{"type":"ScholarlyArticle","title":"Auto-bidding with Budget and ROI Constrained Buyers","authors":[{"name":"Xiaodong Liu","slug":"xiaodong-liu","given":"Xiaodong","family":"Liu","affiliation":"Gaoling School of Artificial Intelligence , Renmin University of China"},{"name":"Weiran Shen","slug":"weiran-shen","given":"Weiran","family":"Shen","affiliation":"Gaoling School of Artificial Intelligence , Renmin University of China"}],"abstract":"In online advertising markets, an increasing number of advertisers are adopting auto-bidders to buy advertising slots. This tool simplifies the process of optimizing bids based on various financial constraints.\r\n\r\nIn our study, we focus on second-price auctions where bidders have both private budget and private ROI (return on investment) constraints. We formulate the auto-bidding system design problem as a mathematical program and analyze the auto-bidders' bidding strategy under such constraints. We demonstrate that our design ensures truthfulness, i.e., among all pure and mixed strategies, always reporting the truthful budget and ROI is an optimal strategy for the bidders. Although the program is non-convex, we provide a fast algorithm to compute the optimal bidding strategy for the bidders based on our analysis. We also study the welfare and provide a lower bound for the PoA (price of anarchy). Moreover, we prove that if all bidders utilize our auto-bidding system, a Bayesian Nash equilibrium exists. We provide a sufficient condition under which the iterated best response process converges to such an equilibrium. Finally, we conduct extensive experiments to empirically evaluate the effectiveness of our design.","doi":"10.24963/ijcai.2023/314","url":"https://ijcai.org/proceedings/2023/314","pdf":"https://ijcai.org/proceedings/2023/0314.pdf","markdown":"https://ijcai.org/proceedings/2023/314.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/314","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":314,"pages":{"first":2817,"last":2825},"keywords":["Game Theory and Economic Paradigms: GTEP: Mechanism design","Game Theory and Economic Paradigms: GTEP: Auctions and market-based systems"],"videos":[],"references":[{"position":1,"raw":"[Aggarwal et al., 2006] Gagan Aggarwal, Ashish Goel, and Rajeev Motwani. Truthful auctions for pricing search key- words. In Proceedings of the 7th ACM Conference on Electronic Commerce, pages 1-7, 2006.","title":"Truthful auctions for pricing search keywords","authors":"Gagan Aggarwal, Ashish Goel, Rajeev Motwani","year":"2006","venue":"Proceedings of the 7th ACM Conference on Electronic Commerce","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Aggarwal et al., 2019] Gagan Aggarwal, Ashwinkumar Badanidiyuru, and Aranyak Mehta. Autobidding with constraints. In International Conference on Web and Internet Economics, pages 17-30. Springer, 2019.","title":"Autobidding with constraints","authors":"Gagan Aggarwal, Ashwinkumar Badanidiyuru, Aranyak Mehta","year":"2019","venue":"International Conference on Web and Internet Economics","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Balseiro and Gur, 2019] Santiago R Balseiro and Yonatan Gur. Learning in repeated auctions with budgets: Re- gret minimization and equilibrium. Management Science, 65(9):3952-3968, 2019.","title":"Learning in repeated auctions with budgets: Regret minimization and equilibrium","authors":"Gur ; Balseiro, R Santiago, Yonatan Balseiro, Gur","year":"2019","venue":"Management Science","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Balseiro et al., 2015] Santiago R Balseiro, Omar Besbes, and Gabriel Y Weintraub. Repeated auctions with budgets in ad exchanges: Approximations and design. Manage- ment Science, 61(4):864-884, 2015.","title":"Repeated auctions with budgets in ad exchanges: Approximations and design","authors":"Omar Santiago R Balseiro, Gabriel Y Besbes, Weintraub","year":"2015","venue":"Management Science","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Balseiro et al., 2017] Santiago Balseiro, Anthony Kim, Mo- hammad Mahdian, and Vahab Mirrokni. Budget manage- ment strategies in repeated auctions. In Proceedings of the 26th International Conference on World Wide Web, pages 15-23, 2017.","title":"Budget management strategies in repeated auctions","authors":"Santiago Balseiro, Anthony Kim, Mohammad Mahdian, Vahab Mirrokni","year":"2017","venue":"Proceedings of the 26th International Conference on World Wide Web","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Balseiro et al., 2021a] Santiago Balseiro, Yuan Deng, Jiem- ing Mao, Vahab Mirrokni, and Song Zuo. Robust auction design in