International Journal of Game Theory

, Volume 46, Issue 1, pp 1–12 | Cite as

Uncertainty in the traveler’s dilemma

Original Paper
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Abstract

We quantify the sensitivity of the traveler’s dilemma (Basu, Am Econ Rev 84:391–395, 1994) to perturbations from common knowledge. The perturbations entail a small uncertainty about the set of admissible actions. We show that the sensitivity scale is exponential in the range of admissible actions in the traveler’s dilemma. Such rapid growth is consistent with the intuition that a wider range makes the outcome of the traveler’s dilemma less intuitive.

Keywords

Incomplete information Traveler’s dilemma Quantification Exponential sensitivity Perturbation Robustness 

JEL Classification

C72 D82 

References

  1. Aumann RJ (1992) Irrationality in game theory. In: Dasgupta P, Gale D, Hart O, Maskin E (eds) Economic analysis of markets and games: essays in honor of Frank Hahn. MIT Press, Cambridge, pp 214–227Google Scholar
  2. Basu K (1994) The traveler’s dilemma: paradoxes of rationality in game theory. Am Econ Rev 84:391–395Google Scholar
  3. Bavly G (2011) Elasticity of games. In: Discussion paper series, dp592. The Center for the Study of Rationality, Hebrew University, JerusalemGoogle Scholar
  4. Fudenberg D, Maskin E (1986) The folk theorem in repeated games with discounting or with incomplete information. Econometrica 54:533–554CrossRefGoogle Scholar
  5. Kajii A, Morris S (1997a) Refinements and higher order beliefs: a unified survey. Discussion paper 1197. Center for Mathematical Studies in Economics and Management Science, Northwestern University, EvanstonGoogle Scholar
  6. Kajii A, Morris S (1997b) The robustness of equilibria to incomplete information. Econometrica 65:1283–1310Google Scholar
  7. Kreps DM, Milgrom P, Roberts J, Wilson R (1982) Rational cooperation in the finitely repeated prisoners’ dilemma. J Econ Theory 27:245–252CrossRefGoogle Scholar
  8. Neyman A (1999) Cooperation in repeated games when the number of stages is not commonly known. Econometrica 67:45–64CrossRefGoogle Scholar
  9. Rubinstein A (1989) The electronic mail game: strategic behavior under ‘almost common knowledge’. Am Econ Rev 79:385–391Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of EconomicsBar-Ilan UniversityRamat-GanIsrael

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