Analysis (b) can't possibly be right, because Alice's actions ought to depend on the actions of Bob. No amount of logical perfection can force Bob to play Cooperate, so Alice is effectively reasoning herself into a hole.

Analysis (a) is correct if, in fact, Bob is the sort of person that will always play Defect.

In fact, it's pretty clear what the optimal algorithm for Alice is: she should cooperate iff she predicts that Bob will cooperate in response. (Well, she should also defect if she predicts that Bob will cooperate in response to a defection, but that's stupid.)

Bob is the only one whose actions could be expressed as an acausal trade. He wants Alice to predict that he will cooperate, because otherwise Alice will defect and they both end up with the (D,D) payouts. He can obtain this by being the sort of person who cooperates in response to cooperation; but this comes at the cost of missing out on his (C,D) payout. This is still worthwhile if Bob tends to play lots of one-shot prisoner dilemmas with people that can see the future.