Although studies of present-day hunters and foragers cannot be used directly to reconstruct the sociology of our Stone Age ancestors, they can, if combined with the archaeological evidence and supplemented by recent research in evolutionary game theory, be used to answer the question how the original bands of hunters and foragers could cohere over many successive generations without either transitive rank-orders headed by dominant males or institutional roles in which leadership was formally vested. The answer lies neither in natural selection for genes favouring altruistic behaviour, nor in the emergence of an egalitarian morality, but in cultural selection for strong reciprocity sustained by specific pressures from the palaeo-ecological environment.