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The best choice problem under ambiguity

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  • Tatjana Chudjakow
  • Frank Riedel

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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

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File URL: http://hdl.handle.net/10.1007/s00199-012-0715-1
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 54 (2013)
Issue (Month): 1 (September)
Pages: 77-97

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Handle: RePEc:spr:joecth:v:54:y:2013:i:1:p:77-97

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Related research

Keywords: Optimal stopping; Ambiguity; Uncertainty aversion; Secretary problem; Best choice problems; D81; C61;

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References

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  1. 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.
  2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  3. 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.
  4. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010. "Rational Preferences under Ambiguity," Carlo Alberto Notebooks 169, Collegio Carlo Alberto.
  5. Larry Epstein & Martin Schneider, 2002. "IID: Independently and Indistinguishably Distributed," RCER Working Papers 496, University of Rochester - Center for Economic Research (RCER).
  6. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  7. Eichberger, Jürgen & Kelsey, David, 2008. "Are the Treasures of Game Theory Ambiguous?," Sonderforschungsbereich 504 Publications 08-08, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  8. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer, vol. 48(2), pages 243-273, October.
  9. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2007. "Irreversible investment and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 136(1), pages 668-694, September.
  10. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, 05.
  11. 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.
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Cited by:
  1. 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.
  2. Sören Christensen, 2013. "Optimal decision under ambiguity for diffusion processes," Computational Statistics, Springer, vol. 77(2), pages 207-226, April.
  3. S\"oren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.

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