Hierarchies of Beliefs and Common Knowledge

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 chapter provides an elementary construction, complementary to the construction already given in the paper by Mertens and Zamir (1985), 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.