“If I find a proof that the other player cooperates with me, cooperate, otherwise defect”
This would cooperate with CooperateBot (algorithm that unconditionally says “Cooperate”).
Yes. The one I described is the one the paper calls FairBot. It also defines PrudentBot, which looks for a proof that the other player cooperates with PrudentBot and a proof that it defects against DefectBot. PrudentBot defects against CooperateBot.
This would cooperate with CooperateBot (algorithm that unconditionally says “Cooperate”).
Yes. The one I described is the one the paper calls FairBot. It also defines PrudentBot, which looks for a proof that the other player cooperates with PrudentBot and a proof that it defects against DefectBot. PrudentBot defects against CooperateBot.