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Higher Order Uncertainty and Information: Static and Dynamic Games

Antonio Penta

Abstract

Weinstein and Yildiz (2007) have shown that in static games, only very weak predictions are robust to perturbations of higher order beliefs. These predictions are precisely those provided by interim correlated rationalizability (ICR). This negative result is obtained under the assumption that agents have no information on payoffs. This assumption is unnatural in many settings. It is therefore natural to ask whether Weinstein and Yildiz's results remain true under more general information structures. This paper characterizes the "robust predictions“ in static and dynamic games, under arbitrary information structures. This characterization is provided by an extensive form solution concept: interim sequential rationalizability (ISR). In static games, ISR coincides with ICR and does not depend on the assumptions on agents' information. Hence the "no information“ assumption entails no loss of generality in these settings. This is not the case in dynamic games, where ISR refines ICR and depends on the details of the information structure. In these settings, the robust predictions depend on the assumptions on agents' information. This reveals a hitherto neglected interaction between information and higher order uncertainty, raising novel questions of robustness.