Some behaviors, ideas or technologies spread and become persistent in society, whereas others vanish. This paper analyzes the role of social influence in determining such distinct collective outcomes. Agents are assumed to acquire information from others through a certain sampling process, that generates an influence network, and they use simple rules to decide whether to adopt or not depending on the behavior of the observed sample. We characterize, as a function of the primitives of the model, the diffusion threshold (i.e., the spreading rate above which the adoption of the new behavior becomes persistent in the population) and the endemic state (i.e., the fraction of adopters in the stationary state of the dynamics). We find that an increase in the correlation between the out-degree (information level) and in-degree (visibility level) of agents may favor or harm diffusion; the effect actually depends on the specific details of the adoption process.
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