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Robust multiplicity with (transfinitely) vanishing naiveté

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  • Aviad Heifetz

    () (Open University of Israel)

Abstract

We extend significantly a result in Heifetz and Kets (Theor Econ 18:415–465, 2018) for Carlsson and van Damme’s (Econometrica 61:989–1018, 1993) global games by which even slight deviations from common belief in infinite depth of reasoning restore the robustness of rationalizable actions multiplicity, in contrast with the intriguing findings of Weinstein and Yildiz (Econometrica 75:365–400, 2007) under an idealized lack of such deviations. Here we show that multiplicity of rationalizable actions is a robust phenomenon even if finite depth of reasoning is an ‘extremely remote rumor’, where someone suspects that someone suspects (...) that somebody might have a finite depth of reasoning, and where the dots range over a transfinite range.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:48:y:2019:i:4:d:10.1007_s00182-019-00670-8
    DOI: 10.1007/s00182-019-00670-8
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    References listed on IDEAS

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    1. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    2. Harrison, Rodrigo & Jara-Moroni, Pedro, 2015. "A dominance solvable global game with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 1-11.
    3. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society, vol. 13(1), January.
    4. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    5. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," CORE Discussion Papers RP 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. 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.
    7. 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.
    8. Yi-Chun Chen & Alfredo Di Tillio & Eduardo Faingold & Siyang Xiong, 2017. "Characterizing the Strategic Impact of Misspecified Beliefs," Review of Economic Studies, Oxford University Press, vol. 84(4), pages 1424-1471.
    9. Morris, Stephen & Shin, Hyun Song & Yildiz, Muhamet, 2016. "Common belief foundations of global games," Journal of Economic Theory, Elsevier, vol. 163(C), pages 826-848.
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