Abstract
In a game with incomplete information, a player may have beliefs about nature, about the other players' beliefs about nature, and so on, in an infinite hierarchy. We generalize a construction of Mertens & Zamir and show, that if nature is any Hausdorff space, and beliefs are regular Borel probability measures, then the space of all such infinite hierarchies of the players is a product of nature and the types of every player, where a type of a player is a belief about nature and the other players' types.
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This work constitutes the main part of my M.Sc. dissertation, and I am grateful to my supervisor, Prof. Dov Samet, for his excellent guidance. I am also indebted to Prof. Shmuel Zamir and Prof. Adam Brandenburger for fruitful discussions.
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Heifetz, A. The bayesian formulation of incomplete information — The non-compact case. Int J Game Theory 21, 329–338 (1993). https://doi.org/10.1007/BF01240148
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DOI: https://doi.org/10.1007/BF01240148