OK, this is off-topic, but why do people stop there? Why not ‘I always cooperate with agents I know will cooperate with me iff I cooperate iff they cooperate’, and so on? These are not equivalent.
Incidentally, in classical logic, I cooperate iff (you cooperate iff (I cooperate iff you cooperate)) is always true. (But we don't really have that here, because the modal operator ‘I know’ interferes.)
People stop there because going further starts hurting instead of helping. The PD payoff matrix implies that I want to avoid cooperating if I can, but it's more important that I get you to cooperate, even if in order to do that, I have to cooperate. Adding more restrictions on your reasons for cooperating can't make the outcome better for me, I only care that you do it.
Update: This post has also been superseded - new comments belong in the latest thread.
The second thread has now also exceeded 500 comments, so after 42 chapters of MoR it's time for a new thread.
From the first thread: