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The Equivalence of the Dekel-Fudenberg Iterative Procedure and Weakly Perfect Rationalizability

Author

Listed:
  • P. Jean-Jacques Herings

    (Dept. Econometrics & Center, Tilburg Univ.)

  • Vincent J. Vannetelbosch

    (IEP, Basque Country University)

Abstract

Two approaches have been proposed in the literature to refine the rationalizability solution concept: either assuming that players make small errors when playing their strategies, or assuming that there is a small amount of payoff uncertainty. We show that both approaches lead to the same refinement if errors are made according to the concept of weakly perfect rationalizability, and there is payoff uncertainty as in Dekel and Fudenberg [Journal of Economic Theory 52 (1990), 243-267]. For both cases, the strategies that survive are obtained by starting with one round of elimination of weakly dominated strategies followed by many rounds of elimination of strictly dominated strategies.

Suggested Citation

  • P. Jean-Jacques Herings & Vincent J. Vannetelbosch, 1998. "The Equivalence of the Dekel-Fudenberg Iterative Procedure and Weakly Perfect Rationalizability," Cowles Foundation Discussion Papers 1173, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1173
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    References listed on IDEAS

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    9. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Stephen Morris & Satoru Takahashi & Olivier Tercieux, 2012. "Robust Rationalizability Under Almost Common Certainty Of Payoffs," The Japanese Economic Review, Japanese Economic Association, vol. 63(1), pages 57-67, March.
    2. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    3. Mauleon, Ana & Vannetelbosch, Vincent, 2004. "Bargaining with endogenous deadlines," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 321-335, July.
    4. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    5. Gilles Grandjean & Ana Mauleon & Vincent Vannetelbosch, 2017. "Strongly rational sets for normal-form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 35-46, April.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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