A note on competitive diffusion through social networks

We introduce a game-theoretic model of diffusion of technologies, advertisements, or influence through a social network. The novelty in our model is that the players are interested parties outside the network. We study the relation between the diameter of the network and the existence of pure Nash equilibria in the game. In particular, we show that if the diameter is at most two then an equilibrium exists and can be found in polynomial time, whereas if the diameter is greater than two then an equilibrium is not guaranteed to exist.