 
Summary: A Note on Competitive Diffusion Through Social Networks
Noga Alon
Michal Feldman
Ariel D. Procaccia
Moshe Tennenholtz §
Abstract
We introduce a gametheoretic 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.
1 Introduction
Social networks such as Facebook and Twitter are modern focal points of human interaction. The
pursuit of insights into the nature of this interaction calls for a gametheoretic analysis. Indeed, a
number of papers (see, e.g., [5]) investigate variations on the following setting. The social network
is represented by an undirected graph, where the vertices are users and edges connect users who
are in a social relationship. Suppose, for example, that there are several competing applications,
e.g., voice over IP systems, that are not interoperable. The users play a coordination game, where
if two neighbors adopt the same system they get some reward that is based on the inherent quality
