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Pathologies of iterated strict dominance revisited

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  • Qian, Xuewen
  • Qu, Chen

Abstract

We revisit two pathologies of iterated elimination of strictly dominated strategies (IESDS) in infinite games: spurious Nash equilibria and order dependence. By introducing bounded dominance relations (Hsieh et al., 2023), we demonstrate that a bounded version of IESDS mitigates the former issue and is neutral to the latter. The second point is illustrated through a series of examples using ordinals. We also provide a sufficient and necessary condition for the non-existence of spurious Nash equilibria.

Suggested Citation

  • Qian, Xuewen & Qu, Chen, 2025. "Pathologies of iterated strict dominance revisited," Economics Letters, Elsevier, vol. 247(C).
    • Handle: RePEc:eee:ecolet:v:247:y:2025:i:c:s0165176525000151
    DOI: 10.1016/j.econlet.2025.112178
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    References listed on IDEAS

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    1. Ehud Kalai & Eitan Zemel, 1988. "On The Order of Eliminating Dominated Strategies," Discussion Papers 789, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Hsieh, Yue-Da & Qian, Xuewen & Qu, Chen, 2023. "Iterated bounded dominance," Economics Letters, Elsevier, vol. 232(C).
    3. Martin Dufwenberg & Mark Stegeman, 2002. "Existence and Uniqueness of Maximal Reductions Under Iterated Strict Dominance," Econometrica, Econometric Society, vol. 70(5), pages 2007-2023, September.
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    8. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
    9. Christian Bach & Jérémie Cabessa, 2012. "Common knowledge and limit knowledge," Theory and Decision, Springer, vol. 73(3), pages 423-440, September.
    10. 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.
    11. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    12. Bonanno, Giacomo & Tsakas, Elias, 2018. "Common belief of weak-dominance rationality in strategic-form games: A qualitative analysis," Games and Economic Behavior, Elsevier, vol. 112(C), pages 231-241.
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    Cited by:

    1. Michele Crescenzi, 2025. "Nested Removal of Strictly Dominated Strategies in Infinite Games," Papers 2501.17685, arXiv.org, revised Feb 2025.

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    More about this item

    Keywords

    Strict dominance; Iterated elimination; Nash equilibrium; Boundedness; Forgetfulness-proofness;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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