Human societies are characterised by high degrees of reciprocal altruism between unrelated individuals. It has even been suggested that humans have evolved a cognitive capacity for effective reasoning about social exchange transactions which does not readily generalise to other, non-social reasoning tasks (Cosmides 1989). Explaining the emergence of this capacity for cooperation is one of the fundamental goals of evolutionary anthropology. Some theorists have suggested that repeated interactions in small, stable social groups could have led to such high levels of cooperation in the course of human evolution (Trivers 1971, 1985). Criteria for stable cooperation in such scenarios include repeated interaction, recognition of the identity of individual participants, and memory of the outcomes of previous encounters. However, recent arguments that human social evolution was characterised by a trend towards increased group sizes (Dunbar 1993, Aiello and Dunbar 1993) have complicated matters, since it is generally believed that large group sizes make cooperation unstable. Clearly, our ancestors cannot have been simultaneously undergoing selection for adaptations for cooperative exchange in a small social group context (as argued by Trivers 1971, 1985) and selection for adaptations to maintaining affiliative networks in the context of a very large social group (as argued by Dunbar 1993). These two approaches to the evolution of human social behaviour would seem to be mutually contradictory. In this paper we will show, through computer simulation, that cooperation can evolve as a stable strategy in large social groups, subject to certain constraints. Our

1.� 1999 by The Wenner-Gren Foundation for Anthropological Research. All rights reserved 0011-3204/99/4003-0005 $1.00. We thank Alan Ingham and Denis Nicole for helpful discussion of this work and Rob Boyd, Robin Dunbar, and Brian Molyneaux for comments on drafts of the paper.