  The spread of new ideas, behaviors or technologies has been extensively
studied using epidemic models. Here we consider a model of diffusion where the
individuals' behavior is the result of a strategic choice. We study a simple
coordination game with binary choice and give a condition for a new action to
become widespread in a random network. We also analyze the possible equilibria
of this game and identify conditions for the coexistence of both strategies in
large connected sets. Finally we look at how can firms use social networks to
promote their goals with limited information. Our results differ strongly from
the one derived with epidemic models and show that connectivity plays an
ambiguous role: while it allows the diffusion to spread, when the network is
highly connected, the diffusion is also limited by high-degree nodes which are
very stable.
