  New ideas and technologies adopted by a small number of individuals
occasionally spread globally through a complex web of social ties. Here, we
present a simple and general approximation method, namely, a message-passing
approach, that allows us to describe the diffusion processes on complex
networks in an almost exact manner. We consider two classes of binary-action
games in each of which the best pure strategy for individual players is
characterized as a variant of the threshold rule. We show that the dynamics of
diffusion observed on synthetic networks are accurately replicated by the
message-passing equation, whose fixed point corresponds to a Nash equilibrium.
In contrast, the mean-field method tends to overestimate the size and frequency
of diffusion. We extend the framework to analyze multiplex networks in which
social interactions take place in multiple layers.

Physics and Society