Revenues of network platforms: can they be expected to follow a growth ‘law’?

Recent papers assume that whereas the value of ‘traditional’ communications networks follows Metcalfe's law – that is, grows with the square of the number of users – the value of group-forming network platforms should increase faster. The papers see evidence in the fact that the advertising revenues of platforms such as Facebook and Tencent follow a cube law or stronger. We argue that such tests do not make much sense, as they lack a theoretical justification. Growth laws such as Metcalfe's and Reed's were conceived with purely one-sided networks in mind, reason in terms of utility for users, and have little to say about the monetisation of the value created. The results of the very papers that we discuss show that the laws have no generality. We also provide a counterexample of our own and proffer an alternative explanation.