Iterated Expectations, Compact Spaces and Common Priors
AbstractExtending 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 3794.
Date of creation: 07 Jun 2007
Date of revision:
common priors; Markov chains; type spaces; iterated expectations;
Other versions of this item:
- Hellman, Ziv, 2011. "Iterated expectations, compact spaces, and common priors," Games and Economic Behavior, Elsevier, vol. 72(1), pages 163-171, May.
- Ziv Hellman, 2009. "Iterated Expectations, Compact Spaces, and Common Priors," Discussion Paper Series dp522, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-07-07 (All new papers)
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