A homeomorphism theorem for the universal type space with the uniform topology

Hellwig, Martin

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A homeomorphism theorem for the universal type space with the uniform topology

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Hellwig, Martin
Max Planck Institute for Research on Collective Goods, Max Planck Society;

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Hellwig, M. (2016). A homeomorphism theorem for the universal type space with the uniform topology.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-BC8A-A

Abstract

The paper shows that the Mertens-Zamir (1985) reconciliation of belief hierarchy and type space models of incomplete information is robust to the requirement that the topology on belief hierarchies reflect the continuity properties of strategic behaviour, taking account of the fact that beliefs of arbitrarily high orders in agents.belief hierarchies can have a signi.cant impact on strategic behaviour. When endowed with one of the .ner topologies proposed by Fudenberg et al. (2006) and Chen et al. (2010, 2017), the space of belief hierarchies is still homeomorphic to the space of probability measures (beliefs) over exogenous data and other agents.belief hierarchies. The canonical mapping from nonredundant abstract type spaces with continuous belief functions to the space of belief hierarchies is an embedding if the range of belief functions has the topology of convergence in total variation.