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Weak assumption and iterative admissibility

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  • Yang, Chih-Chun

Abstract

Brandenburger et al. (2008a) show that rationality and common assumption of rationality (RCAR) is impossible in a complete and continuous type structure. We show, by introducing an alternative notion of assumption, “weak assumption”, that rationality and common weak assumption of rationality (RCWAR) is possible in a complete and continuous type structure. This possibility result provides an epistemic characterization for iterative admissibility.

Suggested Citation

  • Yang, Chih-Chun, 2015. "Weak assumption and iterative admissibility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 87-101.
    • Handle: RePEc:eee:jetheo:v:158:y:2015:i:pa:p:87-101
    DOI: 10.1016/j.jet.2015.03.009
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    References listed on IDEAS

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    1. Keisler, H. Jerome & Lee, Byung Soo, 2011. "Common assumption of rationality," MPRA Paper 34441, University Library of Munich, Germany.
    2. Heifetz, Aviad, 1993. "The Bayesian Formulation of Incomplete Information--The Non-compact Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 329-338.
    3. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    4. Barelli, Paulo & Galanis, Spyros, 2013. "Admissibility and event-rationality," Games and Economic Behavior, Elsevier, vol. 77(1), pages 21-40.
    5. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
    6. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    7. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
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    Citations

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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. Dekel, Eddie & Friedenberg, Amanda & Siniscalchi, Marciano, 2016. "Lexicographic beliefs and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 955-985.
    3. 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.
    4. Burkhard Schipper & Martin Meier & Aviad Heifetz, 2017. "Comprehensive Rationalizability," Working Papers 174, University of California, Davis, Department of Economics.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2019. "Comprehensive rationalizability," Games and Economic Behavior, Elsevier, vol. 116(C), pages 185-202.
    6. Shuige Liu, 2021. "Characterizing permissibility, proper rationalizability, and iterated admissibility by incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 119-148, March.
    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. Lee, Byung Soo, 2016. "A space of lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 16-25.
    9. Lee, Byung Soo, 2016. "Admissibility and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 42-72.
    10. Petri, Henrik, 2020. "Lexicographic probabilities and robustness," Games and Economic Behavior, Elsevier, vol. 122(C), pages 426-439.

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    More about this item

    Keywords

    Iterative admissibility; Weak assumption; Common weak assumption of rationality;
    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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