  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.
