{"type":"ScholarlyArticle","title":"Public Signaling in Bayesian Ad Auctions","authors":[{"name":"Francesco Bacchiocchi","slug":"francesco-bacchiocchi","given":"Francesco","family":"Bacchiocchi","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"},{"name":"Matteo Castiglioni","slug":"matteo-castiglioni","given":"Matteo","family":"Castiglioni","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"},{"name":"Alberto Marchesi","slug":"alberto-marchesi","given":"Alberto","family":"Marchesi","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"},{"name":"Giulia Romano","slug":"giulia-romano","given":"Giulia","family":"Romano","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"},{"name":"Nicola Gatti","slug":"nicola-gatti","given":"Nicola","family":"Gatti","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"}],"abstract":"We study signaling in Bayesian ad auctions, in which bidders' valuations depend on a random, unknown state of nature. The auction mechanism has complete knowledge of the actual state of nature, and it can send signals to bidders so as to disclose information about the state and increase revenue. For instance, a state may collectively encode some features of the user that are known to the mechanism only, since the latter has access to data sources unaccessible to the bidders. We study the problem of computing how the mechanism should send signals to bidders in order to maximize revenue. While this problem has already been addressed in the easier setting of second-price auctions, to the best of our knowledge, our work is the first to explore ad auctions with more than one slot. In this paper, we focus on public signaling and VCG mechanisms, under which bidders truthfully report their valuations. We start with a negative result, showing that, in general, the problem does not admit a PTAS unless P = NP, even when bidders' valuations are known to the mechanism. The rest of the paper is devoted to settings in which such negative result can be circumvented. First, we prove that, with known valuations, the problem can indeed be solved in polynomial time when either the number of states d or the number of slots m is fixed. Moreover, in the same setting, we provide an FPTAS for the case in which bidders are single minded, but d and m can be arbitrary. Then, we switch to the random valuations setting, in which these are randomly drawn according to some probability distribution. In this case, we show that the problem admits an FPTAS, a PTAS, and a QPTAS, when, respectively, d is fixed, m is fixed, and bidders' valuations are bounded away from zero.","doi":"10.24963/ijcai.2022/6","url":"https://ijcai.org/proceedings/2022/6","pdf":"https://ijcai.org/proceedings/2022/0006.pdf","markdown":"https://ijcai.org/proceedings/2022/6.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/6","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":6,"pages":{"first":39,"last":45},"keywords":["Agent-based and Multi-agent Systems: Mechanism Design","Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986919","length_sec":60,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985062","length_sec":188,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Alimonti and Kann, 2000] Paola Alimonti and Viggo Kann. Some APX-completeness results for cubic graphs. Theo- retical Computer Science, 237:123-134, 04 2000.","title":"Paola Alimonti and Viggo Kann. Some APX-completeness results for cubic graphs","authors":"Kann Alimonti","year":"2000","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Alonso and Câmara, 2016] Ricardo Alonso and Odilon Câmara. Persuading voters. American Economic Review, 106(11):3590-3605, 2016.","title":"Persuading voters","authors":"Ricardo Alonso, Odilon Câmara","year":"2016","venue":"American Economic Review","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Babichenko and Barman, 2017] Yakov Babichenko and Siddharth Barman. Algorithmic aspects of private Bayesian persuasion. In ITCS, 2017.","title":"Algorithmic aspects of private Bayesian persuasion","authors":"Barman Babichenko","year":"2017","venue":"ITCS","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Babichenko et al., 2021] Yakov Babichenko, Inbal Talgam- Cohen, Haifeng Xu, and Konstantin Zabarnyi. Regret- minimizing bayesian persuasion. In EC, page 128, 2021.","title":"Regretminimizing bayesian persuasion","authors":"Yakov Babichenko, Inbal Talgam-Cohen, Haifeng Xu, Konstantin Zabarnyi","year":"2021","venue":"EC","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bacchiocchi et al., 2022] Francesco Bacchiocchi, Matteo Castiglioni, Alberto Marchesi, Giulia Romano, and Nicola Gatti. Public signaling in bayesian ad auctions. CoRR, abs/2201.09728, 