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Hierarchies of beliefs and common knowledge. (English) Zbl 0773.90109
Summary: 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 by J.-F. Mertens and S. Zamir [Int. J. Game Theory 14, 1-29 (1985; Zbl 0567.90103)] 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.

MSC:
91A99 Game theory
91E99 Mathematical psychology
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