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Optimal Dynamic Auctions

Author

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  • Mallesh Pai
  • Rakesh Vohra

Abstract

We consider a dynamic auction problem motivated by the traditional single-leg, multi-period revenue management problem. A seller with C units to sell faces potential buyers with unit demand who arrive and depart over the course of T time periods. The time at which a buyer arrives, her value for a unit as well as the time by which she must make the purchase are private information. In this environment, we derive the revenue maximizing Bayesian incentive compatible selling mechanism.

Suggested Citation

  • Mallesh Pai & Rakesh Vohra, 2008. "Optimal Dynamic Auctions," Discussion Papers 1461, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1461
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    References listed on IDEAS

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    1. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    2. Alexey Malakhov & Rakesh V. Vohra, 2004. "Single and Multi-Dimensional Optimal Auctions - A Network Approach," Discussion Papers 1397, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    4. Simon Board, 2008. "Durable-Goods Monopoly with Varying Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(2), pages 391-413.
    5. Jérémie Gallien, 2006. "Dynamic Mechanism Design for Online Commerce," Operations Research, INFORMS, vol. 54(2), pages 291-310, April.
    6. Gustavo Vulcano & Garrett van Ryzin & Costis Maglaras, 2002. "Optimal Dynamic Auctions for Revenue Management," Management Science, INFORMS, vol. 48(11), pages 1388-1407, November.
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    Cited by:

    1. Said, Maher, 2012. "Auctions with dynamic populations: Efficiency and revenue maximization," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2419-2438.
    2. Tao Zhang & Quanyan Zhu, 2019. "On Incentive Compatibility in Dynamic Mechanism Design With Exit Option in a Markovian Environment," Papers 1909.13720, arXiv.org, revised May 2021.
    3. Hinnosaar, Toomas, 2017. "Calendar mechanisms," Games and Economic Behavior, Elsevier, vol. 104(C), pages 252-270.
    4. Vahab Mirrokni & Renato Paes Leme & Pingzhong Tang & Song Zuo, 2020. "Non‐Clairvoyant Dynamic Mechanism Design," Econometrica, Econometric Society, vol. 88(5), pages 1939-1963, September.
    5. Lev, Omer, 2011. "A two-dimensional problem of revenue maximization," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 718-727.
    6. Ron Lavi & Ella Segev, 2014. "Efficiency levels in sequential auctions with dynamic arrivals," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 791-819, November.
    7. 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

    dynamic mechanism design; optimal auctions; virtual valuation; revelation principle;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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