When do types induce the same belief hierarchy?

Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mappe...

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Bibliographic Details
Published in:Games 2016-12, Vol.7 (4), p.1-17
Main Authors: Perea, Andrés, Kets, Willemien
Format: Article
Language:English
Subjects:
belief hierarchies
Devices
epistemic game theory
Games
Hierarchies
morphisms
types
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Summary:Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a hierarchy morphism and vice versa. Importantly, generalized type morphisms do not make reference to belief hierarchies. We use our results to characterize the conditions under which types generate the same belief hierarchy.
ISSN:2073-4336
2073-4336
DOI:10.3390/g7040028