Social Distancing: A Game of Two Locales
The coronavirus pandemic which began late last year in the Chinese city of Wuhan has now spread globally. It continues to take a huge toll on major Western economies including the hardest hit to date: Italy, Spain, the United Kingdom, and the United States.
The slowing down of the virus, which is now conservatively estimated as going to have fatalities in the US upwards of 200,000 when it is all over, is premised on continued social distancing and other safety measures being judiciously carried out, as advised by medical and healthcare professionals.
Globally, the word is also out - countries have to follow the template of social distancing to slow the spread of the virus. This is all the more pressing for developing countries with merely a fraction of the number and quality of healthcare provisions the West has, and yet is struggling to cope.
The media is filled daily with reports of hospitals and treatment facilities having to come up with protocols on who to treat and who not to treat, should it get to that point, due to not having enough treatment apparatus including mechanical ventilations, ICU beds, oxygen therapies etc. This has heightened the sense of desperation in many countries with far fewer capabilities, and very large and densely populated cities, which have so far been spared the onslaught of the virus, but have started showing to be in their early phases of being infected by the virus.
Governments in these nations have therefore taken the template of social distancing and sought to apply the same within their countries, but here is a difficulty that they face. Many of their citizens, in particular the poor, while having been explained to the need for the policy, are all the more perturbed about the fact that for them it is more or less an equally undesirable death sentence to comply. I illustrate this with a very basic game theoretic model below:
The Social Distancing Game
Consider a relatively low income developing nation with a large population, such as Nigeria or any other sub-Saharan African or South-East asian country with similar statistics. I will divide this country into two types of families - the rich and the poor.
My delineation is reflective of the very stark income inequality that persists where the rich are simply those who can, on short notice, stock up on food supplies and other basic necessities able to last them for a few to 14 days. The poor cannot do this, and have to live on a day to day basis from a social hustle that has come to define their existence.
The societal objective is to mitigate the overall impact of the pandemic by slowing the spread through social distancing that is effected through self isolation at home.
Both the Rich and the Poor are faced with two strategy choices: to self isolate at home (SI) or not to self isolate (N) over the next couple weeks. The payoffs from these choices are given in the table below:
Let me explain the structure of the payoffs and the nature of the game. The game is a static one, where each player (the rich or the poor) chooses the strategy that gives her the highest payoff, given what she knows the other player will choose to play. So there is perfect information in the model and payoffs are known.