Iterated Expectations, Compact Spaces and Common Priors

Ziv Hellman ()

MPRA Paper from University Library of Munich, Germany

Abstract: Extending to infinite state spaces that are compact metric spaces a result previously attained by Dov Samet solely in the context of finite state spaces, a necessary and sufficient condition for the existence of a common prior for several players is given in terms of the players’ present beliefs only. A common prior exists if and only if for each random variable it is common knowledge that all its iterated expectations with respect to any permutation converge to the same value; this value is its expectation with respect to the common prior. It is further shown that the restriction to compact metric spaces is ‘natural’ when semantic type spaces are derived from syntactic models, and that compactness is a necessary condition. Many proofs are based on results from the theory of Markov chains.

Keywords: common priors; Markov chains; type spaces; iterated expectations (search for similar items in EconPapers)
JEL-codes: C70 D82 (search for similar items in EconPapers)
Date: 2007-06-07
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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https://mpra.ub.uni-muenchen.de/3794/1/MPRA_paper_3794.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/8733/1/MPRA_paper_8733.pdf revised version (application/pdf)

Related works:
Journal Article: Iterated expectations, compact spaces, and common priors (2011)
Working Paper: Iterated Expectations, Compact Spaces, and Common Priors (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:3794

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