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Auction Design for Bidders with Ex Post ROI Constraints

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Web and Internet Economics (WINE 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14413))

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Abstract

Motivated by practical constraints in online advertising, we investigate single-parameter auction design for bidders with constraints on their Return On Investment (ROI) – a targeted minimum ratio between the obtained value and the payment. We focus on ex post ROI constraints, which require the ROI condition to be satisfied for every realized value profile. With ROI-constrained bidders, we first provide a full characterization of the allocation and payment rules of dominant-strategy incentive compatible (DSIC) auctions. In particular, we show that given any monotone allocation rule, the corresponding DSIC payment should be the Myerson payment with a rebate for each bidder to meet their ROI constraints. Furthermore, we also determine the optimal auction structure when the item is sold to a single bidder under a mild regularity condition. This structure entails a randomized allocation scheme and a first-price payment rule, which differs from the deterministic Myerson auction and previous works on ex ante ROI constraints.

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Notes

  1. 1.

    DMR requires the marginal revenue, \(vf(v)+F(v)-1\) to be non-decreasing in the value space. This is different from the usual definition of regularity which requires the same monotonicity but in the quantile space. Please see the related work section for a more detailed discussion of their differences and more related works.

  2. 2.

    This setting is practical and prevalent in practice, e.g., in online advertising, the targeted ROI typically remains the same over a certain period.

  3. 3.

    The regularity condition is equivalent to the expected revenue being concave in the quantile space, while the DMR condition means the expected revenue is concave in the value space.

  4. 4.

    We omit an ill-defined special case where \(\psi (v)=0, \forall v\in [0,\bar{v}]\), since in such case \(\psi (v)\) will be infinity when \(v\rightarrow 0\).

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Acknowledgement

We thank Hu Fu, Yiqing Wang, Yidan Xing, Xiangyu Liu and anonymous reviewers for their insightful and helpful suggestions. This work was supported in part by National Key R &D Program of China No. 2021YFF0900800, in part by China NSF grant No. 62220106004, 62322206, 62132018, 62272307, 61972254, 62025204, 62302267, in part by the Natural Science Foundation of Shandong (No. ZR202211150156, ZR2021LZH006), in part by Alibaba Group through Alibaba Innovative Research Program, and in part by Tencent Rhino Bird Key Research Project. The opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the funding agencies or the government.

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Authors and Affiliations

  1. School of Software and Joint SDU-NTU Centre for Artificial Intelligence Research (C-FAIR), Shandong University, Jinan, China

    Hongtao Lv

  2. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Xiaohui Bei

  3. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

    Hongtao Lv, Zhenzhe Zheng & Fan Wu

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  1. Hongtao Lv
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  2. Xiaohui Bei
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Correspondence to Zhenzhe Zheng .

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Editors and Affiliations

  1. Department of Industrial and Enterprise Systems Engineering, University of Illinois System, Urbana, IL, USA

    Jugal Garg

  2. Institute of Mathematics, Technische Universität Berlin, Berlin, Berlin, Germany

    Max Klimm

  3. Center on Frontiers of Computing Studies, Peking University, Beijing, Beijing, China

    Yuqing Kong

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Lv, H., Bei, X., Zheng, Z., Wu, F. (2024). Auction Design for Bidders with Ex Post ROI Constraints. In: Garg, J., Klimm, M., Kong, Y. (eds) Web and Internet Economics. WINE 2023. Lecture Notes in Computer Science, vol 14413. Springer, Cham. https://doi.org/10.1007/978-3-031-48974-7_28

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  • DOI: https://doi.org/10.1007/978-3-031-48974-7_28

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