The players don't have to be rational. It is interesting to study PD with non-rational players, e.g. when it arose as a model of the nuclear arms race. It's true that the PD also "shows why two purely 'rational' individuals might not cooperate" but that is not part of the defn of PD.
I was not confusing iterated and n-player versions.
I was not confusing iterated and n-player versions.
For a ref, eg http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.... and it gives some further citations.