Malware, network benefits, and Metcalfe’s law

Arce (2018) presents a game-theoretic model in which users select and hackers target one of two IT platforms based upon the platforms’ network benefits and security levels. Unfortunately, in modelling the network benefits Arce misinterprets Metcalfe’s law. In particular, he assumes that the utility that a user obtains from a platform increases quadratically with the number of users, whereas Metcalfe’s law holds that utility increases linearly with network size. This note shows that with a linear utility function the distribution of hackers across the two platforms is less skewed. In addition, we extend upon Arce’s work by demonstrating that weaker network externalities reduce the set of conditions under which the market can be monopolised.