No it's not. What needs to be explained is why you cooperate if you know that you will never play with the same person again. And the answer is that by doing so

No it's not. What needs to be explained is why you cooperate if you know that you will never play with the same person again. And the answer is that by doing so you get in the habit of automatically cooperating in similar situations in the future and other people recognize this habit and trust you.