Economic Theory

, Volume 54, Issue 1, pp 77–97 | Cite as

The best choice problem under ambiguity

Research Article

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.

Keywords

Optimal stopping Ambiguity Uncertainty aversion  Secretary problem Best choice problems 

JEL Classification

D81 C61 

References

  1. Bearden, J., Rapoport, A., Murphy, R.: Sequential observation and selection with rank-dependent payoffs: an experimental study. Manag. Sci. 52, 1437–1449 (2006)CrossRefGoogle Scholar
  2. Beck, H.: Der Liebesökonom—Nutzen und Kosten einer Himmelsmacht. Frankfurter Allgemeine Buch (2005)Google Scholar
  3. Berezovski, B., Gnedin, A.V.: Problems of Best Choice (in Russian). Akademia Nauk, Moscow (1984)Google Scholar
  4. Cerreia-Vioglio, S., Ghirardato, P., Maccheroni, F., Marinacci, M., Siniscalchi, M.: Rational preferences under ambiguity. Econ. Theory 48, 341–375 (2011)CrossRefGoogle Scholar
  5. Chateauneuf, A., Maccheroni, F., Marinacci, M., Tallon, J.-M.: Monotone continuous multiple priors. Econ. Theory 26(4), 973–982 (2005)CrossRefGoogle Scholar
  6. Chow, Y., Robbins, H., Siegmund, D.: Great expectations: the theory of optimal stopping. Houghton Mifflin Comp, Boston (1971)Google Scholar
  7. de Castro, L.I., Chateauneuf, A.: Ambiguity aversion and trade. Econ. Theory 48, 243–273 (2011)CrossRefGoogle Scholar
  8. Eichberger, J., Kelsey, D.: Are the treasures of game theory ambiguous? Econ. Theory 48, 313–339 (2011)CrossRefGoogle Scholar
  9. Engelage, D.: Essays on Multiple Priors, Ph.D. thesis, Bonn Graduate School of Economics, Bonn (2009)Google Scholar
  10. Epstein, L., Schneider, M.: IID: independently and indistinguishably distributed. J. Econ. Theory 113(1), 32–50 (2003)CrossRefGoogle Scholar
  11. Epstein, L., Schneider, M.: Recursive multiple priors. J. Econ. Theory 113, 1–31 (2003)CrossRefGoogle Scholar
  12. Ferguson, T.: Optimal Stopping and Applications, Electronic Text. http://www.math.ucla.edu/~tom/Stopping/Contents.html, University of California, Los Angeles (2006)
  13. Ferguson, T.S.: Who solved the secretary problem? Stat. Sci. 4(3), 282–289 (1989)CrossRefGoogle Scholar
  14. Freeman, P.: The secretary problem and its extensions—a review. Int. Stat. Rev. 51, 189–206 (1983)CrossRefGoogle Scholar
  15. Gardner, M.: Scientific American (1960)Google Scholar
  16. Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18, 141–153 (1989)CrossRefGoogle Scholar
  17. Nishimura, K.G., Ozaki, H.: Irreversible investment and Knightian uncertainty. J. Econ. Theory 136, 668–694 (2007)CrossRefGoogle Scholar
  18. Presman, E., Sonin, I.: Equilibrium points in a game related to the best choice problem. Theory Probab. Appl. 20, 770–781 (1975)CrossRefGoogle Scholar
  19. Riedel, F.: Optimal stopping with multiple priors. Econometrica 77, 857–908 (2009)CrossRefGoogle Scholar
  20. Seale, D., Rapoport, A.: Sequential decision making with relative ranks: an experimental investigation of the secretary problem. Organ. Behav. Hum. Decis. Process. 69, 221–236 (1997)CrossRefGoogle Scholar
  21. Todd, P.: Searching for the Next Best Mate. Center for Adaptive Behavior and Cognition, Munich University, Working Paper (2009)Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute of Mathematical EconomicsBielefeld UniversityBielefeldGermany
  2. 2.ORFE, Princeton UniversityPrincetonUSA

Personalised recommendations