Abstract To understand how interpersonal agreements can be generated within complexly differentiated social systems, we develop an agent-based computational model of negotiation in which social influence plays a key role in the attainment of social and cognitive integration. The model reflects a view of social influence that is predicated on the interactions among such factors as the agents’ cognition, their abilities to initiate and maintain social behaviour, as well as the structural patterns of social relations in which influence unfolds. Findings from a set of computer simulations of the model show that the degree to which agents are influenced depends on the network of relations in which they are located, on the order in which interactions occur, and on the type of information that these interactions convey. We also find that a fundamental role in explaining influence is played by how inclined the agents are to be conciliatory with each other, how accurate their beliefs are, and how self-confident they are in dealing with their social interactions. Moreover, the model provides insights into the trade-offs typically involved in the exercise of social influence.