2022.","title":"Public signaling in bayesian ad auctions","authors":"Francesco Bacchiocchi, Matteo Castiglioni, Alberto Marchesi, Giulia Romano, Nicola Gatti","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Badanidiyuru et al., 2018] Ashwinkumar Badanidiyuru, Kshipra Bhawalkar, and Haifeng Xu. Targeting and signaling in ad auctions. In SODA, pages 2545-2563, 2018.","title":"Ashwinkumar Badanidiyuru, Kshipra Bhawalkar, and Haifeng Xu. Targeting and signaling in ad auctions","authors":"Badanidiyuru","year":"2018","venue":"SODA","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bhaskar et al., 2016] Umang Bhaskar, Yu Cheng, Young Kun Ko, and Chaitanya Swamy. Hardness results for signaling in bayesian zero-sum and network routing games. In EC, pages 479-496, 2016.","title":"Hardness results for signaling in bayesian zero-sum and network routing games","authors":"Umang Bhaskar, Yu Cheng, Young Kun Ko, Chaitanya Swamy","year":"2016","venue":"EC","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bro Miltersen and Sheffet, 2012] Peter Bro Miltersen and Or Sheffet. Send mixed signals: earn more, work less. In EC, pages 234-247, 2012.","title":"Peter Bro Miltersen and Or Sheffet. Send mixed signals: earn more, work less","authors":"Bro Miltersen, Sheffet","year":"2012","venue":"EC","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Candogan, 2019] Ozan Candogan. Persuasion in networks: Public signals and k-cores. In EC, pages 133-134, 2019.","title":"Persuasion in networks: Public signals and k-cores","authors":"Ozan Candogan","year":"2019","venue":"EC","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Castiglioni and Gatti, 2021] Matteo Castiglioni and Nicola Gatti. Persuading voters in district-based elections. In AAAI, pages 5244-5251, 2021.","title":"Persuading voters in district-based elections","authors":"Matteo Castiglioni, Nicola Gatti","year":"2021","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Castiglioni et al., 2020a] Matteo Castiglioni, Andrea Celli, and Nicola Gatti. Persuading voters: It's easy to whisper, it's hard to speak loud. In AAAI, pages 1870-1877, 2020.","title":"Persuading voters: It's easy to whisper, it's hard to speak loud","authors":"Castiglioni","year":"2020","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Castiglioni et al., 2020b] Matteo Castiglioni, Andrea Celli, and Nicola Gatti. Public bayesian persuasion: Be- ing almost optimal and almost persuasive. CoRR, abs/2002.05156, 2020.","title":"Public bayesian persuasion: Being almost optimal and almost persuasive","authors":"Castiglioni","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Castiglioni et al., 2020c] Matteo Castiglioni, Andrea Celli, Alberto Marchesi, and Nicola Gatti. Online Bayesian per- suasion. In NeurIPS, pages 16188-16198, 2020.","title":"Online Bayesian persuasion","authors":"Castiglioni","year":"2020","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Castiglioni et al., 2021a] Matteo Castiglioni, Andrea Celli, Alberto Marchesi, and Nicola Gatti. Signaling in Bayesian network congestion games: the subtle power of symmetry. In AAAI, pages 5252-5259, 2021.","title":"Signaling in Bayesian network congestion games: the subtle power of symmetry","authors":"Castiglioni","year":"2021","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Castiglioni et al., 2021b] Matteo Castiglioni, Alberto Marchesi, Andrea Celli, and Nicola Gatti. Multi-receiver online Bayesian persuasion. In ICML, pages 1314-1323, 2021.","title":"Multi-receiver online Bayesian persuasion","authors":"Castiglioni","year":"2021","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Castiglioni et al., 2022a] Matteo Castiglioni, Alberto Marchesi, and Nicola Gatti. Bayesian persuasion meets mechanism design: Going beyond intractability with type reporting. In AAMAS, 2022.","title":"Bayesian persuasion meets mechanism design: Going beyond intractability with type reporting","authors":"Castiglioni","year":"2022","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Castiglioni et al., 2022b] Matteo Castiglioni, Giulia Ro- mano, Alberto Marchesi, and Nicola Gatti. Signaling in posted price auctions. In AAAI, 2022.","title":"Signaling in posted price auctions","authors":"Castiglioni","year":"2022","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Cheng et al., 2015] Yu Cheng, Ho Yee Cheung, Shaddin Dughmi, Ehsan Emamjomeh-Zadeh, Li Han, and Shang- Hua Teng. Mixture selection, mechanism design, and sig- naling. In FOCS, pages 1426-1445, 2015.","title":"Mixture selection, mechanism design, and signaling","authors":"Yu Cheng, Yee Ho, Shaddin Cheung, Ehsan Dughmi, Li Emamjomeh-Zadeh, Shang-Hua Han, Teng","year":"2015","venue":"FOCS","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Daskalakis