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.
Going one step further doesn’t (generally) add restrictions; it just changes them. Consider:
I will cooperate if I know anything.
I will cooperate if I know that you will cooperate.
I will cooperate if I know that you will cooperate iff I cooperate.
I will cooperate if I know that you will cooperate iff I cooperate iff you cooperate.
I will cooperate if I know that you will cooperate iff I cooperate iff you cooperate iff I cooperate.
…
Using classical logic after the modal operator, these reduce to:
I will cooperate if I know anything.
I will cooperate if I know that you will cooperate.
I will cooperate if I know that we will perform the same action.
I will cooperate if I know that I will cooperate.
I will cooperate if I know anything.
… (repeats)
Actually, now that I write it out like this, I can see why one would choose (3)!
It’s important that there’s an ‘if I know that’ instead of an ‘iff’, which I’ve seen before. But the version above is how I parsed WrongBot’s statement, so hopefully WrongBot quoted it correctly. (The search function is not helping me find an original.)
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.
Going one step further doesn’t (generally) add restrictions; it just changes them. Consider:
I will cooperate if I know anything.
I will cooperate if I know that you will cooperate.
I will cooperate if I know that you will cooperate iff I cooperate.
I will cooperate if I know that you will cooperate iff I cooperate iff you cooperate.
I will cooperate if I know that you will cooperate iff I cooperate iff you cooperate iff I cooperate.
…
Using classical logic after the modal operator, these reduce to:
I will cooperate if I know anything.
I will cooperate if I know that you will cooperate.
I will cooperate if I know that we will perform the same action.
I will cooperate if I know that I will cooperate.
I will cooperate if I know anything.
… (repeats)
Actually, now that I write it out like this, I can see why one would choose (3)!
It’s important that there’s an ‘if I know that’ instead of an ‘iff’, which I’ve seen before. But the version above is how I parsed WrongBot’s statement, so hopefully WrongBot quoted it correctly. (The search function is not helping me find an original.)