We present and study a model of cultural transmission of social norms in a setting where agents are repeatedly matched to play a one-shot interaction prisoners’ dilemma. There are two types of agents in the society: some that adhere to a social norm of cooperation and some that do not. Limited integration of these two types can bias the matching structure in the sense that types interact with increased probability among themselves. In contrast to many standard evolutionary approaches, we find that cooperation often survives in the long-run. Specifically we find that while high degrees of separation are needed to protect strict norms for cooperation, norms of intermediate strength can survive in a variety of settings. Endogenizing norm strength, we find two scenarios in which pro-social norms survive. One is a rigid society in which separation leads to equilibria with strict norms for cooperation, and one is an integrated society where equilibria display heterogeneity of types and norms of intermediate strength. Furthermore integration and cooperation are not linked in a monotone way.