Dynamic consistency in incomplete information games under ambiguity

• We provide a novel game model that generalizes Bayesian games to include ambiguity.
• We characterize some basic properties of the proposed ex ante and interim solutions.
• We show that the proposed solutions may lead to completely different optimal plays.
• We identify a sufficient condition for dynamic consistency in the current framework.

We develop a general framework of incomplete information games under ambiguity which extends the traditional framework of Bayesian games to the context of Ellsberg-type ambiguity. We then propose new solution concepts called ex ante and interim Γ-maximin equilibrium for solving such games. We show that, unlike the standard notion of Bayesian Nash equilibrium, these concepts may lead to rather different recommendations for the same game under ambiguity. This phenomenon is often referred to as dynamic inconsistency. Moreover, we characterize the sufficient condition under which dynamic consistency is assured in this generalized framework.