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Admissibility and assumption

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  • Lee, Byung Soo

Abstract

Brandenburger et al. (2008) defined the epistemic condition rationality and common assumption of rationality (RCAR) in lexicographic type structures. We define RCAR in the space of coherent lexicographic belief hierarchies and show that it is an epistemic condition for iterated admissibility. We also show that some coherent lexicographic belief hierarchies cannot be represented as types in lexicographic type structures. An advantage of this approach is that RCAR is possible in a canonical hierarchy space.

Suggested Citation

  • Lee, Byung Soo, 2016. "Admissibility and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 42-72.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:42-72
    DOI: 10.1016/j.jet.2016.01.006
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    Cited by:

    1. Geir B. Asheim & Andrés Perea, 2019. "Algorithms for cautious reasoning in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1241-1275, December.
    2. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    3. Burkhard Schipper & Martin Meier & Aviad Heifetz, 2017. "Comprehensive Rationalizability," Working Papers 174, University of California, Davis, Department of Economics.
    4. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    5. Catonini, Emiliano & De Vito, Nicodemo, 2024. "Cautious belief and iterated admissibility," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    6. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    7. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    8. Petri, Henrik, 2020. "Lexicographic probabilities and robustness," Games and Economic Behavior, Elsevier, vol. 122(C), pages 426-439.
    9. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2019. "Comprehensive rationalizability," Games and Economic Behavior, Elsevier, vol. 116(C), pages 185-202.
    10. Keisler, H. Jerome & Lee, Byung Soo, 2023. "Common assumption of rationality," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    11. Dekel, Eddie & Friedenberg, Amanda & Siniscalchi, Marciano, 2016. "Lexicographic beliefs and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 955-985.
    12. Lee, Byung Soo, 2016. "A space of lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 16-25.
    13. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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    More about this item

    Keywords

    Lexicographic probability system; Higher-order beliefs; Coherence; Iterated admissibility; Epistemic game theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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