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The Scope of Sequential Screening with Ex-Post Participation Constraints

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  • Bergemann, Dirk
  • Castro, Francisco
  • Weintraub, Gabriel

Abstract

We study the classic sequential screening problem in the presence of buyers' ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently do not use up-front fees and instead use transaction-contingent fees. We establish conditions under which the optimal selling mechanism is static and buyers are not screened with respect to their interim type, or sequential and the buyers are screened with respect to their interim type. In particular, we provide an intuitive necessary and sufficient condition under which the static contract is optimal for general distributions of ex-post values. Further, we completely characterize the optimal sequential contract with binary interim types and continuum of ex-post values when this condition fails. Importantly, the latter contract randomizes the allocation of the low type buyer while giving a deterministic allocation to the high type. We also provide partial results for the case of multiple interim types.

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  • Bergemann, Dirk & Castro, Francisco & Weintraub, Gabriel, 2018. "The Scope of Sequential Screening with Ex-Post Participation Constraints," CEPR Discussion Papers 13018, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:13018
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    Citations

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    Cited by:

    1. Bergemann, Dirk & Strack, Philipp, 2022. "Progressive participation," Theoretical Economics, Econometric Society, vol. 17(3), July.
    2. Lu, Jingfeng & Wang, Zijia, 2021. "Optimal selling mechanisms with buyer price search," Journal of Economic Theory, Elsevier, vol. 196(C).
    3. Meng, Dawen & Sun, Lei & Tian, Guoqiang, 2022. "Dynamic mechanism design on social networks," Games and Economic Behavior, Elsevier, vol. 131(C), pages 84-120.
    4. Heumann, Tibor, 2020. "Information design and sequential screening with ex post participation constraint," Theoretical Economics, Econometric Society, vol. 15(1), January.
    5. Bergemann, Dirk & Castro, Francisco & Weintraub, Gabriel, 2022. "Third-degree price discrimination versus uniform pricing," Games and Economic Behavior, Elsevier, vol. 131(C), pages 275-291.
    6. Dirk Bergemann & Juuso Välimäki, 2019. "Dynamic Mechanism Design: An Introduction," Journal of Economic Literature, American Economic Association, vol. 57(2), pages 235-274, June.
    7. Bergemann, Dirk & V�lim�ki, Juuso, 2017. "Dynamic Mechanism Design: An Introduction," CEPR Discussion Papers 12240, C.E.P.R. Discussion Papers.
    8. Vahab Mirrokni & Renato Paes Leme & Pingzhong Tang & Song Zuo, 2018. "Optimal Dynamic Auctions are Virtual Welfare Maximizers," Papers 1812.02993, arXiv.org.
    9. Krähmer, Daniel & Strausz, Roland, 2022. "Dynamic Screening with Verifiable Bankruptcy," Rationality and Competition Discussion Paper Series 348, CRC TRR 190 Rationality and Competition.
    10. Yingkai Li & Jonathan Libgober, 2023. "Implementing Evidence Acquisition: Time Dependence in Contracts for Advice," Papers 2310.19147, arXiv.org, revised Sep 2024.
    11. Dirk Bergemann & Francisco Castro & Gabriel Weintraub, 2019. "Uniform Pricing Versus Third-Degree Price Discrimination," Cowles Foundation Discussion Papers 2213r, Cowles Foundation for Research in Economics, Yale University, revised Feb 2020.
    12. Liu, Bin & Liu, Dongri & Lu, Jingfeng, 2020. "Shifting supports in Esö and Szentes (2007)," Economics Letters, Elsevier, vol. 193(C).
    13. Can Küçükgül & Özalp Özer & Shouqiang Wang, 2022. "Engineering Social Learning: Information Design of Time-Locked Sales Campaigns for Online Platforms," Management Science, INFORMS, vol. 68(7), pages 4899-4918, July.

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    More about this item

    Keywords

    Sequential screening; Ex-post participation constraints; Static contract; Sequential contract;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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