A stochastic interactive model for the diffusion of information

Two important generalizations of information diffusion models are the presence of stochastic effects and the possibility of arbitrary patterns of influence among individuals. A Markov random fields model includes both of these features. Under very weak assumptions, there is a unique equilibrium distribution of information patterns for given stochastic (local) interactions among a finite population. This has implications for policies to influence the transmission of information. The dynamic behavior of a special and simple case of the model tends to approximate the standard (logistic) diffusion curve. For an infinite population, uniqueness of equilibrium distributions may fail; some sufficient conditions to ensure uniqueness are given.