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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.

Suggested Citation

  • 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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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d19/d1953.pdf
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    10. Marco Battaglini, 2005. "Long-Term Contracting with Markovian Consumers," American Economic Review, American Economic Association, vol. 95(3), pages 637-658, June.
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    Cited by:

    1. 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.
    2. 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.
    3. Bergemann, Dirk & V�lim�ki, Juuso, 2017. "Dynamic Mechanism Design: An Introduction," CEPR Discussion Papers 12240, C.E.P.R. Discussion Papers.
    4. repec:eee:gamebe:v:104:y:2017:i:c:p:595-612 is not listed on IDEAS
    5. 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.
    6. Qi Luo & Romesh Saigal, 2017. "A Note on the Multi-Agent Contracts in Continuous Time," Papers 1710.00377, arXiv.org, revised Oct 2017.
    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. Bergemann, Dirk & V�lim�ki, Juuso, 2017. "Dynamic Mechanism Design: An Introduction," CEPR Discussion Papers 12240, C.E.P.R. Discussion Papers.

    More about this item

    Keywords

    Mechanism design; Dynamic auctions; Repeated sales;

    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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