We analyze a local interaction model where agents play a bilateral prisoner’s dilemma game with their neighbors. Agents learn about behavior through payoff-biased imitation of their interaction neighbors (and possibly some agents beyond this set). We find that the eshel et al. (am econ rev 88:157–179, 1998) result that polymorphic states are stochastically stable in such a setting is not robust. In particular, whenever agents use information also of some agents beyond their interaction neighbors, the unique stable outcome is one where everyone chooses defection. Introducing a sufficiently strong conformist bias into the imitation process, we find that full cooperation always emerges. Conformism is thus identified as a new mechanism that can stabilize cooperation.