Coronavirus, Stockpiling and the Prisoner’s Dilemma
Before we get onto the main thrust of this blog, the government is giving daily announcements on its strategy to combat the spread of coronavirus and lessen the resultant impact on the economy. The announcements are detailed here and updated regularly. I recommend you bookmark this page and visit daily to keep abreast of developments.
Breaking the Law
The prisoner’s dilemma is probably the most famous thought experiment in a branch of economics called game theory. I first came across the prisoner’s dilemma at university and the counter-intuitive results are such that they stay with you. Let’s set the scene.
Two suspects are separated and questioned, with respect to a robbery, in different rooms of a police station. The police officers are pretty certain of both suspects’ guilt but have insufficient evidence for this to stand up in court. They need at least one of the suspects to confess and to gain this they tell each suspect that they will be rewarded or penalised depending on how each of them acts.
There are three scenarios:
- Both suspects keep quiet. In this case they each receive a 1 year prison sentence
- Both suspects confess. In this case they each receive a 3 year prison sentence
- One confesses while the other keeps quiet. In this case the confessor will be set free and the suspect that kept quiet will receive a heavier 4 year prison sentence
If you were one of the suspects what would your strategy be?
Consider your responses to the choices of the other suspect. If they keep quiet then the logical response is for you to confess because you will be set free. If they confess then your response should also be to confess to avoid the extra year being added to your sentence. The only logical strategy is therefore to confess. This is what’s known in game theory as a dominant strategy.
Your co-suspect, being as logical and rational as yourself, also goes through this analysis and chooses to confess. You both get 3 years at Her Majesty’s pleasure.
Shouldn’t you have both kept quiet? Yes! Instead of serving 3 years in HMP Ne’er-do-well you’d each only have served 1 year. This is why the prisoner’s dilemma is so counter-intuitive: you have to ignore the dominant strategy in order to achieve the best overall outcome. This requires co-operation.
The current stockpiling of food and other essentials is a prisoner’s dilemma playing out in front of our eyes, although much more complicated. The risk of empty shelves leads to the dominant strategy of stockpiling. The best overall outcome, i.e. everybody has access to what they need, is arrived at by not stockpiling and can only be achieved through co-operation.
So why is it so difficult to stop stockpiling occurring, even with expert advice from government advisors?
Split or Steal?
Does anybody remember the game show Golden Balls, hosted by Jasper Carrot? The prize money on offer after various rounds was divided among the final two contestants according to their individual choice of whether to split it or steal it. The three scenarios are as follows:
- They both choose to split. In this case they each receive 50% of the prize pot
- They both choose to steal. In this case they each receive nothing
- One chooses to steal while one chooses to split. The stealer wins the whole prize pot
This is a classic prisoner’s dilemma! The dominant strategy is to steal even though splitting will lead to a better overall result for both contestants and remover the risk of walking away with nothing.
The twist here is that the two contestants are allowed to talk to each other, i.e. co-operate. In one particular episode two contestants, Sarah and Stephen, were discussing their strategies with each other. They both agreed to split because they couldn’t live with the negative public opinion.
Jasper asked them to unveil their choices and Stephen duly revealed that he had chosen to split. Sarah revealed that she had chosen to steal and walked away with all of the £100,150 prize pot! In a previous show, Sarah had been double-crossed herself and clearly believed it would happen again so she played the dominant strategy.
So for everybody to win in a prisoner’s dilemma we need two things: co-operation and trust. It is difficult for us to trust people we don’t know to act sensibly, especially with the threat of coronavirus in the air. This is why even rational people analysing the situation in a logical and rational manner will choose the irrational strategy to stockpile.
What if supermarkets introduced quotas? Think about a two supermarket scenario. Maximum sales of, for example, hand sanitiser under a quota system would be £1m while without quotas it would be £3m. What are the options?
- Both introduce quotas and make £1m of sales each. Both have stock in reserve but miss out on £2m extra cash now
- Both keep unlimited purchases and make £3m sales each. Both have an extra £2m now but have no stock in reserve
- One introduces quotas while one keeps unlimited purchases. The quota supermarket sells £1m worth while the unlimited supermarket sells £3m worth. One has stock in reserve but the other has £2m extra cash now, which provides a competitive advantage
That’s right: we’ve just described another prisoner’s dilemma!
The Moral of the Story
The prisoner’s dilemma, in its various guises, highlights the importance of co-operation and trust in achieving end results that keep everybody healthy. We need to co-operate with other shoppers by not stockpiling and we need to trust in what we are being told by government advisors in that there is enough for everybody if we shop sensibly.
