Positive feedback and lock-in
Carl Shapiro and Hal Varian wrote Information Rules (Harvard Business School Press, 1999) as a strategy guide for managers of information businesses, and organised it around two forces. The first is positive feedback: as a network's installed base grows, more people find it worth adopting, and in their words "positive feedback makes the strong get stronger and the weak get weaker, leading to extreme outcomes". Economists call such a market tippy, because it can tip to one standard and orphan the others, as the VHS video cassette format did to Sony's Beta. The second force is lock-in. Once customers have invested in one system, moving to another costs them retraining, converted files and replacement equipment. Shapiro and Varian's rule of thumb is that the profit a supplier can expect from a customer equals those total switching costs, plus whatever advantage its product or its costs give it over rivals.
Luís Cabral's Dynamic Price Competition with Network Effects (The Review of Economic Studies, 2011) puts the tipping story into a formal model and qualifies it. Two firms own rival networks. Consumers arrive, join one of them, and eventually leave, and each firm sets an entry price for newcomers, which may be below cost. Two forces act on that price: a larger network is more attractive, so it can charge more, but a larger firm also has more to gain from growing further, so it has reason to price lower.
The result is a U-shaped pricing function in which very small and very large networks charge the most. Market shares show increasing dominance around an even split, where the larger network tends to pull ahead, and reversion to the mean near monopoly, where it tends to shrink. With strong network effects the market spends most of its time with one network holding between 50 and 100 per cent of it, rather than all of it. Cabral also measures network effects as a barrier to entry: the fall in an entrant's value that their presence causes.