The e-mail game in Rubinstein (1989) shows that types with arbitrarily close higher-order beliefs may differ substantially in strategic behaviors. We define a notion called strategic discontinuity in arbitrary incomplete-information scenarios to generalize this e-mail game phenomenon. We show...

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...

We prove that the type structure constructed in [Epstein, L., Wang, T., 1996. 'Belief about belief' without probabilities. Econometrica 64, 1343-1373] is a universal/terminal type structure into which every suitably regular type structure can be embedded. Moreover, it is unique up to a...