A Homeomorphism Theorem for the Universal Type Space with the Uniform Topology

Martin Hellwig

No 2016_17, Discussion Paper Series of the Max Planck Institute for Research on Collective Goods from Max Planck Institute for Research on Collective Goods

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.

Keywords: incomplete information; universal type space; uniform weak topology; uniform strategic topology; homeomorphism theorem (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
Date: 2016-11, Revised 2022-07
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.coll.mpg.de/pdf_dat/2016_17online.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:mpg:wpaper:2016_17

Access Statistics for this paper

More papers in Discussion Paper Series of the Max Planck Institute for Research on Collective Goods from Max Planck Institute for Research on Collective Goods Contact information at EDIRC.
Bibliographic data for series maintained by Marc Martin ().