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The Simplicity of Optimal Dynamic Mechanisms

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  • Jose Correa
  • Andres Cristi
  • Laura Vargas Koch

Abstract

A fundamental economic question is that of designing revenue-maximizing mechanisms in dynamic environments. This paper considers a simple yet compelling market model to tackle this question, where forward-looking buyers arrive at the market over discrete time periods, and a monopolistic seller is endowed with a limited supply of a single good. In the case of i.i.d. and regular valuations for the buyers, Board and Skrzypacz (2016) characterized the optimal mechanism and proved the optimality of posted prices in the continuous-time limit. Our main result considers the limit case of a continuum of buyers, establishing that for arbitrary independent buyers' valuations, posted prices and capacity rationing can implement the optimal anonymous mechanism. Our result departs from the literature in three ways: It does not make any regularity assumptions, it considers the case of general, not necessarily i.i.d., arrivals, and finally, not only posted prices but also capacity rationing takes part in the optimal mechanism. Additionally, if supply is unlimited, we show that the rationing effect vanishes, and the optimal mechanism can be implemented using posted prices only, \`a la Board (2008).

Suggested Citation

  • Jose Correa & Andres Cristi & Laura Vargas Koch, 2024. "The Simplicity of Optimal Dynamic Mechanisms," Papers 2410.11738, arXiv.org.
    • Handle: RePEc:arx:papers:2410.11738
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    References listed on IDEAS

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    1. Mierendorff, Konrad, 2016. "Optimal dynamic mechanism design with deadlines," Journal of Economic Theory, Elsevier, vol. 161(C), pages 190-222.
    2. 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.
    3. Qian Liu & Garrett J. van Ryzin, 2008. "Strategic Capacity Rationing to Induce Early Purchases," Management Science, INFORMS, vol. 54(6), pages 1115-1131, June.
    4. Simon Board & Andrzej Skrzypacz, 2016. "Revenue Management with Forward-Looking Buyers," Journal of Political Economy, University of Chicago Press, vol. 124(4), pages 1046-1087.
    5. Volker Nocke & Martin Peitz, 2007. "A Theory of Clearance Sales," Economic Journal, Royal Economic Society, vol. 117(522), pages 964-990, July.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Alessandro Pavan & Ilya Segal & Juuso Toikka, 2014. "Dynamic Mechanism Design: A Myersonian Approach," Econometrica, Econometric Society, vol. 82(2), pages 601-653, March.
    8. Mallesh M. Pai & Rakesh Vohra, 2013. "Optimal Dynamic Auctions and Simple Index Rules," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 682-697, November.
    9. Vincenzo Denicolo' & Paolo Garella, 1999. "Rationing in a Durable Goods Monopoly," RAND Journal of Economics, The RAND Corporation, vol. 30(1), pages 44-55, Spring.
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