Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v58y2012i3p570-586.html
   My bibliography  Save this article

Bayesian Dynamic Pricing Policies: Learning and Earning Under a Binary Prior Distribution

Author

Listed:
  • J. Michael Harrison

    (Graduate School of Business, Stanford University, Stanford, California 94305)

  • N. Bora Keskin

    (Graduate School of Business, Stanford University, Stanford, California 94305)

  • Assaf Zeevi

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract
Motivated by applications in financial services, we consider a seller who offers prices sequentially to a stream of potential customers, observing either success or failure in each sales attempt. The parameters of the underlying demand model are initially unknown, so each price decision involves a trade-off between learning and earning. Attention is restricted to the simplest kind of model uncertainty, where one of two demand models is known to apply, and we focus initially on performance of the myopic Bayesian policy (MBP), variants of which are commonly used in practice. Because learning is passive under the MBP (that is, learning only takes place as a by-product of actions that have a different purpose), it can lead to incomplete learning and poor profit performance. However, under one additional assumption, a constrained variant of the myopic policy is shown to have the following strong theoretical virtue: the expected performance gap relative to a clairvoyant who knows the underlying demand model is bounded by a constant as the number of sales attempts becomes large. This paper was accepted by Gérard P. Cachon, stochastic models and simulation.

Suggested Citation

  • J. Michael Harrison & N. Bora Keskin & Assaf Zeevi, 2012. "Bayesian Dynamic Pricing Policies: Learning and Earning Under a Binary Prior Distribution," Management Science, INFORMS, vol. 58(3), pages 570-586, March.
    • Handle: RePEc:inm:ormnsc:v:58:y:2012:i:3:p:570-586
    DOI: 10.1287/mnsc.1110.1426
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1110.1426
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1110.1426?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Godfrey Keller & Sven Rady, 1999. "Optimal Experimentation in a Changing Environment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 475-507.
    2. Philippe Aghion & Patrick Bolton & Christopher Harris & Bruno Jullien, 1991. "Optimal Learning by Experimentation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(4), pages 621-654.
    3. Yossi Aviv & Amit Pazgal, 2005. "A Partially Observed Markov Decision Process for Dynamic Pricing," Management Science, INFORMS, vol. 51(9), pages 1400-1416, September.
    4. Vivek F. Farias & Benjamin Van Roy, 2010. "Dynamic Pricing with a Prior on Market Response," Operations Research, INFORMS, vol. 58(1), pages 16-29, February.
    5. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    6. McLennan, Andrew, 1984. "Price dispersion and incomplete learning in the long run," Journal of Economic Dynamics and Control, Elsevier, vol. 7(3), pages 331-347, September.
    7. Anderson, T W & Taylor, John B, 1976. "Some Experimental Results on the Statistical Properties of Least Squares Estimates in Control Problems," Econometrica, Econometric Society, vol. 44(6), pages 1289-1302, November.
    8. Tatsiana Levina & Yuri Levin & Jeff McGill & Mikhail Nediak, 2009. "Dynamic Pricing with Online Learning and Strategic Consumers: An Application of the Aggregating Algorithm," Operations Research, INFORMS, vol. 57(2), pages 327-341, April.
    9. Omar Besbes & Assaf Zeevi, 2009. "Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms," Operations Research, INFORMS, vol. 57(6), pages 1407-1420, December.
    Full references (including those not matched with items on IDEAS)

    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. Arnoud V. den Boer & Bert Zwart, 2014. "Simultaneously Learning and Optimizing Using Controlled Variance Pricing," Management Science, INFORMS, vol. 60(3), pages 770-783, March.
    2. Philipp Afèche & Barış Ata, 2013. "Bayesian Dynamic Pricing in Queueing Systems with Unknown Delay Cost Characteristics," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 292-304, May.
    3. Hao Zhang, 2022. "Analytical Solution to a Discrete-Time Model for Dynamic Learning and Decision Making," Management Science, INFORMS, vol. 68(8), pages 5924-5957, August.
    4. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.
    5. Wieland, Volker, 2000. "Learning by doing and the value of optimal experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 501-534, April.
    6. N. Bora Keskin & Assaf Zeevi, 2017. "Chasing Demand: Learning and Earning in a Changing Environment," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 277-307, May.
    7. Maxime C. Cohen, & Georgia Perakis & Robert S. Pindyck, 2021. "A Simple Rule for Pricing with Limited Knowledge of Demand," Management Science, INFORMS, vol. 67(3), pages 1608-1621, March.
    8. Christos Koulovatianos & Leonard J. Mirman & Marc Santugini, 2006. "Investment in a Monopoly with Bayesian Learning," Vienna Economics Papers vie0603, University of Vienna, Department of Economics.
    9. Christos Koulovatianos & Leonard J. Mirman & Marc Santugini, 2006. "Investment in a Monopoly with Bayesian Learning," Vienna Economics Papers 0603, University of Vienna, Department of Economics.
    10. Arnoud V. den Boer, 2014. "Dynamic Pricing with Multiple Products and Partially Specified Demand Distribution," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 863-888, August.
    11. Maxime C. Cohen & Georgia Perakis & Robert S. Pindyck, 2015. "Pricing with Limited Knowledge of Demand," NBER Working Papers 21679, National Bureau of Economic Research, Inc.
    12. J. Michael Harrison & Nur Sunar, 2015. "Investment Timing with Incomplete Information and Multiple Means of Learning," Operations Research, INFORMS, vol. 63(2), pages 442-457, April.
    13. Mason, Robin & Välimäki, Juuso, 2011. "Learning about the arrival of sales," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1699-1711, July.
    14. Yiwei Chen & Vivek F. Farias, 2013. "Simple Policies for Dynamic Pricing with Imperfect Forecasts," Operations Research, INFORMS, vol. 61(3), pages 612-624, June.
    15. Jason Delaney & Sarah Jacobson & Thorsten Moenig, 2020. "Preference discovery," Experimental Economics, Springer;Economic Science Association, vol. 23(3), pages 694-715, September.
    16. Klimenko, Mikhail M., 2004. "Industrial targeting, experimentation and long-run specialization," Journal of Development Economics, Elsevier, vol. 73(1), pages 75-105, February.
    17. Bergemann, Dirk & Valimaki, Juuso, 1996. "Learning and Strategic Pricing," Econometrica, Econometric Society, vol. 64(5), pages 1125-1149, September.
    18. Heski Bar-Isaac, 2001. "Self-Confidence and Survival," FMG Discussion Papers dp395, Financial Markets Group.
    19. N. Bora Keskin & John R. Birge, 2019. "Dynamic Selling Mechanisms for Product Differentiation and Learning," Operations Research, INFORMS, vol. 67(4), pages 1069-1089, July.
    20. Vives, Xavier, 1997. "Learning from Others: A Welfare Analysis," Games and Economic Behavior, Elsevier, vol. 20(2), pages 177-200, August.

    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:inm:ormnsc:v:58:y:2012:i:3:p:570-586. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.