Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/97243 
Year of Publication: 
2012
Series/Report no.: 
Discussion Paper No. 1550
Publisher: 
Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, Evanston, IL
Abstract: 
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 naiveté suffices to overturn the classical uniqueness results in that literature.
Subjects: 
Level-k models
cognitive hierarchy models
universal type space
global games
Level-k models
cognitive hierarchy models
universal type space
global games
JEL: 
C70
C72
D80
D83
Document Type: 
Working Paper

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