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Open AccessArticle

When Do Types Induce the Same Belief Hierarchy?

1
EpiCenter and Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
2
MEDS, Kellogg School of Management, Northwestern University, Evanston, IL 60208-2001, USA
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Author to whom correspondence should be addressed.
Academic Editor: Paul Weirich
Games 2016, 7(4), 28; https://doi.org/10.3390/g7040028
Received: 22 August 2016 / Revised: 29 September 2016 / Accepted: 30 September 2016 / Published: 9 October 2016
(This article belongs to the Special Issue Epistemic Game Theory and Logic)
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. View Full-Text
Keywords: types; belief hierarchies; epistemic game theory; morphisms types; belief hierarchies; epistemic game theory; morphisms
MDPI and ACS Style

Perea, A.; Kets, W. When Do Types Induce the Same Belief Hierarchy? Games 2016, 7, 28.

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