Telepocalypse

An optional question

Many of you will have heard of the famous Black-Scholes equation for the pricing of financial options. The basic idea is that an option contract to buy a thing at some future date at a fixed price has some potential premium over the current price of the asset because it may allow you to buy at a discount some day (i.e. the strike price is below the market price on the day the option is exercised). Black-Scholes lets you calculate this premium.

A stupid network is like an infinite sequence of discrete options to communicate between connected parties. At the finest granularity, every frame or packet contains a message from a pool of possible messages. A stupid network makes that pool of possible messages larger by deferring optimisation for any particular message type. (For example, IMS networks pre-optimise on SIP, which would exclude a more bandwidth-efficient signalling protocol such as IAX — which could be a problem for wireless devices.) The assumptions for a “stupid” network is that networks have considerable longevity, there is high uncertainty about the future returns of different “messages”, and high initial cost — otherwise we could just build more and more application-optimised networks. These respectively map onto “low interest rate”, “big standard deviation in returns” and “high current stock price” in Black-Scholes, maybe perhaps, if I interpret things correctly.

I’m wondering if any network economists or general econometricians out there have done the work to adapt and extend Black-Scholes to model communications networks from an option theory viewpoint. If any of you know the answer, I’m curious to find out what they discovered.

As someone with a degree in mathematics, I would regard the problem as “non-trivial”, and definitely well beyond my aptitude.

Naturally, the option price may be somewhat different for the owner and user of the network, depending on how good the owner is at price discrimination (i.e. manipulating the strike price) — something the “stupid” network is notoriously poor at. There could be some interesting consequences for muni network advocates. Spreading superfast broadband to people who won’t today pay for it at market-clearing prices is a way of foisting options to communicate onto the economy, with the hope that someone will invent crazy new applications to redeem them. Perhaps there’s a sounder theoretical basis for muni networks yet to be explored?