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Robust multiplicity with a grain of naiveté

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  • Heifetz, Aviad

    () (Department of Economics, Open University of Israel)

  • Kets, Willemien

    () (Managerial Economics and Decision Science, Kellogg School of Management, Northwestern University)

Abstract

Rationalizability is a central concept in game theory. Since there may be many rationalizable strategies, applications commonly use refinements to obtain sharp predictions. In an important paper, Weinstein and Yildiz [2007] show that no refinement is robust to perturbations of high-order beliefs. We show that robust refinements do exist if we relax the assumption that all players are unlimited in their reasoning ability. In particular, for a class of models, every strict Bayesian-Nash equilibrium is robust. In these environments, a researcher interested in making sharp predictions can use refinements to select among the strict equilibria of the game, and these predictions will be robust.

Suggested Citation

  • Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society, vol. 13(1), January.
  • Handle: RePEc:the:publsh:2098
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    References listed on IDEAS

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    Cited by:

    1. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society, vol. 13(1), January.
    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. 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.
    4. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    5. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    6. Andrés Perea & Willemien Kets, 2016. "When Do Types Induce the Same Belief Hierarchy?," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-17, October.
    7. Kota Murayama, 2020. "Robust predictions under finite depth of reasoning," The Japanese Economic Review, Springer, vol. 71(1), pages 59-84, January.
    8. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.

    More about this item

    Keywords

    Robustness; games with incomplete information; rationalizability; finite depth of reasoning; higher-order beliefs; level-k models; global games; refinements;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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