. Optimal mechanisms for selling information. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC 2012), pages 92-109, 2012. Google Scholar
  3. Yakov Babichenko and Siddharth Barman. Algorithmic aspects of private bayesian persuasion. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. Google Scholar
  4. Yakov Babichenko, Inbal Talgam-Cohen, Haifeng Xu, and Konstantin Zabarnyi. Multi-channel bayesian persuasion. In Proceedings of 13th Innovations in Theoretical Computer Science Conference (ITCS 2022), volume 215, page 11. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  5. Ashwinkumar Badanidiyuru, Kshipra Bhawalkar, and Haifeng Xu. Targeting and signaling in ad auctions. In Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018), pages 2545-2563, 2018. Google Scholar
  6. Santiago Balseiro, Yuan Deng, Jieming Mao, Vahab Mirrokni, and Song Zuo. Robust auction design in the auto-bidding world. Advances in Neural Information Processing Systems, 34:17777-17788, 2021. Google Scholar
  7. Santiago R Balseiro, Yuan Deng, Jieming Mao, Vahab S Mirrokni, and Song Zuo. The landscape of auto-bidding auctions: Value versus utility maximization. In Proceedings of the 22nd ACM Conference on Economics and Computation, pages 132-133, 2021. Google Scholar
  8. Santiago R Balseiro and Yonatan Gur. Learning in repeated auctions with budgets: Regret minimization and equilibrium. Management Science, 65(9):3952-3968, 2019. Google Scholar
  9. Dirk Bergemann, Alessandro Bonatti, and Alex Smolin. The design and price of information. American economic review, 108(1):1-48, 2018. Google Scholar
  10. Dirk Bergemann, Yang Cai, Grigoris Velegkas, and Mingfei Zhao. Is selling complete information (approximately) optimal? In Proceedings of the 23rd ACM Conference on Economics and Computation, (EC 2022), 2022. Google Scholar
  11. Dirk Bergemann, Paul Dütting, Renato Paes Leme, and Song Zuo. Calibrated click-through auctions. In Proceedings of the ACM Web Conference 2022, pages 47-57, 2022. Google Scholar
  12. Dirk Bergemann, Tibor Heumann, Stephen Morris, Constantine Sorokin, and Eyal Winter. Optimal information disclosure in auctions. American Economic Review: Insights (forthcoming), 2022. Google Scholar
  13. Umang Bhaskar, Yu Cheng, Young Kun Ko, and Chaitanya Swamy. Hardness results for signaling in bayesian zero-sum and network routing games. In Proceedings of the 2016 ACM Conference on Economics and Computation, pages 479-496, 2016. Google Scholar
  14. Peter Bro Miltersen and Or Sheffet. Send mixed signals: earn more, work less. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC 2012), pages 234-247, 2012. Google Scholar
  15. Yang Cai and Grigoris Velegkas. How to sell information optimally: An algorithmic study. In Proceedings of the 12th Innovations in Theoretical Computer Science Conference (ITCS 2021), volume 185, 2021. Google Scholar
  16. Shuchi Chawla, Jason D Hartline, and Robert Kleinberg. Algorithmic pricing via virtual valuations. In Proceedings of the 8th ACM Conference on Electronic Commerce, pages 243-251, 2007. Google Scholar
  17. Yiling Chen, Haifeng Xu, and Shuran Zheng. Selling information through consulting. In Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), pages 2412-2431. SIAM, 2020. Google Scholar
  18. Yu Cheng, Ho Yee Cheung, Shaddin Dughmi, Ehsan Emamjomeh-Zadeh, Li Han, and Shang-Hua Teng. Mixture selection, mechanism design, and signaling. In 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS 2015), pages 1426-1445. IEEE, 2015. Google Scholar
  19. Constantinos Daskalakis, Christos Papadimitriou, and Christos Tzamos. Does information revelation improve revenue? In Proceedings of the 17th ACM Conference on Economics and Computation (EC 2016), pages 233-250, 2016. Google Scholar
  20. Yuan Deng, Negin Golrezaei, Patrick Jaillet, Jason Cheuk Nam Liang, and Vahab Mirrokni. Fairness in the autobidding world with machine-learned advice. arXiv preprint, 2022. URL: https://arxiv.org/abs/2209.04748.
