In interactive contexts such as games and economies, it is important to take account not only of what the players believe about substantive matters (such as payoffs), but also of what they believe about the beliefs of other players. Two different but equivalent ways of dealing with this matter, the semantic and the syntactic, are set forth. Canonical and universal semantic systems are then defined and constructed, and the concepts of common knowledge and common priors formulated and characterized. The last two sections discuss relations with Bayesian games of incomplete information and their applications, and with interactive epistemology -- the theory of multi-agent knowledge and belief as formulated in mathematical logic.
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ReDIF This chapter was published in: R.J. Aumann & S. Hart (ed.) Handbook of Game Theory with Economic Applications, , chapter 43, pages 1665-1686, 2002.
Aumann, Robert J. & Heifetz, Aviad, 2001.
"Incomplete Information,"
Working Papers
1124, California Institute of Technology, Division of the Humanities and Social Sciences.
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