There's a very beautiful reason why it's unintuitive (as a special case, it also explains why the PD itself is unintuitive): in real life, there is always another iteration
. To understand this assertion, one must consider the "Environment of Evolutionary Adaptedness". During most of the period that is relevant to our current evolutionary make up, we lived in small tribes of around 100 or so. In such a context, there are no one-time encounters. Therefore, we never evolved a mechanism for subconsious (intuitive) reasoning about finite iteration games.
This last statement requires an explanation. It turns out that we reason about logical propositions by turning them into games in our head. Thus, even if the IPD is presented in an abstract manner, we interpret it in a tribal context. To prove this, Cosmides and Tooby performed a brilliant experiment in which they asked test subjects to evaluate a simple boolean formulas (IIRC, something that would simplify with a single application of De Morgan's laws). Lacking mathematical sophistication, the test subjects mostly failed. When given the same formula, however, with the variable names and relations replaced by "Alice", "cheated on", "Bob" and so on, not only did they succeed, their answers were so instantaneous as to have been necessarily subconscious.
I might have mangled some details of the experiment, but that's essentially it. To me it is one of the best science experiments ever.
Actually, the above explanation also solves the paradox of the Ultimatum game
, and it doesn't seem to have been proposed yet. Maybe I should write a paper on it :)