All types naive and canny

Aviad Heifetz, Willemien Kets

Research output: Working paperDiscussion paper


This paper constructs a type space that contains all types with a finite depth of
reasoning, as well as all types with an infinite depth of reasoning – in particular those types for whom finite-depth types are conceivable, or think that finite depth types are conceivable in the mind of other players, etcetera. We prove that this type space is universal with respect to the class of type spaces that include types with a finite or infinite depth of reasoning. In particular, we show that it contains the standard universal type space of Mertens and Zamir (1985) as a belief-closed subspace, and that this subspace is characterized by common belief of infinite-depth reasoning. This framework allows us to study the robustness of classical results to small deviations from perfect rationality. As an example, we demonstrate that in the global games of Carlsson and van Damme
(1993), a small ‘grain of naivet´e’ suffices to overturn the classical uniqueness results in that literature.
Original languageAmerican English
Place of PublicationKellogg School of Management, Center for Mathematical Studies in Economics and Management Science, Evanston, IL
PublisherNorthwestern University
Number of pages34
StatePublished - 4 Aug 2012

Bibliographical note

Discussion Paper #1550
JEL Classification: C700, C720, D800, D830


  • Level-k models
  • global games
  • universal type space
  • cognitive hierarchy models


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