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Critical Types


  • Jeffrey C. Ely
  • Marcin Pęski


How can we know in advance whether simplifying assumptions about beliefs will make a difference in the conclusions of game-theoretic models? We define critical types to be types whose rationalizable correspondence is sensitive to assumptions about arbitrarily high-order beliefs. We show that a type is critical if and only if it exhibits common belief in some non-trivial event. We use this characterization to show that all types in commonly used type spaces are critical. On the other hand, we show that regular types (types that are not critical) are generic, although perhaps inconvenient to use in applications. Copyright 2011, Oxford University Press.

Suggested Citation

  • Jeffrey C. Ely & Marcin Pęski, 2011. "Critical Types," Review of Economic Studies, Oxford University Press, vol. 78(3), pages 907-937.
  • Handle: RePEc:oup:restud:v:78:y:2011:i:3:p:907-937

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    Cited by:

    1. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    2. Xiong, Siyang & Chen, Yi-Chun & di Tillio, Alfredo & Faingold, Eduardo, 2010. "Uniform topologies on types," Theoretical Economics, Econometric Society, vol. 5(3), September.
    3. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2014. "The robust selection of rationalizability," Journal of Economic Theory, Elsevier, vol. 151(C), pages 448-475.
    4. Oury, Marion, 2015. "Continuous implementation with local payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 656-677.

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