Four-State Model of Cybersecurity

Abstract

Here we introduce yet another concrete MFG model in the framework of cybersecurity. It is a four-state model, and it models the response of computer owners to various offers of defense systems against a cyberhacker (for instance, a botnet attack). The model takes into account both the random process of the propagation of the infection (controlled by the botnet herder) and the decision-making process of customers. Its stationary version is again exactly solvable (but not at all trivial), though under an additional asymptotic assumption that the execution time of the decisions of the customers (say, switch on or out the defense system) is much faster that the infection rates. In particular, the phase transitions and the bifurcation points changing the number of solutions can be found explicitly.