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On the Structure of Rationalizability for Arbitrary Spaces of Uncertainty

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  • Antonio Penta

    (Department of Economics, University of Pennsylvania)

Abstract

This note characterizes the set A¡∞ of actions of player ¡ that are uniquely rationalizable for some hierarchy of beliefs on an arbitrary space of uncertainty. It is proved that for any rationalizable action a¡ for the type t¡, if a¡ belongs to A¡∞ and is justified by conjectures concentrated on A-¡∞, then there exists a sequence of types converging to t¡ for which a¡ is uniquely rationalizable.

Suggested Citation

  • Antonio Penta, 2008. "On the Structure of Rationalizability for Arbitrary Spaces of Uncertainty," PIER Working Paper Archive 09-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 05 Jun 2008.
    • Handle: RePEc:pen:papers:09-021
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    References listed on IDEAS

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    9. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, March.
    10. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
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    14. Chen, Yi-Chun, 2012. "A structure theorem for rationalizability in the normal form of dynamic games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 587-597.
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    Citations

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    Cited by:

    1. Antonio Penta & Peio Zuazo-Garin, 2022. "Rationalizability, Observability, and Common Knowledge [Player Importance and Forward Induction]," Review of Economic Studies, Oxford University Press, vol. 89(2), pages 948-975.
    2. Aviad Heifetz, 2019. "Robust multiplicity with (transfinitely) vanishing naiveté," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1277-1296, December.
    3. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    4. Germano, Fabrizio & Weinstein, Jonathan & Zuazo-Garin, Peio, 2020. "Uncertain rationality, depth of reasoning and robustness in games with incomplete information," Theoretical Economics, Econometric Society, vol. 15(1), January.
    5. Weinstein, Jonathan & Yildiz, Muhamet, 2011. "Sensitivity of equilibrium behavior to higher-order beliefs in nice games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 288-300, May.
    6. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    7. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2022. "Robust refinement of rationalizability with arbitrary payoff uncertainty," Games and Economic Behavior, Elsevier, vol. 136(C), pages 485-504.
    8. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society, vol. 13(1), January.
    9. Mariann Ollár & Antonio Penta, 2019. "Implementation via transfers with identical but unknown distributions," Economics Working Papers 1676, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Fabrizio Germano & Peio Zuazo-Garin, 2015. "Uncertain rationality and robustness in games with incomplete information," Economics Working Papers 1470, Department of Economics and Business, Universitat Pompeu Fabra.
    11. Oury, Marion, 2015. "Continuous implementation with local payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 656-677.
    12. Safronov, Mikhail, 2018. "Coalition-proof full efficient implementation," Journal of Economic Theory, Elsevier, vol. 177(C), pages 659-677.

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    More about this item

    Keywords

    Rationalizability; incomplete information; robustness; refinement; higher order beliefs; dominance solvability; richness;
    All these keywords.

    JEL classification:

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

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