Rationalizability in infinite, dynamic games with incomplete information

Abstract

In this paper, we analyze two nested iterative solution procedures for infinite, dynamic games of incomplete information. These procedures do not rely on the specification of a type space à la Harsanyi. Weak rationalizability is characterized by common certainty of rationality at the beginning of the game. Strong rationalizability also incorporates a notion of forward induction. The solutions may take as given some exogenous restrictions on players' conditional beliefs. In dynamic games, strong rationalizability is a refinement of weak rationalizability. Existence, regularity properties, and equivalence with the set of iteratively interim undominated strategies are proved under standard assumptions. The analysis mainly focus on two-player games with observable actions, but we show how to extend it to n-player games with imperfectly observable actions. Finally, we briefly survey some applications of the proposed approach.