AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties

We provide a general notion of perfect Bayesian equilibrium which can be applied to arbitrary extensive-form games and is intermediate between subgame-perfect equilibrium and sequential equilibrium. The essential ingredient of the proposed definition is the qualitative notion of AGM-consistency, which has an epistemic justification based on the theory of belief revision introduced by Alchourrón, Gärdenfors and Makinson. AGM-consistency is a generalization of the notion of consistency introduced by Kreps and Wilson as part of the definition of sequential equilibrium.