IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v54y2013i1p77-97.html
   My bibliography  Save this article

The best choice problem under ambiguity

Author

Listed:
  • Tatjana Chudjakow
  • Frank Riedel

Abstract

We model and solve best choice problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. The agent faces ambiguity about the probability that a candidate—a relatively top applicant—is actually best among all applicants. We show that our model covers the classical secretary problem, but also other interesting classes of problems. We provide a closed form solution of the problem for time-consistent priors using backward induction. As in the classical case, the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule. Copyright Springer-Verlag 2013

Suggested Citation

  • Tatjana Chudjakow & Frank Riedel, 2013. "The best choice problem under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 77-97, September.
    • Handle: RePEc:spr:joecth:v:54:y:2013:i:1:p:77-97
    DOI: 10.1007/s00199-012-0715-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-012-0715-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-012-0715-1?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
    ---><---

    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. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 243-273, October.
    2. Jürgen Eichberger & David Kelsey, 2011. "Are the treasures of game theory ambiguous?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 313-339, October.
    3. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 973-982, November.
    4. J. Neil Bearden & Amnon Rapoport & Ryan O. Murphy, 2006. "Sequential Observation and Selection with Rank-Dependent Payoffs: An Experimental Study," Management Science, INFORMS, vol. 52(9), pages 1437-1449, September.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    7. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    8. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2007. "Irreversible investment and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 136(1), pages 668-694, September.
    9. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    10. Epstein, Larry G. & Schneider, Martin, 2003. "IID: independently and indistinguishably distributed," Journal of Economic Theory, Elsevier, vol. 113(1), pages 32-50, November.
    11. Alain Chateauneuf & Luciano De Castro, 2011. "Ambiguity Aversion and Absence of Trade," Discussion Papers 1535, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Seale, Darryl A. & Rapoport, Amnon, 1997. "Sequential Decision Making with Relative Ranks: An Experimental Investigation of the "Secretary Problem">," Organizational Behavior and Human Decision Processes, Elsevier, vol. 69(3), pages 221-236, March.
    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. Lazar Obradović, 2020. "Robust best choice problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 435-460, December.
    2. M. Aloqeili & G. Carlier & I. Ekeland, 2014. "Restrictions and identification in a multidimensional risk-sharing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 409-423, June.
    3. Federica Ceron & Vassili Vergopoulos, 2021. "On stochastic independence under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 925-960, April.
    4. Kleinberg, Jon & Kleinberg, Robert & Oren, Sigal, 2022. "Optimal stopping with behaviorally biased agents: The role of loss aversion and changing reference points," Games and Economic Behavior, Elsevier, vol. 133(C), pages 282-299.
    5. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    6. Martin Meier & Leopold Sögner, 2023. "Hunting for superstars," Mathematics and Financial Economics, Springer, volume 17, number 1, March.
    7. Obradović, Lazar, 2018. "Robust Maximum Detection: Full Information Best Choice Problem under Multiple Priors," Center for Mathematical Economics Working Papers 580, Center for Mathematical Economics, Bielefeld University.
    8. Sören Christensen, 2013. "Optimal decision under ambiguity for diffusion processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 207-226, April.

    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. Paul Viefers, 2012. "Should I Stay or Should I Go?: A Laboratory Analysis of Investment Opportunities under Ambiguity," Discussion Papers of DIW Berlin 1228, DIW Berlin, German Institute for Economic Research.
    2. Michele Lombardi & Naoki Yoshihara, 2013. "A full characterization of nash implementation with strategy space reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 131-151, September.
    3. Beißner, Patrick, 2016. "Radner Equilibria under Ambiguous Volatility," Center for Mathematical Economics Working Papers 493, Center for Mathematical Economics, Bielefeld University.
    4. Yehuda Izhakian & Zur Izhakian, 2015. "Decision making in phantom spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 59-98, January.
    5. Gonçalo Faria & João Correia-da-Silva, 2012. "The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices," Annals of Finance, Springer, vol. 8(4), pages 507-531, November.
    6. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    7. Garlappi, Lorenzo & Giammarino, Ron & Lazrak, Ali, 2017. "Ambiguity and the corporation: Group disagreement and underinvestment," Journal of Financial Economics, Elsevier, vol. 125(3), pages 417-433.
    8. Luis H. R. Alvarez E. & Soren Christensen, 2019. "A Class of Solvable Multidimensional Stopping Problems in the Presence of Knightian Uncertainty," Papers 1907.04046, arXiv.org.
    9. Miao, Jianjun & Wang, Neng, 2011. "Risk, uncertainty, and option exercise," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 442-461, April.
    10. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    11. José Faro, 2013. "Cobb-Douglas preferences under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 273-285, October.
    12. Daniele Pennesi, 2013. "Asset Prices in an Ambiguous Economy," Carlo Alberto Notebooks 315, Collegio Carlo Alberto.
    13. Soren Christensen & Luis H. R. Alvarez E, 2019. "A Solvable Two-dimensional Optimal Stopping Problem in the Presence of Ambiguity," Papers 1905.05429, arXiv.org.
    14. Eisei Ohtaki, 2023. "Optimality in an OLG model with nonsmooth preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 611-659, September.
    15. Heyen, Daniel, 2014. "Learning under Ambiguity - A Note on the Belief Dynamics of Epstein and Schneider (2007)," Working Papers 0573, University of Heidelberg, Department of Economics.
    16. Frederik S. Herzberg, 2013. "The (im)possibility of collective risk measurement: Arrovian aggregation of variational preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 69-92, May.
    17. Philipp Strack & Paul Viefers, 2021. "Too Proud to Stop: Regret in Dynamic Decisions," Journal of the European Economic Association, European Economic Association, vol. 19(1), pages 165-199.
    18. Kishishita, Daiki, 2020. "(Not) delegating decisions to experts: The effect of uncertainty," Journal of Economic Theory, Elsevier, vol. 190(C).
    19. Luis H. R. Alvarez E. & Soren Christensen, 2019. "The Impact of Ambiguity on the Optimal Exercise Timing of Integral Option Contracts," Papers 1906.07533, arXiv.org.
    20. Moreno Othón M., 2014. "Consumption of Durable Goods under Ambiguity," Working Papers 2014-02, Banco de México.

    More about this item

    Keywords

    Optimal stopping; Ambiguity; Uncertainty aversion; Secretary problem; Best choice problems; D81; C61;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:spr:joecth:v:54:y:2013:i:1:p:77-97. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.