IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/6439.html
   My bibliography  Save this paper

The Dynamic Assignment of Heterogenous Objects: A Mechanism Design Approach

Author

Listed:
  • moldovanu, benny
  • Gershkov, Alex

Abstract

We study the allocation of several heterogenous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially according to a Poisson or renewal process. We analyze and compare the policies that maximize either welfare or revenue. We focus on two cases: 1. There is a deadline after which no more objects can be allocated; 2. The horizon is potentially infinite and there is time discounting. We first characterize all implementable allocation schemes, and we compute the expected revenue for any implementable, deterministic and Markovian allocation policy. These properties are shared by the welfare and revenue maximizing policies. Moreover, we show that these policies do not depend on the characteristics of the available objects at each point in time. The revenue-maximizing allocation scheme is obtained by a variational argument which sheds somewhat more light on its properties than the usual dynamic programming approach. We also obtain several properties of the welfare maximizing policy using stochastic dominance measures of increased variability and majorization arguments. These results yield upper/lower bounds on efficiency/revenue for large classes of distributions of agents' characteristics or of distributions of inter-arrival times for which explicit solutions cannot be obtained in closed form.

Suggested Citation

  • moldovanu, benny & Gershkov, Alex, 2007. "The Dynamic Assignment of Heterogenous Objects: A Mechanism Design Approach," CEPR Discussion Papers 6439, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:6439
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP6439
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    2. Jérémie Gallien, 2006. "Dynamic Mechanism Design for Online Commerce," Operations Research, INFORMS, vol. 54(2), pages 291-310, April.
    3. Susan Athey & Ilya Segal, 2013. "An Efficient Dynamic Mechanism," Econometrica, Econometric Society, vol. 81(6), pages 2463-2485, November.
    4. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
    5. 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.
    6. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, vol. 21(1), pages 60-67, September.
    7. Gabriel R. Bitran & Susana V. Mondschein, 1997. "Periodic Pricing of Seasonal Products in Retailing," Management Science, INFORMS, vol. 43(1), pages 64-79, January.
    8. Das Varma, Gopal & Vettas, Nikolaos, 2001. "Optimal dynamic pricing with inventories," Economics Letters, Elsevier, vol. 72(3), pages 335-340, September.
    9. 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.
    10. Dirk Bergemann & Juuso Välimäki, 2006. "Efficient Dynamic Auctions," Levine's Bibliography 321307000000000580, UCLA Department of Economics.
    11. Michael A. Arnold & Steven A. Lippman, 2001. "The analytics of search with posted prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(2), pages 447-466.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Benny Moldovanu & Alex Gershkov, 2008. "The Trade-off Between Fast Learning and Dynamic Efficiency," 2008 Meeting Papers 348, Society for Economic Dynamics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xuanming Su, 2007. "Intertemporal Pricing with Strategic Customer Behavior," Management Science, INFORMS, vol. 53(5), pages 726-741, May.
    2. 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.
    3. Pavithra Harsha & Shivaram Subramanian & Joline Uichanco, 2019. "Dynamic Pricing of Omnichannel Inventories," Service Science, INFORMS, vol. 21(1), pages 47-65, January.
    4. Ibrahim, Michael Nawar & Atiya, Amir F., 2016. "Analytical solutions to the dynamic pricing problem for time-normalized revenue," European Journal of Operational Research, Elsevier, vol. 254(2), pages 632-643.
    5. Kyle Y. Lin, 2004. "A sequential dynamic pricing model and its applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 501-521, June.
    6. Guillermo Gallego & Michael Z. F. Li & Yan Liu, 2020. "Dynamic Nonlinear Pricing of Inventories over Finite Sales Horizons," Operations Research, INFORMS, vol. 68(3), pages 655-670, May.
    7. Yalç{i}n Akçay & Harihara Prasad Natarajan & Susan H. Xu, 2010. "Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice," Management Science, INFORMS, vol. 56(8), pages 1345-1361, August.
    8. Muzaffer Buyruk & Ertan Güner, 2022. "Personalization in airline revenue management: an overview and future outlook," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(2), pages 129-139, April.
    9. Dan Zhang & Zhaosong Lu, 2013. "Assessing the Value of Dynamic Pricing in Network Revenue Management," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 102-115, February.
    10. Zhang, Dan & Cooper, William L., 2009. "Pricing substitutable flights in airline revenue management," European Journal of Operational Research, Elsevier, vol. 197(3), pages 848-861, September.
    11. Gökgür, Burak & Karabatı, Selçuk, 2019. "Dynamic and targeted bundle pricing of two independently valued products," European Journal of Operational Research, Elsevier, vol. 279(1), pages 184-198.
    12. Dasci, A. & Karakul, M., 2009. "Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly," European Journal of Operational Research, Elsevier, vol. 197(3), pages 945-968, September.
    13. Yiwei Chen & Vivek F. Farias, 2013. "Simple Policies for Dynamic Pricing with Imperfect Forecasts," Operations Research, INFORMS, vol. 61(3), pages 612-624, June.
    14. Adam J. Mersereau & Dan Zhang, 2012. "Markdown Pricing with Unknown Fraction of Strategic Customers," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 355-370, July.
    15. Sabri Çelik & Alp Muharremoglu & Sergei Savin, 2009. "Revenue Management with Costly Price Adjustments," Operations Research, INFORMS, vol. 57(5), pages 1206-1219, October.
    16. Lingxiu Dong & Panos Kouvelis & Zhongjun Tian, 2009. "Dynamic Pricing and Inventory Control of Substitute Products," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 317-339, December.
    17. Goker Aydin & Serhan Ziya, 2008. "Pricing Promotional Products Under Upselling," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 360-376, June.
    18. Stefanus Jasin, 2014. "Reoptimization and Self-Adjusting Price Control for Network Revenue Management," Operations Research, INFORMS, vol. 62(5), pages 1168-1178, October.
    19. Serguei Netessine & Sergei Savin & Wenqiang Xiao, 2006. "Revenue Management Through Dynamic Cross Selling in E-Commerce Retailing," Operations Research, INFORMS, vol. 54(5), pages 893-913, October.
    20. Dasu, Sriram & Tong, Chunyang, 2010. "Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes," European Journal of Operational Research, Elsevier, vol. 204(3), pages 662-671, August.

    More about this item

    Keywords

    Dynamic pricing; Mechanism design; Revenue management; Sequential assignment;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cpr:ceprdp:6439. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.