  21. Nikhil R Devanur, Bach Q Ha, and Jason D Hartline. Prior-free auctions for budgeted agents. In Proceedings of the fourteenth ACM conference on Electronic commerce, pages 287-304, 2013. Google Scholar
  22. Shaddin Dughmi. On the hardness of signaling. In 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, pages 354-363. IEEE, 2014. Google Scholar
  23. Shaddin Dughmi. Algorithmic information structure design: a survey. ACM SIGecom Exchanges, 15(2):2-24, 2017. Google Scholar
  24. Shaddin Dughmi and Haifeng Xu. Algorithmic persuasion with no externalities. In Proceedings of the 18th ACM Conference on Economics and Computation (EC 2017), pages 351-368, 2017. Google Scholar
  25. Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz. Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords. American economic review, 97(1):242-259, 2007. Google Scholar
  26. Yuval Emek, Michal Feldman, Iftah Gamzu, Renato PaesLeme, and Moshe Tennenholtz. Signaling schemes for revenue maximization. ACM Transactions on Economics and Computation (TEAC), 2(2):1-19, 2014. Google Scholar
  27. Seyf Emen. A beginners guide to generalized second-price auctions, 2022. URL: https://www.topsort.com/post/generalized-second-price-auctions-how#:~:text=The%20second%2Dprice%20auction%20is,bid%20to%20win%20the%20auction.
  28. Yiding Feng, Brendan Lucier, and Aleksandrs Slivkins. Strategic budget selection in a competitive autobidding world. arXiv preprint, 2023. URL: https://arxiv.org/abs/2307.07374.
  29. Dean P Foster and Rakesh V Vohra. Calibrated learning and correlated equilibrium. Games and Economic Behavior, 21(1-2):40, 1997. Google Scholar
  30. Hu Fu, Patrick Jordan, Mohammad Mahdian, Uri Nadav, Inbal Talgam-Cohen, and Sergei Vassilvitskii. Ad auctions with data. In International Symposium on Algorithmic Game Theory (SAGT 2012), pages 168-179. Springer, 2012. Google Scholar
  31. Ronen Gradwohl, Niklas Hahn, Martin Hoefer, and Rann Smorodinsky. Algorithms for persuasion with limited communication. In Proceedings of the 32nd ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), pages 637-652, 2021. Google Scholar
  32. Jason D Hartline and Tim Roughgarden. Simple versus optimal mechanisms. In Proceedings of the 10th ACM conference on Electronic commerce (EC 2009), pages 225-234, 2009. Google Scholar
  33. Emir Kamenica. Bayesian persuasion and information design. Annual Review of Economics, 11:249-272, 2019. Google Scholar
  34. Emir Kamenica and Matthew Gentzkow. Bayesian persuasion. American Economic Review, 101(6):2590-2615, 2011. Google Scholar
  35. Yoav Kolumbus and Noam Nisan. Auctions between regret-minimizing agents. In Proceedings of the ACM Web Conference 2022, pages 100-111, 2022. Google Scholar
  36. Yoav Kolumbus and Noam Nisan. How and why to manipulate your own agent: On the incentives of users of learning agents. Advances in Neural Information Processing Systems, 35:28080-28094, 2022. Google Scholar
  37. Yingkai Li. Selling data to an agent with endogenous information. In Proceedings of the 23rd ACM Conference on Economics and Computation (EC 2022), 2022. Google Scholar
  38. Zhuoshu Li and Sanmay Das. Revenue enhancement via asymmetric signaling in interdependent-value auctions. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 2093-2100, 2019. Google Scholar
  39. Shuze Liu, Weiran Shen, and Haifeng Xu. Optimal pricing of information. In Proceedings of the 22nd ACM Conference on Economics and Computation (EC 2021), pages 693-693, 2021. Google Scholar
  40. Aranyak Mehta and Andres Perlroth. Auctions without commitment in the auto-bidding world. arXiv preprint, 2023. URL: https://arxiv.org/abs/2301.07312.
  41. Roger B Myerson. Optimal auction design. Mathematics of operations research, 6(1):58-73, 1981. Google Scholar
  42. Michael Ostrovsky and Michael Schwarz. Reserve prices in internet advertising auctions: A field experiment. In Proceedings of the 12th ACM conference on Electronic commerce, pages 59-60, 2011. Google Scholar
  43. Renato Paes Leme, Martin Pal, and Sergei Vassilvitskii. A field guide to personalized reserve prices. In Proceedings of the 25th international conference on world wide web, pages 1093-1102, 2016. Google Scholar
  44. Hal R Varian. Position auctions. international Journal of industrial Organization, 25(6):1163-1178, 2007. Google Scholar
  45. Haifeng Xu. On the tractability of public persuasion with no externalities. In Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), pages 2708-2727. SIAM, 2020. Google Scholar
  46. Shuran Zheng and Yiling Chen. Optimal advertising for information products. In Proceedings of the 22nd ACM Conference on Economics and Computation (EC 2021), pages 888-906, 2021. Google Scholar