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A Bayesian Approach to a Generalized House Selling Problem

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  • 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
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    File URL: http://dx.doi.org/10.1287/mnsc.24.4.432
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    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. 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.
    4. Tapan Biswas & Jolian Mchardy, 2012. "Asking Price And Price Discounts: The Strategy Of Selling An Asset Under Price Uncertainty," Review of Economic Analysis, Rimini Centre for Economic Analysis, vol. 4(1), pages 17-37, June.
    5. Gershkov, Alex & Moldovanu, Benny, 2013. "Non-Bayesian optimal search and dynamic implementation," Economics Letters, Elsevier, vol. 118(1), pages 121-125.
    6. 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.
    7. Dirk Bergemann & Juuso Valimaki, 2017. "Dynamic Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 2102R, Cowles Foundation for Research in Economics, Yale University, revised Jun 2018.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Benny Moldovanu & Alex Gershkov, 2008. "The Trade-off Between Fast Learning and Dynamic Efficiency," 2008 Meeting Papers 348, Society for Economic Dynamics.

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