the auto-bidding world. Advances in Neural In- formation Processing Systems, 34:17777-17788, 2021.","title":"Robust auction design in the auto-bidding world","authors":"Balseiro","year":"2021","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Balseiro et al., 2021b] Santiago R Balseiro, Yuan Deng, Jieming Mao, Vahab S Mirrokni, and Song Zuo. The land- scape of auto-bidding auctions: Value versus utility maxi- mization. In Proceedings of the 22nd ACM Conference on Economics and Computation, pages 132-133, 2021.","title":"The landscape of auto-bidding auctions: Value versus utility maximization","authors":"Balseiro","year":"2021","venue":"Proceedings of the 22nd ACM Conference on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Balseiro et al., 2022] Santiago Balseiro, Yuan Deng, Jiem- ing Mao, Vahab Mirrokni, and Song Zuo. Optimal mech- anisms for value maximizers with budget constraints via target clipping. Available at SSRN, 2022.","title":"Optimal mechanisms for value maximizers with budget constraints via target clipping","authors":"Santiago Balseiro, Yuan Deng, Jieming Mao, Vahab Mirrokni, Song Zuo","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Borgs et al., 2007] Christian Borgs, Jennifer Chayes, Nicole Immorlica, Kamal Jain, Omid Etesami, and Mohammad Mahdian. Dynamics of bid optimization in online advertisement auctions. In Proceedings of the 16th international conference on World Wide Web, pages 531-540, 2007.","title":"Dynamics of bid optimization in online advertisement auctions","authors":"Borgs","year":"2007","venue":"Proceedings of the 16th international conference on World Wide Web","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Brouwer, 1911] Luitzen Egbertus Jan Brouwer. Über ab- bildung von mannigfaltigkeiten. Mathematische annalen, 71(1):97-115, 1911.","title":"Luitzen Egbertus Jan Brouwer. Über abbildung von mannigfaltigkeiten","authors":"Brouwer","year":"1911","venue":"Mathematische annalen","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Chen et al., 2021] Xi Chen, Christian Kroer, and Rachitesh Kumar. The complexity of pacing for second-price auc- tions. arXiv preprint arXiv:2103.13969, 2021.","title":"The complexity of pacing for second-price auctions","authors":"Xi Chen, Christian Kroer, Rachitesh Kumar","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Clarke, 1971] Edward H Clarke. Multipart pricing of public goods. Public choice, pages 17-33, 1971.","title":"Multipart pricing of public goods","authors":"Clarke Edward","year":"1971","venue":"Public choice","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Conitzer et al., 2017] Vincent Conitzer, Christian Kroer, Eric Sodomka, and Nicolas E Stier-Moses. Multiplica- tive pacing equilibria in auction markets. arXiv preprint arXiv:1706.07151, 2017.","title":"Multiplicative pacing equilibria in auction markets","authors":"Vincent Conitzer, Christian Kroer, Eric Sodomka, Nicolas E Stier-Moses","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Conitzer et al., 2018] Vincent Conitzer, Christian Kroer, Debmalya Panigrahi, Okke Schrijvers, Eric Sodomka, Nicolas E Stier-Moses, and Chris Wilkens. Pacing equi- librium in first-price auction markets. arXiv preprint arXiv:1811.07166, 2018.","title":"Pacing equilibrium in first-price auction markets","authors":"Vincent Conitzer, Christian Kroer, Debmalya Panigrahi, Okke Schrijvers, Eric Sodomka, Nicolas E Stier-Moses, Chris Wilkens","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Conitzer et al., 2022] Vincent Conitzer, Christian Kroer, Eric Sodomka, and Nicolas E Stier-Moses. Multiplicative pacing equilibria in auction markets. Operations Research, 70(2):963-989, 2022.","title":"Multiplicative pacing equilibria in auction markets","authors":"Vincent Conitzer, Christian Kroer, Eric Sodomka, Nicolas E Stier-Moses","year":"2022","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Cramton et al., 2004] Peter Cramton, Yoav Shoham, Richard Steinberg, et al. Combinatorial auctions. Tech- nical report, University of Maryland, Department of Economics-Peter Cramton, 2004.","title":"Combinatorial auctions","authors":"Yoav Peter Cramton, Richard Shoham, Steinberg","year":"2004","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Deng et al., 2021] Yuan Deng, Jieming Mao, Vahab Mir- rokni, and Song Zuo. Towards efficient auctions in an auto-bidding world. In Proceedings of the Web Confer- ence 2021, pages 3965-3973, 2021.","title":"Towards efficient auctions in an auto-bidding world","authors":"Yuan Deng, Jieming Mao, Vahab Mirrokni, Song Zuo","year":"2021","venue":"Proceedings of the Web Conference 