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Beliefs Revealed in Bayesian-Nash Equilibrium

Standard belief hierarchies are an insufficient description of uncertainty for the BayesianNash Equilibrium (BNE) solution concept. Two states with the same belief hierarchy profile may have different sets of BNE action profiles, for many games. We construct new hierarchy profiles with explicit beliefs about payoff irrelevant signals. We show that BNE can be described within those hierarchy profiles and is characterized by Bayesian rationality conditions. We also show that those hierarchy profiles are minimal, revealed by the BNE play, in the following sense: if any two states differ on them, then there is a game for which they have different sets of BNE action profiles.