Monopolies in Network Industries

A question that has been bugging me: Do monopolists restrict output if they are operating in an industry characterized by network effects?

Perhaps I should explain a bit. The classic problem with monopolies is that a monopolist won't set prices equal to marginal cost and produce the requisite number of items. Rather, a monopolist will restrict output and correspondingly raise the price. This is inefficient, because a lot of consumers won't pay the higher price, even though they would have made the exchange if the price had been at marginal cost (and the output correspondingly higher).

But what about industries with network effects? The classic example is a fax machine. If you own the first fax machine in the world, it's not much use, because there is no one to whom you can send faxes. If you own the second fax machine in the world, it's a little more valuable, but only slightly because there's only one person with whom you can exchange faxes. And so on -- the value of the network rises with the total number of fax machine owners. In other words, the usefulness of a given fax machine rises if there are more owners out there. So the 100 millionth owner should logically value the fax machine more than the first owner.

So what does this imply for the monopolist in a network industry? If there were a monopolist who made all fax machines, would it restrict output and attempt to raise the price? Or might it be able to raise prices even further by increasing output thereby increasing the value of the network? How do the incentives work here? I've tried to explore the economics literature a bit on this, but with little luck, probably because I don't know where exactly to look.