Sunday, December 27, 2020

The Prisoners’ Dilemma of Covid 19 ••

By Madeleine Kando

The Prisoner’s dilemma is a concept in game theory that demonstrates how two prisoners acting in their own self interest both end up with a worse outcome than if they had coordinated their behavior.

This applies to the current situation and it maybe explains why the infection (and death) rate is so high the United States.

In the game, two bank robbers have been arrested. They cannot communicate with each other. The police have no proof of a major crime, but can convict them on a lesser charge. They have two options: to confess or to remain silent. If both remain silent, they each get a 2-year sentence for the lesser charge. If one confesses and the other one remains silent, the confesser gets a 1-year sentence and the other gets an 8-year sentence. And vice versa. If both confess, both receive a 5-year sentence.

The optimal decision would be for both prisoners to remain silent, but they are out to get the least amount of prison time, and do not care about the other prisoner.

If we replace the 2 prisoners with 2 states (California and Arizona), we can see why there is no incentive on the part of the Governors to keep their state on lockdown. (see next illustration).

The blue square is obviously the best option. The states cooperate with each other and will be able to reopen safely.

In the green square, Arizona tries to stop the virus by locking down, but California, which is open, transmits the virus. Arizona does not get the benefit from locking down, so reopens the state. This is called the Nash Equilibrium. If the states coordinated their strategy of moderate reopening, both would have been better off.

In the purple square the situation is reversed, but just as bad. In the red square, both states are open, the virus is out of control and both states are forced to lock down. 

The same applies to businesses. If local restaurants stay closed, they lose money. If one restaurant reopens, it makes money and takes away business from the closed restaurants. Which forces all restaurants to reopen. Infection and competition rates go up and everyone is worse off.

It also applies to individuals. If everyone wears a mask, everyone is protected. But if you don’t wear a mask and others do, you negatively impact their outcome. They will reconsider wearing a mask.

The prisoner’s dilemma shows that, in the case of the virus, self-interest is neither good for the group nor the individual. leave comment here

** The source for this post can be found here: A COVID-19 prisoner’s dilemma