*Isn’t it more likely to result in underinvestment? Let’s say that there are 5 companies who all have the idea of building a high-speed link. All of them know that only the fastest one will be able to generate any revenue. They’re all wildly optimistic, so each of them believes that there is a 50% probability that they will be the winners. Even in this scenario, the investment will only happen if the social benefit (which is the most that the winner can collect in revenue) exceeds the cost by at least a factor of 2. So it seems like there’s a cliff effect, if the benefit is less than 2x the cost, no-one will invest and no link will get built. If it’s more than 2x the cost, all 5 of them will invest and we’ll end up with 5 links of which only one is useful.*

I don’t think you’ve described an equilibrium. If nobody builds, then everyone wants to build.

The equilibrium is that everyone builds with probability p, where the fact that everyone else is building with probability p is just enough to make me indifferent between building and not building.

To compute that probability p, I’d have to know how your expectation of success varies with the number of other entrants. If I take your model seriously, it says that my expectation of success is 50% *regardless* of the number of other entrants, but that’s not plausible. So: You give me the expectation as a realistic function of the number of other entrants and I’ll compute p for you.

]]>*You’ve lost me. I don’t understand how this relates to my last response to you.*

That’s because you’ve so thoroughly ignored my question that at this point we’re talking about two different things.

]]>So let’s make sure I understand this:

I’m in the jungle, where I’m periodically chased by lions, and periodically chased by snakes. If both I and the lions double our running times, my risk from the lions is unchanged but my risk from the snakes is reduced. Is that, in essence, your story?

]]>*Your normalization (denominator) is the number of seconds in the year.*

Not at all. I said that a 15-trillion dollar-a-year economy produces about $1500 worth of output in .003 seconds.

I could just as easily have said that a 150-trillion-dollar-a-decade economy produces about $1500 worth of output in .003 seconds.

Or that a 1.25-trillion-dollar-a-month economy produces about $1500 worth of output in .003 seconds.

It doesn’t make a bit of difference whether you quote the rate of output in years, decades, months or seconds. I quoted it in years because 15-trillion-a-year is an easily recognizable figure.

What matters is the $1500-per-.003 seconds. That’s an absolute figure. It’s not relative to anything. There is no “one year baseline”. You are extremely confused.

]]>Isn’t it more likely to result in underinvestment? Let’s say that there are 5 companies who all have the idea of building a high-speed link. All of them know that only the fastest one will be able to generate any revenue. They’re all wildly optimistic, so each of them believes that there is a 50% probability that they will be the winners. Even in this scenario, the investment will only happen if the social benefit (which is the most that the winner can collect in revenue) exceeds the cost by at least a factor of 2. So it seems like there’s a cliff effect, if the benefit is less than 2x the cost, no-one will invest and no link will get built. If it’s more than 2x the cost, all 5 of them will invest and we’ll end up with 5 links of which only one is useful.

What reason do we have to believe that we are in the region where overinvestment is likely as opposed to underinvestment?

]]>There are two sources of risk to a market maker — the first is informed, sophisticated traders who have access to the same high-speed technology as the market maker himself, and who *may* (not all of them are high-speed traders) speed up by the same degree with lower latency links. The second is random noise, from events in the real world as well as from uninformed traders who are not using high-speed links (because it isn’t worth paying for it to them).

A model for a market maker could be that he posts bids and offers around his estimate of fair value. Uninformed traders at random times hit his bids or lift his offers in random size. All this happens in continuous time (the real world is continuous time, not subject to a discrete ticking clock). The “inventory”, or net risk position of the market maker will follow a random walk, with deviations increasing with the square root of real time. To control his risk, the market maker must become a more aggressive buyer if his risk position drifts to the short side, and vice versa a more aggressive seller if his risk position drifts to the long side, purely from chance fluctuations. The quicker he can make adjustments, the lower the capital he needs to support his risk, and the tighter he can make his bid/ask spread.

This also applies to a market maker operating in both Chicago and New York. He has to communicate his updated risk positions back and forth between the two markets, and the faster he can do it, the lower the bid/ask he needs to charge in both markets.

]]>Assume a spherical lion….

]]>You’ve lost me. I don’t understand how this relates to my last response to you.

]]>