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The best choice problem under ambiguity

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  • 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
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    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.
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    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, June.
    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.

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    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

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