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The Best Choice Problem under Ambiguity

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  • Chudjakow, Tatjana

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

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 decision 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 minimax backward induction. As in the classical case the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule.

Suggested Citation

  • Chudjakow, Tatjana & Riedel, Frank, 2010. "The Best Choice Problem under Ambiguity," Center for Mathematical Economics Working Papers 413, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:413
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    References listed on IDEAS

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    1. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
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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. 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.
    3. 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.
    4. 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.
    5. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    6. 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.
    7. Martin Meier & Leopold Sögner, 2023. "Hunting for superstars," Mathematics and Financial Economics, Springer, volume 17, number 1, December.
    8. 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.

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    More about this item

    Keywords

    Best choice problem; Secretary problem; Optimal stopping; Ambiguity;
    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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