You also have to deceive them into believing that you, personally, won't defect. For humans, who almost never really face one-off decision problems, your strategy isn't supposed to work both because the other people shouldn't cooperate for high stakes without having a way of getting the strong knowledge that the opponent will cooperate given that they cooperate (some kind of publicly announced externally controlled commitment), and because you have too few shots at defecting before you get bad reputation.