A stochastic interactive model for the diffusion of information

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Abstract
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.

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