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Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach


  • Alex Gershkov
  • Benny Moldovanu


We study the revenue-maximizing allocation of several heterogeneous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially. There is a deadline after which no more objects can be allocated. We first characterize implementable allocation schemes, and compute the expected revenue for any implementable, deterministic and Markovian allocation policy. The revenue-maximizing policy is obtained by a variational argument which sheds more light on its properties than the usual dynamic programming approach. Finally, we use our main result in order to derive the optimal inventory choice, and explain empirical regularities about pricing in clearance sales. (JEL C61, D21, D82)

Suggested Citation

  • Alex Gershkov & Benny Moldovanu, 2009. "Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 168-198, August.
  • Handle: RePEc:aea:aejmic:v:1:y:2009:i:2:p:168-98 Note: DOI: 10.1257/mic.1.2.168

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    References listed on IDEAS

    1. Das Varma, Gopal & Vettas, Nikolaos, 2001. "Optimal dynamic pricing with inventories," Economics Letters, Elsevier, vol. 72(3), pages 335-340, September.
    2. Wang, Ruqu, 1993. "Auctions versus Posted-Price Selling," American Economic Review, American Economic Association, vol. 83(4), pages 838-851, September.
    3. Guillermo Gallego & Garrett van Ryzin, 1997. "A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management," Operations Research, INFORMS, vol. 45(1), pages 24-41, February.
    4. Pashigian, B Peter, 1988. "Demand Uncertainty and Sales: A Study of Fashion and Markdown Pricin g," American Economic Review, American Economic Association, vol. 78(5), pages 936-953, December.
    5. Gabriel Bitran & René Caldentey, 2003. "An Overview of Pricing Models for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 203-229, August.
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    Cited by:

    1. Johannes Hörner & Larry Samuelson, 2011. "Managing Strategic Buyers," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 379-425.
    2. Dirk Bergemann & Maher Said, 2010. "Dynamic Auctions: A Survey," Cowles Foundation Discussion Papers 1757, Cowles Foundation for Research in Economics, Yale University.
    3. Hinnosaar, Toomas, 2017. "Calendar mechanisms," Games and Economic Behavior, Elsevier, vol. 104(C), pages 252-270.
    4. repec:eee:gamebe:v:104:y:2017:i:c:p:595-612 is not listed on IDEAS
    5. Said, Maher, 2012. "Auctions with dynamic populations: Efficiency and revenue maximization," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2419-2438.
    6. 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.
    7. Mierendorff, Konrad, 2016. "Optimal dynamic mechanism design with deadlines," Journal of Economic Theory, Elsevier, vol. 161(C), pages 190-222.
    8. Dupuis, Nicolas & Ivaldi, Marc & Pouyet, Jérôme, 2015. "A Welfare Assessment of Revenue Management Systems," CEPR Discussion Papers 10385, C.E.P.R. Discussion Papers.
    9. Daniel F. Garrett, 2016. "Intertemporal Price Discrimination: Dynamic Arrivals and Changing Values," American Economic Review, American Economic Association, vol. 106(11), pages 3275-3299, November.
    10. Francis Bloch & David Cantala, 2013. "Markovian assignment rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 1-25, January.
    11. Moldovanu, Benny & Dizdar, Deniz & Gershkov, Alex, 2011. "Revenue maximization in the dynamic knapsack problem," Theoretical Economics, Econometric Society, vol. 6(2), May.
    12. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    13. Hitoshi Matsushima, 2012. "Optimal Multiunit Exchange Design with Single-Dimensionality," CARF F-Series CARF-F-292, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2012.
    14. Garrett, Daniel F., 2017. "Dynamic mechanism design: Dynamic arrivals and changing values," Games and Economic Behavior, Elsevier, vol. 104(C), pages 595-612.
    15. Pancs, Romans, 2013. "Sequential negotiations with costly information acquisition," Games and Economic Behavior, Elsevier, vol. 82(C), pages 522-543.
    16. Francis Bloch & David Cantala, 2017. "Dynamic Assignment of Objects to Queuing Agents," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 88-122, February.
    17. Ryuji Sano, 2015. "A Dynamic Mechanism Design for Scheduling with Different Use Lengths," KIER Working Papers 924, Kyoto University, Institute of Economic Research.
    18. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications, Elsevier.
    19. Arieh Gavious & Ella Segev, 2017. "Price Discrimination Based on Buyers’ Purchase History," Dynamic Games and Applications, Springer, vol. 7(2), pages 229-265, June.
    20. 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.
    21. Morimitsu Kurino, 2014. "House Allocation with Overlapping Generations," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 258-289, February.
    22. Gershkov, Alex & Moldovanu, Benny, 2012. "Dynamic allocation and pricing: A mechanism design approach," International Journal of Industrial Organization, Elsevier, vol. 30(3), pages 283-286.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design


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