COVID-19 and Game Theory

As the UK faces increasingly severe lockdown measures, it is ironic that we are stuck in a very real prisoner’s dilemma.

For those uninitiated with game theory, the prisoner’s dilemma is a situation in which we have an incentive to make a choice that does not produce the optimal result for the group. 

In the classic case of the prisoner’s dilemma, two members of a criminal gang are arrested and imprisoned. They cannot communicate. The authorities cannot convict them on the main charge, but they can on a minor charge. If they both stay silent they get they both get the lesser charge, the optimal result between the two of them. 

But, if one speaks out then they are released, and the other person is put away for years. The incentive is for both to betray the other, in the hope of getting a reduced sentence, but which results in them both getting a medium sentence. The implication of the game is that two individuals acting in their own interest reach a suboptimal outcome.

Stuck in isolation, we have no idea as to how our fellow city-dwellers will act, and many choose to act in self-interested manner since they can assume others will as well. Let’s take the case of supermarket stockpiling. The media might have us believe that the virus has led to a plague of ‘covidiots’; revellers and hoarders hell bent on and single-handedly clearing out supermarket shelves. 

But are people acting irrationally? At a collective level, it is leading to shortages of goods. But in a direct sense, people are acting rationally. It becomes optimal rather than suboptimal to start stockpiling if everyone else does because their stockpiling creates the very supply problem they are trying to avoid in the first place.

No one particularly wants to hoard hand sanitiser, but will do so if they think others are doing so. The stockpiling of toilet roll doesn’t even have the same disease-preventing benefits of grabbing extra soap, but no one wants to be caught out without any loo roll if all their neighbours raid the local store shelves.

This perspective does not seem to be one entirely shared by supermarkets or the government, with the suggestion today that supermarkets will be advised to allow only 10 people in at a time, alongside the already implemented two or three items per person rules to stave off induced shortages. These policies are based on a cynical intuition that the majority of shoppers are irrational hoarders, that they will purchase these items whatever the price, and consequently that price rises are an equally cynical attempt at profiteering during an emergency. 

The item limit policies function as a blunt tool to prevent overbuying, but it comes with costs. It disproportionately endangers those who might need more like families and vulnerable members of society who will be forced to go into the shops more regularly to adequately supply themselves. This is likely to become increasingly difficult as further measures are taken to discourage time spent in public spaces. 

By increasing prices on certain goods like toilet paper, those who don’t want to be caught without it could opt to buy in smaller volumes, leaving more stock on the shelf and increasing buyer confidence that stock isn’t dwindling. In the case of meat and dairy, this has the added benefit of displacing demand onto cheaper vegetables of which there is a greater supply. As buyer confidence in the supply chain is restored, prices could be returned to standard levels. Government is rightly increasing welfare payments to compensate the least-well off for these short-term hikes. 

While perhaps counter-intuitive, raising prices in our current context is not a cynical cash grab, but an effective means of restoring consumer confidence and ensuring we can all access the goods we need during these strange and difficult times. While purely anecdotal, the supermarkets near me haven’t had eggs for days, but the corner-shop has plenty after raising prices to 40p an egg, and for that, I am glad. 

The broader experience of this pandemic might also point to other economic insights, like that of the tragedy of the commons, in which people overuse a shared resource. The classic case being overgrazing by farmers of a shared field of grass.

When the PM announced that pubs, clubs, bars and gyms should close down, he inadvertently created an incentive to flock towards public parks and holiday homes as the last vestiges of unrestricted leisure. What better time for a breath of fresh air than when your compatriots are cooped up inside?

Somewhat predictably, the media has us staring at images of parks heaving with joggers and tube stations chock-full of commuters (only worsened by the Mayor’s decision to reduce services at a time when people need to socially distance).

If everyone believes it is optimal for themselves to go to the park, it quickly becomes sub-optimal because the park becomes unpleasantly full, increasingly hazardous and precipitates further government lockdown. Social distancing is enforced either through individual inference or law enforcement. As per the tragedy of the commons, our own self interest has created a suboptimal state of affairs for everyone in jeopardizing public health, and incurring increasingly necessary restrictions on personal freedom. 

However, if YouGov is to be believed, 93% of us back protocols recommended by the Government, with those who do not forming a hyper-visible minority. Corroborated by recent observations that footfall in public spaces is dropping, we can conclude that as society adapts to this new normal, most of us will make mutually beneficial decisions.