Consensus on Social Graphs under Increasing Peer Pressure

In this paper, we present a novel generalized framework for expressing peer influence dynamics over time in a set of connected individuals, or agents. The proposed framework supports the representation of individual variability through parametrization accounting for differences in susceptibility to peer influence and pairwise relationship strengths. Modeling agents' opinions and behaviors as strategies changing discretely and simultaneously, we formally describe the evolution of strategies in a social network as the composition of contraction maps. We identify points of convergence and analyze these points under various conditions.