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Common belief and common knowledge

Authors
Journal
Journal of Mathematical Economics
0304-4068
Publisher
Elsevier
Publication Date
Volume
22
Issue
5
Identifiers
DOI: 10.1016/0304-4068(93)90039-n

Abstract

Abstract In the universal belief space [Mertens and Zamir (1985)] which incorporated all situations of incomplete information concerning a state space S, we define a ‘knowledge operator’ in terms of beliefs. From this operator we derive (in the usual way) the concept of common knowledge and the result is: An event E is common knowledge if and only if it is a belief subspace. Recalling that any game model, with complete or incomplete information, is a belief subspace, this result may be regarded as a considerable weakening of the common knowledge assumption that is: If we adopt the universal belief space as a general framework model for incomplete information games, then the statement ‘the game (i.e. the belief subspace) is Common Knowledge’ is a formal provable statement within the model. Since a belief subspace may or may not be consistent (in Harsanyi's sense), it follows that with this definition, and unlike in Aumann's model, players may agree to disagree.

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