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Dynamic Revenue Maximization: A Continuous Time Approach

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Abstract

We characterize the profit-maximizing mechanism for repeatedly selling a non-durable good in continuous time. The valuation of each agent is private information and changes over time. At the time of contracting every agent privately observes his initial type which influences the evolution of his valuation process. In the profit-maximizing mechanism the allocation is distorted in favor of agents with high initial types. We derive the optimal mechanism in closed form, which enables us to compare the distortion in various examples. The case where the valuation of the agents follows an arithmetic/geometric Brownian motion, Ornstein-Uhlenbeck process, or is derived from a Bayesian learning model are discussed. We show that depending on the nature of the private information and the valuation process the distortion might increase or decrease over time.

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  • Dirk Bergemann & Philipp Strack, 2014. "Dynamic Revenue Maximization: A Continuous Time Approach," Cowles Foundation Discussion Papers 1953, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1953
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    Cited by:

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    2. Bergemann, Dirk & Strack, Philipp, 2022. "Progressive participation," Theoretical Economics, Econometric Society, vol. 17(3), July.
    3. Gonzalo Cisternas & Aaron Kolb, 2020. "Signaling with Private Monitoring," Papers 2007.15514, arXiv.org.
    4. Kiho Yoon, 2021. "The Uniqueness of Dynamic Groves Mechanisms on Restricted Domains," Korean Economic Review, Korean Economic Association, vol. 37, pages 263-285.
    5. Alex Bloedel & R. Vijay Krishna & Oksana Leukhina, 2018. "Insurance and Inequality with Persistent Private Information," Working Papers 2018-020, Federal Reserve Bank of St. Louis, revised 12 Dec 2021.
    6. Georgii Riabov & Aleh Tsyvinski, 2021. "Policy with stochastic hysteresis," Papers 2104.10225, arXiv.org.
    7. Garrett, Daniel F., 2017. "Dynamic mechanism design: Dynamic arrivals and changing values," Games and Economic Behavior, Elsevier, vol. 104(C), pages 595-612.
    8. Marco Buso & Cesare Dosi & Michele Moretto, 2023. "Dynamic Regulation of Public Franchises with Imperfectly Correlated Demand Shocks," Working Papers 2023.03, Fondazione Eni Enrico Mattei.
    9. Bergemann, Dirk & Pavan, Alessandro, 2015. "Introduction to Symposium on Dynamic Contracts and Mechanism Design," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 679-701.
    10. Lu, Jingfeng & Wang, Zijia, 2021. "Optimal selling mechanisms with buyer price search," Journal of Economic Theory, Elsevier, vol. 196(C).
    11. Meng, Dawen & Sun, Lei & Tian, Guoqiang, 2022. "Dynamic mechanism design on social networks," Games and Economic Behavior, Elsevier, vol. 131(C), pages 84-120.
    12. Dirk Bergemann & Juuso Välimäki, 2019. "Dynamic Mechanism Design: An Introduction," Journal of Economic Literature, American Economic Association, vol. 57(2), pages 235-274, June.
    13. Bergemann, Dirk & V�lim�ki, Juuso, 2017. "Dynamic Mechanism Design: An Introduction," CEPR Discussion Papers 12240, C.E.P.R. Discussion Papers.
    14. Zwart, Gijsbert, 2021. "Optimal regulation of energy network expansion when costs are stochastic," Journal of Economic Dynamics and Control, Elsevier, vol. 126(C).
    15. Rosella Levaggi & Michele Moretto & Paolo Pertile, 2023. "Dynamic, incentive-compatible contracting for health services," Working Papers 2023.16, Fondazione Eni Enrico Mattei.
    16. Haupt, Alexander & Krieger, Tim, 2020. "The role of relocation mobility in tax and subsidy competition," Journal of Urban Economics, Elsevier, vol. 116(C).
    17. Mark Braverman & Jon Schneider & S. Matthew Weinberg, 2021. "Prior-free Dynamic Mechanism Design With Limited Liability," Papers 2103.01868, arXiv.org.
    18. Qi Luo & Romesh Saigal, 2017. "A Note on the Multi-Agent Contracts in Continuous Time," Papers 1710.00377, arXiv.org, revised Oct 2017.
    19. Yingkai Li & Jonathan Libgober, 2023. "Optimal Scoring for Dynamic Information Acquisition," Papers 2310.19147, arXiv.org.
    20. Di Corato, Luca & Moretto, Michele, 2016. "Selling real assets: the impact of idiosyncratic project risk in an auction environment," Working Paper Series 2016:9, Swedish University of Agricultural Sciences, Department Economics.
    21. Chawla, Shuchi & Devanur, Nikhil R. & Karlin, Anna R. & Sivan, Balasubramanian, 2022. "Simple pricing schemes for consumers with evolving values," Games and Economic Behavior, Elsevier, vol. 134(C), pages 344-360.
    22. Abdoulaye Ndiaye, 2017. "Flexible Retirement and Optimal Taxation," Working Paper Series WP-2018-18, Federal Reserve Bank of Chicago.
    23. Dirk Bergemann & Alessandro Pavan, 2015. "Introduction to JET Symposium Issue on "Dynamic Contracts and Mechanism Design"," Cowles Foundation Discussion Papers 2016, Cowles Foundation for Research in Economics, Yale University.
    24. Alex Gershkov & Benny Moldovanu & Philipp Strack, 2018. "Revenue-Maximizing Mechanisms with Strategic Customers and Unknown, Markovian Demand," Management Science, INFORMS, vol. 64(5), pages 2031-2046, May.

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    More about this item

    Keywords

    Mechanism design; Dynamic auctions; Repeated sales;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • 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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