et al., 2016] Constantinos Daskalakis, Chris- tos H. Papadimitriou, and Christos Tzamos. Does informa- tion revelation improve revenue? In EC, pages 233-250, 2016.","title":"Does information revelation improve revenue?","authors":"Constantinos Daskalakis, Christos H Papadimitriou, Christos Tzamos","year":"2016","venue":"EC","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Dughmi, 2014] Shaddin Dughmi. On the hardness of sig- naling. In FOCS, pages 354-363. IEEE, 2014.","title":"Shaddin Dughmi. On the hardness of signaling","authors":"Dughmi","year":"2014","venue":"FOCS","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[eMarketer, 2021] eMarketer. Worldwide digital ad spend- ing year-end update. https://www.emarketer.com/content/ worldwide-digital-ad-spending-year-end-update, 2021. Accessed: 2022-01-09.","title":"eMarketer. Worldwide digital ad spending year-end update","authors":null,"year":"2021","venue":null,"doi":null,"url":"https://www.emarketer.com/content/worldwide-digital-ad-spending-year-end-update","internal_url":null},{"position":22,"raw":"[Emek et al., 2014] Yuval Emek, Michal Feldman, Iftah Gamzu, Renato PaesLeme, and Moshe Tennenholtz. Sig- naling schemes for revenue maximization. TEAC, 2(2):1- 19, 2014.","title":"Signaling schemes for revenue maximization","authors":"Yuval Emek, Michal Feldman, Iftah Gamzu, Renato Paesleme, Moshe Tennenholtz","year":"2014","venue":"TEAC","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Fu et al., 2012] Hu Fu, Patrick R. Jordan, Mohammad Mah- dian, Uri Nadav, Inbal Talgam-Cohen, and Sergei Vassil- vitskii. Ad auctions with data. In SAGT, pages 168-179, 2012.","title":"Ad auctions with data","authors":"Hu Fu, Patrick R Jordan, Mohammad Mahdian, Uri Nadav, Inbal Talgam-Cohen, Sergei Vassilvitskii","year":"2012","venue":"SAGT","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Kamenica and Gentzkow, 2011] Emir Kamenica and Matthew Gentzkow. Bayesian persuasion. American Economic Review, 101(6):2590-2615, 2011.","title":"Emir Kamenica and Matthew Gentzkow","authors":"Gentzkow Kamenica","year":"2011","venue":"American Economic Review","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Li and Das, 2019] Zhuoshu Li and Sanmay Das. Revenue enhancement via asymmetric signaling in interdependent- value auctions. In AAAI, pages 2093-2100, 2019.","title":"Zhuoshu Li and Sanmay Das. Revenue enhancement via asymmetric signaling in interdependentvalue auctions","authors":"Das Li","year":"2019","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Mansour et al., 2016] Yishay Mansour, Aleksandrs Slivkins, Vasilis Syrgkanis, and Zhiwei Steven Wu. Bayesian exploration: Incentivizing exploration in Bayesian games. In EC, pages 661-661, 2016.","title":"Bayesian exploration: Incentivizing exploration in Bayesian games","authors":"Yishay Mansour, Aleksandrs Slivkins, Vasilis Syrgkanis, Zhiwei Steven Wu","year":"2016","venue":"EC","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Nisan and Ronen, 2001] Noam Nisan and Amir Ronen. Al- gorithmic mechanism design. Games and Economic be- havior, 35(1-2):166-196, 2001.","title":"Noam Nisan and Amir Ronen. Algorithmic mechanism design","authors":"Ronen Nisan","year":"2001","venue":"Games and Economic behavior","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Rabinovich et al., 2015] Zinovi Rabinovich, Albert Xin Jiang, Manish Jain, and Haifeng Xu. Information disclo- sure as a means to security. In AAMAS, pages 645-653, 2015.","title":"Information disclosure as a means to security","authors":"Rabinovich","year":"2015","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Vasserman et al., 2015] Shoshana Vasserman, Michal Feld- man, and Avinatan Hassidim. Implementing the wisdom of waze. In IJCAI, pages 660-666, 2015.","title":"Implementing the wisdom of waze","authors":"Shoshana Vasserman, Michal Feldman, Avinatan Hassidim","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/99"},{"position":30,"raw":"[Xu et al., 2016] Haifeng Xu, Rupert Freeman, Vincent Conitzer, Shaddin Dughmi, and Milind Tambe. Signaling in Bayesian Stackelberg games. In AAMAS, pages 150- 158, 2016.","title":"Signaling in Bayesian Stackelberg games","authors":"Haifeng Xu, Rupert Freeman, Vincent Conitzer, Shaddin Dughmi, Milind Tambe","year":"2016","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Zu et al., 2021] You Zu, Krishnamurthy Iyer, and Haifeng Xu. Learning to persuade on the fly: Robustness against ignorance. In EC, pages 927-928, 2021.","title":"Learning to persuade on the fly: Robustness against ignorance","authors":"Zu","year":"2021","venue":"EC","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}