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In (Bonanno, Int J Game Theory 42:567–592, 2013) a general notion of perfect Bayesian equilibrium (PBE) for extensive-form games was introduced and shown to be intermediate between subgame-perfect equilibrium and sequential equilibrium. Besides sequential rationality, the ingredients of the proposed notion are (1) the existence of a plausibility order on the set of histories that rationalizes the given assessment and (2) the notion of Bayesian consistency relative to the plausibility order. We show that a cardinal property of the plausibility order and a strengthening of the notion of Bayesian consistency provide necessary and sufficient conditions for a PBE to be a sequential equilibrium.

AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium