# Prisoner’s Dilemma and the Lockdown

The Prisoner’s Dilemma is a famous mental experiment in game theory (a branch of applied mathematics that studies strategic situations where participants choose different actions in an attempt to improve their return), which despite variations in values, can be exemplified as:

Two people are arrested (A and B) for a crime and kept in separate cells. Then they both present the same proposal:
if you confess and your partner remain silent, you will be free and your partner will serve 10 years in prison;
if you remain silent and your partner confesses, you will serve 10 years in prison and he will be free;
if you and your partner confess, you will both serve 5 years in prison;
if neither confesses, both will serve 1 year in prison.

In this dilemma each prisoner needs to make his decision without knowing what decision the other is going to make, and neither is sure of the other’s decision. So in this dilemma the question arises of distrust when looking for a small consequence for both parties (keep silence) and the fear of being betrayed by the partner who can act selfishly, thus obtaining freedom regardless of what happens to the other. In such a situation, how would you act?

The mutual fear of being “betrayed” in this case, leads both to confess, causing them to suffer a penalty far greater than maintaining silence.

Okay, but what does this have to do with Lockdown?

In fact, we are going to change the protagonists from prisoners to hairdressers in the dilemma.

In a small community well isolated from any other, the only face-to-face service that serves that population is that of hairdressers, and there are two hairdressers (X and Y) that meet all the demand of that population. But with the pandemic and the emergence of cases of COVID-19 in that region, they decreed the closure of their establishments until there was a great reduction in the cases. However, the bills keep coming up and both hairdressers need to deal with this situation:
if I obey the restriction while my competitor work hidden, I will start accumulating debts, but he will earn more (since now all clients would go to him only), and the number of cases will not decrease, then the restriction would continue;
if I work hidden while my competitor obeys the restriction, he will start accumulating debts, but I will bill more (since now all clients would go to me only), and the number of cases will not decrease, so the restriction would continue;
if we both work hidden, we will keep the same billing as before, we will not have debts, but the number of cases will not decrease, so the restriction would continue;
if we both comply with the restrictions, we will both accumulate debt, but the number of cases would decrease, then the restriction would end.

In this dilemma each hairdresser needs to make his decision without knowing what decision the other will make (otherwise it would not be a hidden service), and neither is sure of the other’s decision. So in this dilemma the question arises of distrust when looking for a small consequence for both parties (having losses / accumulating debts) and the fear of being betrayed by the partner who can act selfishly, thus obtaining his profit (or maintaining his earnings ) regardless of what happens to the other. In such a situation, how would you act?

The mutual fear of being “betrayed” in this case, leads both to answer in secret, causing their billings to remain but the number of COVID-19 cases to continue.

Have you noticed the relationship between this dilemma and Lockdown?

In this simplified context, we have only two establishments (two prisoners), while in contexts closer to reality we have countless establishments (countless prisoners), being tempted with the offer to act selfishly (confess) without caring about the consequences that this it will work for others (both your partners and the fact that the number of COVID-19 cases continues).

The solution to the Prisoner’s Dilemma is collaborative thinking, to understand that if everyone seeks only the best for themselves, they will arrive at a worse result than if they seek a better solution for the collective. I leave the reader with the task of finding the solution to the Hairdresser’s Dilemma.

Cover image credit to Robert Pastryk from Pixabay