Immunisation and the game of chicken

Immunisation is good. I'm a big fan. I'm going to write that first before anyone misunderstands me. But it's also a dressed up game of chicken, which means that it makes logical sense for people not to get themselves vaccinated when other people do. (I've seen immunisation described as an example of the prisoner's dilemma, but I think this reasoning is false - see post script.)



We need to think about the payoffs of immunisation versus the costs. I'll use a made-up example but you'll see how the logic extends.

Consider disease X which is highly contagious and that you really don't want to get. Let's call the cost of getting disease X to you A.

There is a vaccination you can get for X which comes with potential side effects. Let's call the cost of the side effects if you get them B.

The expected payoffs are:

Not vaccinated: A x Probability of catching X
Vaccinated: B x Probability of side effects

Note that the cost to you of not getting vaccinated is a function of what everyone else does since the more others are immunised the less chance you have of catching X (herd immunity). The cost to you of vaccination remains fixed no matter what everyone else does. Therefore with some reasonable assumptions we will see a tipping point where the benefits of immunisation are outweighed by the cost of the vaccination.

The tipping point will occur at different points for different people. As such I may choose not to vaccinate when it would be better for you if I did so. This can lead to situations where the socially optimal level of vaccination is not reached. This seems to me a real barrier to socially effective immunisation programmes.

Post script:

The original title of this post was "Immunisation and the prisoner's dilemma". If immunisation really were an example of a prisoner's dilemma then under certain circumstances it would always be better for me not to vaccinate myself no matter what you do, even though collectively we would be better off if we both vaccinated ourselves. I don't think this arises in this example, and the reason is that the cost of vaccination is fixed for me no matter what you do.