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The Best Choice Problem under ambiguity

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  • Tatjana Chudjakow

    (Institute of Mathematical Economics, Bielefeld University)

  • Frank Riedel

    ()
    (Institute of 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.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-413.pdf
File Function: First version, 2009
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 413.

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Length: 24 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:bie:wpaper:413

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Keywords: Best Choice Problem;

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References

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  1. Jürgen Eichberger & David Kelsey, 2008. "Are the Treasures of Game Theory Ambiguous?," Working Papers 0469, University of Heidelberg, Department of Economics, revised Jul 2008.
  2. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  3. repec:hal:cesptp:halshs-00177057 is not listed on IDEAS
  4. Larry Epstein & Martin Schneider, 2002. "IID: Independently and Indistinguishably Distributed," RCER Working Papers 496, University of Rochester - Center for Economic Research (RCER).
  5. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer, vol. 48(2), pages 243-273, October.
  6. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010. "Rational Preferences under Ambiguity," Carlo Alberto Notebooks 169, Collegio Carlo Alberto.
  7. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2007. "Irreversible investment and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 136(1), pages 668-694, September.
  8. 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.
  9. Massimo Marinacci & Fabio Maccheroni & Alain Chateauneuf & Jean-Marc Tallon, 2003. "Monotone Continuous Multiple Priors," ICER Working Papers - Applied Mathematics Series 30-2003, ICER - International Centre for Economic Research.
  10. 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.
  11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  12. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, 05.
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Cited by:
  1. S\"oren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
  2. M. Aloqeili & G. Carlier & I. Ekeland, 2014. "Restrictions and identification in a multidimensional risk-sharing problem," Economic Theory, Springer, vol. 56(2), pages 409-423, June.
  3. Sören Christensen, 2013. "Optimal decision under ambiguity for diffusion processes," Computational Statistics, Springer, vol. 77(2), pages 207-226, April.

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