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

• DOI: 10.1007/s00182-011-0296-4
• Publication Date: 2011-07-26T07:31:25Z
• Authors: Giacomo Bonanno
• Keywords: Subgame perfect equilibrium; Sequential equilibrium; Markov perfect equilibrium; Subgame; Extensive-form game; Bayesian game

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 Alchourron, Gardenfors 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.