  Getting agents in the Internet, and in networks in general, to invest in and
deploy security features and protocols is a challenge, in particular because of
economic reasons arising from the presence of network externalities. Our goal
in this paper is to carefully model and quantify the impact of such
externalities on the investment in, and deployment of, security features and
protocols in a network.
  Specifically, we study a network of interconnected agents, which are subject
to epidemic risks such as those caused by propagating viruses and worms, and
which can decide whether or not to invest some amount to self-protect and
deploy security solutions. We make three contributions in the paper. First, we
introduce a general model which combines an epidemic propagation model with an
economic model for agents which captures network effects and externalities.
Second, borrowing ideas and techniques used in statistical physics, we
introduce a Local Mean Field (LMF) model, which extends the standard mean-field
approximation to take into account the correlation structure on local
neighborhoods. Third, we solve the LMF model in a network with externalities,
and we derive analytic solutions for sparse random graphs, for which we obtain
asymptotic results. We explicitly identify the impact of network externalities
on the decision to invest in and deploy security features. In other words, we
identify both the economic and network properties that determine the adoption
of security technologies.
