# The Prisoner's Dilemma

Posted by Jason Polak on 08. March 2018 · 2 comments · Categories: math · Tags:

Suppose the police suspect you and your friend of robbing one billion dollars in bitcoin. The police can only charge you and your friend with the small crime of possession of a sawed-off shotgun, however, and want both of you to confess to the robbery. So, you and your friend are put in separate rooms and given two decisions:

1. Stay silent, in which case you'll only be charged with weapons possession
2. Confess

If both of you stay silent, then both of you will get a minor prison term. If you confess and your partner stays silent, then the police will let you go in exchange for prosecuting your partner, and vice-verson. Since your partner stayed silent, they will get the maximum sentence. If both of you confess, both of you get serious prison time but a little less than the maximum because both of you cooperated.

Since each of you is in separate rooms, you have to make the decision without knowing what your partner decides. What is the best strategy?

Game theorists like to put all the possibilities in a 'payoff matrix', which describes the possible outcome for each combination of decisions. Here is the payoff matrix in this case:

 Confess Stay Silent Confess (-3,-3) (0,-4) Stay Silent (4,0) (-1,-1)