IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v24y1977i4p432-440.html
   My bibliography  Save this article

A Bayesian Approach to a Generalized House Selling Problem

Author

Listed:
  • S. Christian Albright

    (Indiana University)

Abstract

The problem of choosing the one best or several best of a set of sequentially observed random variables has been treated by many authors. For example, the seller of a house has this problem when deciding which bids on the house to accept and which to reject. We assume that the bids are identically distributed random variables and at most n can be observed. Each bid is accepted or rejected when received; a bid rejected now cannot be accepted later on. The object is to maximize the expected value of the bid actually accepted. Unlike most previous authors, we examine the case where one or more parameters of the common underlying distribution are unknown and information on these is updated in a Bayesian manner as the successive random variables are observed. Using the properties of location and scale parameters, an explicit form for the optimal policy is found when the underlying distribution is normal, uniform, or gamma and the prior is from the natural conjugate family. Simulation results concerning sensitivity of the value obtained to the amount and correctness of the prior information for these three families is then presented.

Suggested Citation

  • S. Christian Albright, 1977. "A Bayesian Approach to a Generalized House Selling Problem," Management Science, INFORMS, vol. 24(4), pages 432-440, December.
  • Handle: RePEc:inm:ormnsc:v:24:y:1977:i:4:p:432-440
    DOI: 10.1287/mnsc.24.4.432
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.24.4.432
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.24.4.432?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
    ---><---

    Citations

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


    Cited by:

    1. Gershkov, Alex & Moldovanu, Benny, 2012. "Optimal search, learning and implementation," Journal of Economic Theory, Elsevier, vol. 147(3), pages 881-909.
    2. Glazer, Amihai & Hassin, Refael, 2010. "Inducing search by periodic advertising," Information Economics and Policy, Elsevier, vol. 22(3), pages 276-286, July.
    3. Egozcue, Martin & Fuentes García, Luis & Zitikis, Ricardas, 2012. "An optimal strategy for maximizing the expected real-estate selling price: accept or reject an offer?," MPRA Paper 40694, University Library of Munich, Germany.
    4. Sofronov, Georgy, 2013. "An optimal sequential procedure for a multiple selling problem with independent observations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 332-336.
    5. Tianke Feng & Joseph C. Hartman, 2015. "The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 267-292, June.
    6. Arash Khatibi & Sheldon H. Jacobson, 2016. "Doubly Stochastic Sequential Assignment Problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 124-137, March.
    7. Tapan Biswas & Jolian Mchardy, 2012. "Asking Price And Price Discounts: The Strategy Of Selling An Asset Under Price Uncertainty," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 4(1), pages 17-37, June.
    8. Arash Khatibi & Golshid Baharian & Banafsheh Behzad & Sheldon Jacobson, 2015. "Extensions of the sequential stochastic assignment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 317-340, December.
    9. Golshid Baharian & Sheldon H. Jacobson, 2013. "Limiting behavior of the stochastic sequential assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 321-330, June.
    10. Dirk Bergemann & Juuso Välimäki, 2019. "Dynamic Mechanism Design: An Introduction," Journal of Economic Literature, American Economic Association, vol. 57(2), pages 235-274, June.
    11. Gershkov, Alex & Moldovanu, Benny, 2013. "Non-Bayesian optimal search and dynamic implementation," Economics Letters, Elsevier, vol. 118(1), pages 121-125.
    12. Georgy Yu. Sofronov, 2016. "A multiple optimal stopping rule for a buying–selling problem with a deterministic trend," Statistical Papers, Springer, vol. 57(4), pages 1107-1119, December.
    13. Hwa‐Ming Yang, 1987. "Optimal selection of the t best of a sequence with sampling cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 281-292, April.
    14. Gerald Häubl & Benedict G. C. Dellaert & Bas Donkers, 2010. "Tunnel Vision: Local Behavioral Influences on Consumer Decisions in Product Search," Marketing Science, INFORMS, vol. 29(3), pages 438-455, 05-06.
    15. Ben Abdelaziz, F. & Krichen, S., 2005. "An interactive method for the optimal selection problem with two decision makers," European Journal of Operational Research, Elsevier, vol. 162(3), pages 602-609, May.
    16. Yen‐Ming Lee & Sheldon M. Ross, 2013. "Bayesian selling problem with partial information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(7), pages 557-570, October.
    17. Ahn, Jae-Hyeon & Kim, John J., 1998. "Action-timing problem with sequential Bayesian belief revision process," European Journal of Operational Research, Elsevier, vol. 105(1), pages 118-129, February.
    18. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    19. Xuanming Su & Stefanos A. Zenios, 2005. "Patient Choice in Kidney Allocation: A Sequential Stochastic Assignment Model," Operations Research, INFORMS, vol. 53(3), pages 443-455, June.
    20. Benny Moldovanu & Alex Gershkov, 2008. "The Trade-off Between Fast Learning and Dynamic Efficiency," 2008 Meeting Papers 348, Society for Economic Dynamics.

    More about this item

    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:inm:ormnsc:v:24:y:1977:i:4:p:432-440. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.