No, my (admittedly nonexpert) understanding is that cooperation emerges from games of strategic self-interest only when the players suspect the repetitions could be indefinite, as in infinite. Only then would there be no final benefit from betraying the opponent since the opponent would always have the chance to retaliate and to even the score. Only then does betrayal become pointless. But that takes game theory into theology since only a supernatural domain could conduct an infinite series of prisoners' dilemmas.

I'm not arguing that morality doesn't exist or that it didn't evolve. So that's a red herring.

It would also be fallacious to argue that because capitalist countries are more cooperative than noncapitalist ones, therefore capitalism is necessarily the cause of the cooperation. There could be another factor, such as the Judeo-Christian background in which capitalism emerged from Protestant Europe. Or the increased cooperation could be a side-effect of First World wealth which was obtained not just by "free markets" but by Northern imperialism (European and American economic exploitation of weaker countries).