Communication and coordination in social networks

I model people in a coordination game who use a communication network to tell each other their willingness to participate. The minimal sufficient networks for coordination can be interpreted as placing people into a hierarchy of social roles or "stages": "initial adopters", then "followers", and so on down to "late adopters". A communication network helps coordination in exactly two ways: by informing each stage about earlier stages, and by creating common knowledge within each stage. We then consider two examples: first we show that "low dimensional" networks can be better for coordination even though they have far fewer links than "high dimensional" networks; second we show that wide dispersion of "insurgents",:people predisposed toward participation, can be good for coordination but too much dispersion can be bad.