You got the analogy, but missed the point

... that's something like saying that a network that isn't working can't be used.

Right. And the proposed network that can't overcome the barrier to entry can't be used, either. That's what I meant in saying a new internet wouldn't get off the ground.

If you could promise people $5/month for high-speed access they'd flock to you in droves. But if the only way to make money at that price is to already be the only game in town, you're not going to build it.

Even if there is only one game in town, the value of the network affects how much people will be willing to pay for it, and how much usage of the network there will be.

You're using "value" for "utility". The "value" of the network is how much people are willing to pay for it. They don't pay because it's valuable. It's valuable because people are willing to pay.

I just thought of another thing. In your explanation of why larger networks want smaller networks to pay when they merge, you used Metcalfe's Law to describe the value of the networks. It would make more sense to use Zipf's Law. If the smaller network has all of the top third most-popular nodes, it will probably be more valuable.

You're using "value" for "utility". The "value" of the network is how much people are willing to pay for it. They don't pay because it's valuable. It's valuable because people are willing to pay.

Whenever two parties enter into a reasoned voluntary trade, it is because each values what they are getting more than what they are giving up. To the network owner, the value of the network is what you're being paid. To the network user, the value of the network is what you'd have been willing to pay if you were forced. Those two numbers tend to be different, often substantially so. Vendors would like the gap to be small, and customers want it large.

Metcalfe's Law is about the value that customers perceive, not what vendors get.

In general in a competitive market, the gap tends to be fairly large (in fact economics says that the price should be the marginal cost of the last provider). In a monopoly the gap tends to be much smaller. If Metcalfe's Law holds, then a vendor should be able to dominate a market, and then proceed to jack up prices substantially, trusting to network effects to keep competitors from getting established. So the market should tend towards a monopoly that eventually becomes very profitable.

This plan doesn't seem to work as well in practice as Metcalfe's Law would predict.

As for your comment about where we should use Zipf's law vs Metcalfe's, we didn't use either. We used our own n log(n) law instead. As for whether to use a variation, while it is possible that the smaller network has all of the value, it is highly unlikely in practice. If you disagree, I'd be interested in hearing about specific examples.

Cheers,
Ben

Welcome to IWETHEY!