“Metcalfe’s Law: Not so Wrong After All”, Leo Van Hove2014-06-12 (Metcalfe’s Law)⁠:

Briscoe et al 2006 claim that Metcalfe’s law is “wrong”. One of their arguments is that “if Metcalfe’s Law were true, then two networks ought to interconnect regardless of their relative sizes”.

This paper shows that this argument is flawed.

[Keywords: Metcalfe’s law, Zipf’s law, networks, telecommunications, network effects]

…this inference is flawed. Briscoe et al 2006 make two related mistakes. For one, they reason in static terms and apparently fail to realise that interconnection alters the networks’ competitive positions and may, over time, very well impact their market shares. Second, mainly reason in aggregate terms, whereas the strategic implications are best analysed by looking at the utility of individual users and how this utility would be affected by interconnection. In what follows, these points are first made in a largely non-formal way; that is, in terms of the example used by themselves; see §2. Subsequently, §3 restates our criticism more formally, by relying on the theoretical literature on network externalities.