2021","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Edelman et al., 2007] Benjamin Edelman, Michael Ostro- vsky, 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.","title":"Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords","authors":"Benjamin Edelman, Michael Ostrovsky, Michael Schwarz","year":"2007","venue":"American economic review","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Golrezaei et al., 2021] Negin Golrezaei, Ilan Lobel, and Re- nato Paes Leme. Auction design for roi-constrained buy- ers. In Proceedings of the Web Conference 2021, pages 3941-3952, 2021.","title":"Auction design for roi-constrained buyers","authors":"Negin Golrezaei, Ilan Lobel, Renato Paes, Leme","year":"2021","venue":"Proceedings of the Web Conference 2021","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Groves, 1973] Theodore Groves. Incentives in teams. Econometrica: Journal of the Econometric Society, pages 617-631, 1973.","title":"Theodore Groves. Incentives in teams","authors":"Groves","year":"1973","venue":"Econometrica: Journal of the Econometric Society","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Gummadi et al., 2012] Ramakrishna Gummadi, Peter Key, and Alexandre Proutiere. Repeated auctions under budget constraints: Optimal bidding strategies and equilibria. In the Eighth Ad Auction Workshop, volume 4, 2012.","title":"Repeated auctions under budget constraints: Optimal bidding strategies and equilibria","authors":"Gummadi","year":"2012","venue":"the Eighth Ad Auction Workshop","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Liao et al., 2014] Hairen Liao, Lingxiao Peng, Zhenchuan Liu, and Xuehua Shen. ipinyou global rtb bidding algo- rithm competition dataset. In Proceedings of the Eighth International Workshop on Data Mining for Online Ad- vertising, pages 1-6, 2014.","title":"ipinyou global rtb bidding algorithm competition dataset","authors":"Liao","year":"2014","venue":"Proceedings of the Eighth International Workshop on Data Mining for Online Advertising","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Mehta, 2022] Aranyak Mehta. Auction design in an auto- bidding setting: Randomization improves efficiency be- yond vcg. In Proceedings of the ACM Web Conference 2022, pages 173-181, 2022.","title":"Auction design in an autobidding setting: Randomization improves efficiency beyond vcg","authors":"Aranyak Mehta, Mehta","year":"2022","venue":"Proceedings of the ACM Web Conference 2022","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Myerson, 1981] Roger B Myerson. Optimal auction design. Mathematics of operations research, 6(1):58-73, 1981.","title":"Optimal auction design","authors":"Roger B Myerson","year":"1981","venue":"Mathematics of operations research","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Pai and Vohra, 2014] Mallesh M Pai and Rakesh Vohra. Op- timal auctions with financially constrained buyers. Journal of Economic Theory, 150:383-425, 2014.","title":"Optimal auctions with financially constrained buyers","authors":"M Mallesh, Rakesh Pai, Vohra","year":"2014","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Shen et al., 2020] Weiran Shen, Binghui Peng, Hanpeng Liu, Michael Zhang, Ruohan Qian, Yan Hong, Zhi Guo, Zongyao Ding, Pengjun Lu, and Pingzhong Tang. Re- inforcement mechanism design: With applications to dy- namic pricing in sponsored search auctions. In Proceed- ings of the AAAI Conference on Artificial Intelligence, vol- ume 34, pages 2236-2243, 2020. [Statista, 2022] Statista. Digital ad spend worldwide 2026. https://www.statista.com/statistics/237974/ online-advertising-spending-worldwide/, 2022. Ac- cessed: 2023-05-25.","title":"Reinforcement mechanism design: With applications to dynamic pricing in sponsored search auctions","authors":"Shen","year":"2020","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":"https://www.statista.com/statistics/237974/online-advertising-spending-worldwide/,2022.Ac-cessed:2023-05-25","internal_url":null},{"position":27,"raw":"Hal R Varian. Position auctions. interna- tional Journal of industrial Organization, 25(6):1163- 1178, 2007.","title":"Position auctions","authors":"Hal R Varian","year":"2007","venue":"international Journal of industrial Organization","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Vickrey, 1961] William Vickrey. Counterspeculation, auc- tions, and competitive sealed tenders. The Journal of fi- nance, 16(1):8-37, 1961.","title":"Counterspeculation, auctions, and competitive sealed tenders","authors":"William Vickrey","year":"1961","venue":"The Journal of finance","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}