The Covid-19-prisoner’s dilemma

According to this renowned game theory postulate, cooperation is not always the best way to maximise individual benefit. The key thing about the prisoner’s dilemma model is that what you don’t know prompts you to adopt the position of lowest risk. The classic illustration offered by Albert Tucker involves two criminals who have been arrested and imprisoned. The Coronavirus crisis, however, suggests a new formulation. It goes like this:

Two people living in the same area and knowing each other relatively well decide to leave their house. They run into each other on the way to the supermarket. They’ve both been bored out of their minds being in solitary confinement and they crave social contact. They have an opportunity to spend some time together. They’ve both been out shopping and jogging regularly and may have been infected at some point. Neither of them shows any symptoms. Neither of them wishes to infect the other person. Before they decide to spend time together, they pause to think about their options, individually.  It turns out there are four outcomes:

1. If both approach each other and they are both healthy or unknowingly contagious, their situation won’t change and they will have a good time together. Maximum benefit, let’s say 10 points.

2. If one approaches the other and the other is contagious, the other one gets the virus and is very likely to develop symptoms. It is assumed that neither of them will attempt to approach the other knowing they are contagious. The one who gets nearer may also be contagious without knowing it. Minimum benefit, 0 points.

3. If one approaches the other and the other is not contagious, the latter will fear the former might be contagious and will move back. 0 points plus embarrassment.

4. If neither of them approaches each other, their situation won’t change (i.e. they’ll still think they’re virus-free) but they will slide back into their solitude, no interaction or fun to be had. Medium benefit, 5 points.

Needless to say, governments have advised the 5-point strategy, the one of medium benefit. Many non-contagious people could safely get together these days, visit each other, play sports together, have a drink in the park, but the ignorance as to the other person’s health as well as our own keeps bringing the 0-point outcome to our minds each time. What if they’re sick and they don’t know it? So we rationally stay home and stay 2m apart from each other.