The Strategic Impact of Higher-Order Beliefs

Previous research has established that the predictions made by game theory about strategic behavior in incomplete information games are quite sensitive to the assumptions made about the players' infinite hierarchies of beliefs. We evaluate the severity of this robustness problem by characterizing conditions on the primitives of the model -- the players’ hierarchies of beliefs -- for the strategic behavior of a given Harsanyi type to be approximated by the strategic behavior of (a sequence of) perturbed types. This amounts to providing characterizations of the strategic topologies of Dekel, Fudenberg, and Morris (2006) in terms of beliefs. We apply our characterizations to a variety of questions concerning robustness to perturbations of higher-order beliefs, including genericity of common priors, and the connections between robustness of strategic behavior and the notion of common p-belief of Monderer and Samet (1989).