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Dynamic Revenue Maximization: A Continuous Time Approach

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Abstract

We characterize the revenue-maximizing mechanism for time separable allocation problems 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. The leading example is the repeated sales of a good or a service. We derive the optimal dynamic mechanism, analyze its qualitative structure and frequently derive its closed form solution. This enables us to compare the distortion in various settings. In particular, we discuss the cases where the type of each agent follows an arithmetic or geometric Brownian motion or a mean reverting process. We show that depending on the nature of the private information the distortion might increase or decrease over time.

Suggested Citation

  • Dirk Bergemann & Philipp Strack, 2014. "Dynamic Revenue Maximization: A Continuous Time Approach," Cowles Foundation Discussion Papers 1953R2, Cowles Foundation for Research in Economics, Yale University, revised Jan 2015.
  • Handle: RePEc:cwl:cwldpp:1953r2
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Bergemann, Dirk & V�lim�ki, Juuso, 2017. "Dynamic Mechanism Design: An Introduction," CEPR Discussion Papers 12240, C.E.P.R. Discussion Papers.
    5. Qi Luo & Romesh Saigal, 2017. "A Note on the Multi-Agent Contracts in Continuous Time," Papers 1710.00377, arXiv.org, revised Oct 2017.
    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. Lu, Jingfeng & Wang, Zijia, 2021. "Optimal selling mechanisms with buyer price search," Journal of Economic Theory, Elsevier, vol. 196(C).
    8. Abdoulaye Ndiaye, 2017. "Flexible Retirement and Optimal Taxation," Working Paper Series WP-2018-18, Federal Reserve Bank of Chicago.
    9. Zwart, Gijsbert, 2021. "Optimal regulation of energy network expansion when costs are stochastic," Journal of Economic Dynamics and Control, Elsevier, vol. 126(C).
    10. Kiho Yoon, 2021. "The Uniqueness of Dynamic Groves Mechanisms on Restricted Domains," Korean Economic Review, Korean Economic Association, vol. 37, pages 263-285.
    11. 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.
    12. 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.
    13. Garrett, Daniel F., 2017. "Dynamic mechanism design: Dynamic arrivals and changing values," Games and Economic Behavior, Elsevier, vol. 104(C), pages 595-612.
    14. Georgii Riabov & Aleh Tsyvinski, 2021. "Policy with stochastic hysteresis," Papers 2104.10225, arXiv.org.
    15. Haupt, Alexander & Krieger, Tim, 2020. "The role of relocation mobility in tax and subsidy competition," Journal of Urban Economics, Elsevier, vol. 116(C).

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    More about this item

    Keywords

    Mechanism design; Dynamic auctions; Repeated sales; Impulse response function; Stochastic flow;
    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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