Do you want to play a game?

Sarayu Bacchu

As the world finds itself embroiled in a difficult war against COVID-19, it seems unexpected to compare this crisis to a game. But the ‘game’ I refer to here is not your typical football, tennis or chess; rather it is a set of tactical interactions. We as a society partake in these interactions - between us and the virus, between fellow citizens and internationally, between different countries. Thus, the analytical tools to assess these situations can be derived from the field of game theory, and can provide some very useful insights.

Game theory is a way of thinking about strategic interactions between self-interested people. Note the word ‘self-interested’ – emotions and cognitive biases that influence human behaviour are excluded from these calculations. The average player is thought to be a cold, selfish and rational agent. Of course this poses certain limitations to the veracity of results obtained, but on the whole game theory is still extremely relevant to several issues, especially during this pandemic. The fate of each player depends not only on individual actions but also on the actions of the other players.

As we face severe lockdowns across the world, it is ironic that we happen to be trapped in a quite literal prisoner’s dilemma! A prisoner’s dilemma is a famous coordination problem, and one which is very pertinent to this current crisis.

The dilemma goes as follows: Two criminals are arrested and imprisoned, let’s call them Annie and Bob. No communication is allowed between them. The police have enough evidence to convict them both on a smaller crime, but no evidence for the main crime. However, if Annie defects and betrays Bob, she walks free but he gets 10 years in prison. Annie has a utility of 8 but Bob has a utility of 0. This is true vice versa as well. If they both cooperate and stay silent, they only get a sentence of 1 year, and their utilities are 5 & 5. However is they both defect, they get a sentence of 5 years each. In this case, their utilities are 1 & 1.  This is represented in the matrix below.

Obviously the best collective outcome is for Annie and Bob to both cooperate, resulting in 5, 5. 5, 5 Pareto dominates 1, 1. However, each acts in their own self-interest, and working through the logic, it becomes evident that the only rational option for both prisoners is to defect, and so the rational yet sub-optimal outcome is 1, 1.

This thought experiment can be applied to whether or not people follow social distancing and self-isolation. Let us now say that Annie and Bob are two Londoners. It is in both their interests to wash their hands and stay at home – it minimises their risk of catching coronavirus. This is the cooperate-cooperate option giving them a payoff of 5, 5. But Bob becomes tempted by the sunshine outside, and decides to go to a friend’s barbecue. He defects and gets a benefit of 8, whilst Annie at home gets 0. Likewise, the opposite would be true if Annie went out and Bob remained home. However, if both Annie and Bob defect and go to a social gathering, then their payoff becomes 1, 1.

To get from the defect-defect option to the cooperate-cooperate option, Thomas Hobbes in his 1651 classic Leviathan calls for a third party to enforce this cooperation between citizens. In Bob, Annie and our case, this is the government mandated lockdown.

The brilliant nature of the prisoner’s dilemma allows it to be extended into massive multiplayer coordination games, allowing for modelling of lockdowns in cities and towns. The problem that policy-makers and the government faces is when and how to ease this lockdown, and game theory may be able to point us in the right direction.

How can people be persuaded to prioritise the health of society over their individual happiness? How can we convince people to abandon their rational instincts of pursuing their own desires? How can we promote eudaemonism to prevail over hedonism?

These are the questions faced by governments across the world, and finding the answers to them is challenging, at the very least, and delves into uncharted territory for economists. Other ‘newer’ areas of economics, like behavioural economics, could hold some potentially valuable clues for us.

Nevertheless, as we wait and see what the future holds, we can only trust in the altruistic nature of humans and hope for rational irrationality.