Iterated Expectations, Compact Spaces, and Common Priors
AbstractExtending to infinite state spaces that are compact metric spaces a result previously attained by D. Samet solely in the context of finite state spaces, a necessary and suficient 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 Cesaro means of 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 compactness is a necessary condition for some of the results.
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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp522.
Length: 16 pages
Date of creation: Oct 2009
Date of revision:
Publication status: Published in Games and Economic Behavior, 72 (2011) 163 – 171.
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.
- Hellman, Ziv, 2007. "Iterated Expectations, Compact Spaces and Common Priors," MPRA Paper 3794, University Library of Munich, Germany.
- 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-2009-10-31 (All new papers)
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