A structure theorem for rationalizability in the normal form of dynamic games

Abstract

We prove that the structure theorem for rationalizability originally from Weinstein and Yildiz (2007) applies to any finite extensive-form game with perfect recall and suitably rich payoffs. We demonstrate that the ties induced by the extensive form do not change the result of Weinstein and Yildiz (2007). Specifically, like Weinstein and Yildiz (2007), we adopt the normal-form concept of interim correlated rationalizability and we assume that players have no relevant knowledge of the extensive-form payoff structure. The extensive-form result is weaker in the sense that while the result of Weinstein and Yildiz (2007) does not depend on the latter assumption, our result does. Our result implies that without restrictions on players' knowledge of payoffs, the dynamic structure of extensive-form games offers no force for robust refinements of rationalizability. We also strengthen the main selection result of Weinstein and Yildiz (2007) by showing that the result holds for any (not necessarily finite) type. © 2012 Elsevier Inc.