A Local Mean Field Analysis of Security Investments in Networks

TL;DR

This paper models how network externalities influence security investment decisions among interconnected agents facing epidemic risks, using a novel Local Mean Field approach to derive analytical insights for sparse networks.

Contribution

It introduces a combined epidemic-economic model and extends mean-field techniques to account for local correlations in networks, providing analytical solutions for security adoption.

Findings

Network externalities significantly impact security investment decisions.

Analytical solutions reveal how network structure influences security adoption.

The model predicts conditions under which security deployment is optimal.

Abstract

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.