Affordable Access

Publisher Website

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.

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Knowledge and beliefs about common eye diseases.

on Australian and New Zealand jou... November 1997

Hierarchies of Beliefs and Common Knowledge

on Journal of Economic Theory Jan 01, 1993

Knowledge and beliefs about common eye diseases.

on Australian and New Zealand jou... November 1997
More articles like this..