Game theory and the risks of cycling vs driving

I've been reading Richard Tay's short article from 2002 on "The Prisoner's Dilemma and Vehicle Safety". Tay uses game theory to examine the implications of different fatality rates for drivers of small cars and four-wheel drives (4WD) in Australia. He finds that even though smaller cars are safer in that a collision between two small cars is less likely to result in fatality than one between two 4WDs, drivers will tend to prefer 4WD because in a collision between a small car and a 4WD the driver of the small car has a much greater risk of death. In the language of game theory it is a classic prisoners' dilemma, set out in the box below (the relative risk rates are taken from Australian data).

I thought I'd try and repeat the exercise for the relative risks of cycling and driving in the UK. I got data on the number of miles travelled and the number deaths or serious injuries (KSI, standing for 'killed or seriously injured') from accidents involving bikes and/or cars from the Department for Transport's 2009 road casualties report (tables 1a and 23c respectively), summarised below.

Using the KSI rates we can produce a new version of Tay's table as follows:

There is a similar outcome to the one Tay found, but the relative risks are much more extreme. In a collision between a bicycle and a car, the bike rider is roughly 100 times more likely to be killed or seriously injured than the car driver (1988 divided by 17). But the risk of a fatality is twice as high for a collision between two cars as for one between two bikes*.

None of this is particularly surprising, I suppose - I think everyone knows that if you're going to be in a road collision, it's better to be in a car than on a bike. But it does show how everyone making that calculation means that as a society we choose a sub-optimal equilibrium - a world in which the vast majority of people drive and the overall risk of death or serious injury is higher than it would be in a hypothetical world in which the vast majority of people rode bikes. That hypothetical world may not be a reasonable prospect, but we could surely do with getting a bit closer to it. Since the relative risks in a bike/car collision are probably not going to change very much, significantly reducing the rate of collisions has to be the aim.

*Incidentally, I used KSIs rather than just deaths as there were zero deaths resulting from bike-to-bike collisions in 2009. 


[Update, 5th May - I've corrected an error in the table, but not one that changes the conclusions]