Theoretical and computational characterizations of interaction mechanisms on Facebook dynamics using a common knowledge model

Web-based interactions enable agents to coordinate and generate collective action. Coordination can facilitate the spread of contagion to large groups within networked populations. In game theoretic contexts, coordination requires that agents share common knowledge about each other. Common knowledge emerges within a group when each member knows the states and the thresholds (preferences) of the other members, and critically, each member knows that everyone else has this information. Hence, these models of common knowledge and coordination on communication networks are fundamentally different from influence-based unilateral contagion models, such as those devised by Granovetter and Centola. Moreover, these models utilize different mechanisms for driving contagion. We evaluate three mechanisms of a common knowledge model that can represent web-based communication among groups of people on Facebook, using nine social (media) networks. We provide theoretical results indicating the intractability in identifying all node-maximal bicliques in a network, which is the characterizing network structure that produces common knowledge. Bicliques are required for model execution. We also show that one of the mechanisms (named PD2) dominates another mechanism (named ND2). Using simulations, we compute the spread of contagion on these networks in the Facebook model and demonstrate that different mechanisms can produce widely varying behaviors in terms of the extent of the spread and the speed of contagion transmission. We also quantify, through the fraction of nodes acquiring contagion, differences in the effects of the ND2 and PD2 mechanisms, which depend on network structure and other simulation inputs.