When Do Types Induce the Same Belief Hierarchy?

A. Perea, Willemien Kets

Research output: Working paperDiscussion paper

Abstract

Type structures are a simple device to describe higher-order beliefs. But 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.
Original languageEnglish (US)
Number of pages25
StatePublished - Dec 13 2015

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Morphism
Morphisms
Higher Order
If and only if
Generalise
Beliefs
Hierarchy

Cite this

Perea, A. ; Kets, Willemien. / When Do Types Induce the Same Belief Hierarchy?. 2015.
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When Do Types Induce the Same Belief Hierarchy? / Perea, A.; Kets, Willemien.

2015.

Research output: Working paperDiscussion paper

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N2 - Type structures are a simple device to describe higher-order beliefs. But 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.

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