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.
The first draft of the 2012 Less Wrong Census/Survey is complete (see 2011 here). I will link it below if you promise not to try to take the survey because it's not done yet and this is just an example!
2012 Less Wrong Census/Survey Draft
I want three things from you.
First, please critique this draft. Tell me if any questions are unclear, misleading, offensive, confusing, or stupid. Tell me if the survey is so unbearably long that you would never possibly take it. Tell me if anything needs to be rephrased.
Second, I am willing to include any question you want in the Super Extra Bonus Questions section, as long as it is not offensive, super-long-and-involved, or really dumb. Please post any questions you want there. Please be specific - not "Ask something about abortion" but give the exact question you want me to ask as well as all answer choices.
Try not to add more than five or so questions per person, unless you're sure yours are really interesting. Please also don't add any questions that aren't very easily sort-able by a computer program like SPSS unless you can commit to sorting the answers yourself.
Third, please suggest a decent, quick, and at least somewhat accurate Internet IQ test I can stick in a new section, Unreasonably Long Bonus Questions.
I will probably post the survey to Main and officially open it for responses sometime early next week.