Collective Action Through Common Knowledge Using a Facebook Model

We develop a dynamic game-theoretic model of information (contagion) propagation using a Facebook-type of communication. The model accounts for information posted on a member's wall or timeline by her friends, which can be read by all friends. This communication facilitates coordination by creating common knowledge among users. We illustrate subtle features of the model, which generalize a host of influence-based contagion mechanisms, and prove characteristics of its dynamics. We show that a complete bipartite graph within a certain group of agents is a necessary and sufficient condition for common knowledge of relevant information to arise among that group's members. Finally, we illustrate the behavior of our model through simulation, and compare it to the classic diffusion model and Chwe's model of common knowledge, using a real Facebook network, a high school social network and a friendship network.