PayWallNews

Last week I was named as the 103^rd most influential person in British science by the Times' Eureka science magazine.

So - only 102 people to bump off, then...

I am, of course, very grateful to the Times for considering me, and for the party that they organised in the Science Museum in South Kensington for us all.

In addition to lots of my fellow scientists and engineers, there were quite a few people from the Times at the party, and the conversation turned to News International's paywall.  Behind this their online newspaper content now resides.  There was much rather anxious discussion about whether or not it was going to work.  I said that it ought to be straightforward to predict if it will or not using evolutionary game theory, and on the train on the way back home, I worked it out.

Here's the result.  The Y axis is the income that a news site gets, which is made up from advertising and - for non-free sites - the paywall subscriptions.  The X axis is the proportion from 0 to 1 of news sites that are behind a paywall.  The blue curve is the income a paywall site gets, and the red curve is the income a free site gets.

The actual Y-axis numbers are arbitrary.  What's interesting is the shape of the curves.  As more and more sites go behind paywalls the income per site drops because the paying customers have more choice, and there is less advertising income per site.  The free sites' incomes rise, because all the remaining newsreaders go to them, and so - consequently - does most of the advertising.

With the numbers I used the evolutionarily-stable proportion of paywall sites is about 0.2 of all news sites, with 0.8 of them remaining free.  If you change the assumptions the curves change and so does the crossing point, of course.  But the principles remain the same.  If the number of paywall sites is to the right of the crossing point, you make more money if you run a free site; if it is to the left you make more money with a paywall.  That's why the crossing point is evolutionarily stable.

This graph must be the reason that News International broke ranks and went paywall first.  That means that they are operating at the left-hand end of the graph on the blue curve.  If you are a big news organization it makes sense to occupy as much of that left-hand end as possible.  Indeed, if the total of all your own paywall sites just makes your proportion of all the news sites in the world the crossing point, then you get all the paywall income that the world has to offer, and your rivals will do better to stay free...