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Auctions with Dynamic Populations: Efficiency and Revenue Maximization

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  • Said, Maher

Abstract

We examine an environment where goods and privately informed buyers arrive stochastically to a market. A seller in this setting faces a sequential allocation problem with a changing population. We characterize the set of incentive compatible allocation rules and provide a generalized revenue equivalence result. In contrast to a static setting where incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object, in this dynamic setting, incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object sooner. We also characterize the set of efficient allocation rules and show that a dynamic Vickrey-Clarke-Groves mechanism is efficient and dominant strategy incentive compatible. We then derive an optimal direct mechanism. We show that the revenue-maximizing direct mechanism is a pivot mechanism with a reserve price. Finally, we consider sequential ascending auctions in this setting, both with and without a reserve price. We construct memoryless equilibrium bidding strategies in this indirect mechanism. Bidders reveal their private information in every period, yielding the same outcomes as the direct mechanisms. Thus, the sequential ascending auction is a natural institution for achieving either efficient or optimal outcomes. Interestingly, this is not the case for sequential second-price auctions, as the bids in a second-price auction do not reveal sufficient information to realize either the efficient or optimal allocation.

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  • Said, Maher, 2008. "Auctions with Dynamic Populations: Efficiency and Revenue Maximization," MPRA Paper 11456, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:11456
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    References listed on IDEAS

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    Cited by:

    1. Dirk Bergemann & Maher Said, 2010. "Dynamic Auctions: A Survey," Cowles Foundation Discussion Papers 1757, Cowles Foundation for Research in Economics, Yale University.
    2. Hinnosaar, Toomas, 2017. "Calendar mechanisms," Games and Economic Behavior, Elsevier, vol. 104(C), pages 252-270.
    3. repec:eee:gamebe:v:104:y:2017:i:c:p:595-612 is not listed on IDEAS
    4. 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.
    5. Hummel, Patrick, 2015. "Simultaneous use of auctions and posted prices," European Economic Review, Elsevier, vol. 78(C), pages 269-284.
    6. Kenju Kamei, 2018. "Group Size Effect and Over-Punishment in the Case of Third Party Enforcement of Social Norms," Working Papers 2018_04, Durham University Business School.
    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. Ryuji Sano, 2015. "A Dynamic Mechanism Design for Scheduling with Different Use Lengths," KIER Working Papers 924, Kyoto University, Institute of Economic Research.
    9. repec:the:publsh:2234 is not listed on IDEAS
    10. Daniel F. Garrett & Alessandro Pavan, 2012. "Managerial Turnover in a Changing World," Journal of Political Economy, University of Chicago Press, vol. 120(5), pages 879-925.
    11. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications, Elsevier.
    12. Ryuji Sano, 2017. "A Dynamic Mechanism Design with Overbooking, Different Deadlines, and Multi-unit Demands," KIER Working Papers 963, Kyoto University, Institute of Economic Research.
    13. Lavi, Ron & Nisan, Noam, 2015. "Online ascending auctions for gradually expiring items," Journal of Economic Theory, Elsevier, vol. 156(C), pages 45-76.
    14. 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.
    15. Hanzhe Zhang, 2013. "The Optimal Sequence of Costly Mechanisms," Working Papers 2014-005, Becker Friedman Institute for Research In Economics.
    16. Ely, Jeffrey & Garrett, Daniel F. & Hinnosaar, Toomas, 2016. "Overbooking," TSE Working Papers 16-678, Toulouse School of Economics (TSE).

    More about this item

    Keywords

    Dynamic mechanism design; Random arrivals; Revenue equivalence; Indirect mechanisms; Sequential ascending auctions;

    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
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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