Robust multiplicity with (transfinitely) vanishing naiveté

  • Aviad HeifetzEmail author
Original Paper


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.


k-level reasoning Robust multiplicity Rationalizability 



  1. Billingsley P (1968) Convergence of probability measures. Wiley, New YorkGoogle Scholar
  2. Bosch-Domènech A, Montalvo J, Nagel R, Satorra A (2002) One, two, (three), infinity,. : newspaper and lab beauty-contest experiments. Am Econ Rev 92(5):1687–1701CrossRefGoogle Scholar
  3. Carlsson H, van Damme E (1993) Global games and equilibrium selection. Econometrica 61:989–1018CrossRefGoogle Scholar
  4. Chen Y, Di Tillio A, Faingold E, Xiong S (2010) Uniform topologies on types. Theor Econ 5:445–479CrossRefGoogle Scholar
  5. Chen Y, Takahashi S, Xiong S (2014) The Weinstein–Yildiz critique and robust predictions with arbitrary payoff uncertainty, MimeoGoogle Scholar
  6. Chen Y, Di Tillio A, Faingold E, Xiong S (2017) Characterizing the strategic impact of misspecified beliefs. Rev Econ Stud 84:1424–1471Google Scholar
  7. Dekel E, Fudenberg D, Morris S (2006) Topologies on types. Theor Econ 1:175–209Google Scholar
  8. Dekel E, Fudenberg D, Morris S (2007) Interim correlated rationalizability. Theor Econ 2:15–40Google Scholar
  9. Frankel D, Morris S, Pauzner A (2003) Equilibrium selection in global games with strategic complementarities. J Econ Theory 108:1–44CrossRefGoogle Scholar
  10. Germano F, Weinstein J, Zuazo-Garin P (2017) Uncertain rationality, depth of reasoning and robustness in games with incomplete information, MimeoGoogle Scholar
  11. Harrison R, Jara P (2015) A dominance solvable global game with strategic substitutes. J Math Econ 57:111CrossRefGoogle Scholar
  12. Heifetz A (1993) The Bayesian formulation of incomplete information—the non-compact case. Int J Game Theory 21:329–338CrossRefGoogle Scholar
  13. Heifetz A, Kets W (2018) Robust multiplicity with a grain of Naiveté. Theor Econ 18:415–465CrossRefGoogle Scholar
  14. Jech TJ (2003) Set theory—the third millennium edition. Springer, BerlinGoogle Scholar
  15. Mertens JF, Zamir S (1985) Formulation of Bayesian analysis for games with incomplete information. Int J Game Theory 14:1–29CrossRefGoogle Scholar
  16. Morris S, Shin H, Yildiz M (2016) Common belief foundations of global games. J Econ Theory 163:826–848CrossRefGoogle Scholar
  17. Penta A (2013) On the structure of rationalizability for arbitrary spaces of uncertainty. Theor Econ 8:405–430CrossRefGoogle Scholar
  18. Simmons H (2008) Fruitful and helpful ordinal functions. Arch Math Logic 47(7):677–709CrossRefGoogle Scholar
  19. Takeuti G (1987) Proof theory, 2nd ed. North HollandGoogle Scholar
  20. Weinstein J, Yildiz M (2007) A structure theorem for rationalizability with application to robust predictions of refinements. Econometrica 75:365–400CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Management and EconomicsOpen University of IsraelRaananaIsrael

Personalised recommendations