Hierarchies of beliefs and common knowledge

Adam Brandenburger, Eddie Dekel

Research output: Contribution to journalArticlepeer-review


Game-theoretic analysis often leads to consideration of an infinite hierarchy of beliefs for each player. Harsanyi suggested that such a hierarchy of beliefs could be summarized in a single entity, called the player’s type. This paper provides an elementary construction, complementary to the construction already given in [J-F. Mertens and S. Zamir, Formulation of Bayesian analysis for games with incomplete information, Int. J. Game Theory14 (1985), 1-29] of Harsanyi’s notion of a type. It is shown that if a player’s type is coherent then it induces a belief over the types of the other players. Imposing common knowledge of coherency closes the model of beliefs. We go on to discuss the question that often arises as to the sense in which the structure of a game-theoretic model is, or can be assumed to be, common knowledge. Journal of Economic Literature Classification Number: 026.

Original languageEnglish
Pages (from-to)189-198
Number of pages10
JournalJournal of Economic Theory
Issue number1
StatePublished - Feb 1993
Externally publishedYes


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