The e-mail game phenomenon

•We define strategic discontinuity for types.•It generalizes Rubinsteinʼs e-mail-game argument.•Most economic types display strategic discontinuity in simple games.•Some types display strategic discontinuity only in complicated games.

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 that almost all types involved in economic analysis - types in finite or common-prior models - display strategic discontinuity in simple games.