Although the abstraction of a world that continues indefinitely is a useful device, modeling individuals as infinitely lived is less attractive. It seems important to inquire, then, into the possibilities of self-enforcing agreements amongst finitely lived agents in an infinite horizon world.
...
In an overlapping generations model, suppose that society acknowledges that in the final three periods of his life, say, no individual will act cooperatively. Hence, selfish behavior by the aged is part of the implicit agreement. But, if any young person fails to cooperate, the accord is broken and everyone subsequently optimizes myopically. Young person will choose not to defect, because they would lose the benefits of social cooperation for the rest of their lives. Folk theorems similar to those discussed earlier hold here, and Kandori (1992) shows that, if successive individuals are born far enough apart in time, there is no need to invoke any full dimension restriction. Recall that this assumption is usually made to ensure that punishers can be rewarded for minimaxing a defector, without incidentally also rewarding the defector himself. In Kandori's construction, the punishers wait until the defector dies, and then celebrate their earlier self-discipline.

(Pearce (1992), p.148-9)

References

Kandori (1992) "Repeated Games Played by Overlapping Generations of Players" RES, 59-1
Pearce (1992) "Repeated games: cooperation and rationality" in Advances in economic theory