Rationalization and incomplete information

We analyze a family of extensive-form solution procedures for games with incomplete information that do not require the specification of an epistemic type space a la Harsanyi, but can accommodate a (commonly known) collection of explicit restrictions D on first-order beliefs. For any fixed D we obtain a solution called D-rationalizability. In static games, D-rationalizability characterizes the set of outcomes (combinations of payoff types and strategies) that may occur in any Bayesian equilibrium model consistent with D: these are precisely the outcomes consistent with common certainty of rationality and of the restrictions D. Hence, our approach to the analysis of incomplete- information games is consistent with Harsanyi's, and it may be viewed as capturing the robust implications of Bayesian equilibrium analysis. In dynamic games, D-rationalizability yields a forward-induction refinement of this set of Bayesian equilibrium outcomes. Focusing on the restriction that first-order beliefs be consistent with a given distribution on terminal nodes, we obtain a refinement of self-confirming equilibrium. In signalling games, this refinement coincides with the Iterated Intuitive Criterion.