Unit 3: The Prisoners Dilemma

The Prisoners' Dilemma

Non-zero sum games are more complex to analyse as a result. The classic case of the non zero-sum game is the so-called Prisoners' Dilemma.

The dilemma is based around the following scenario. Two people are arrested and placed in separate rooms on a charge of (let us say) robbery. Each is then questioned and faces the following options. They can either confess to the crime or stay silent. They are each fully aware of the consequences of their action which is represented in the matrix below.

Let us investigate the possible outcomes of this matrix.

If Dave pleads guilty and Henry pleads not guilty, Dave gets 1 yr and Henry gets 5.
If both plead guilty, they get 3 years in jail
If Dave pleads not guilty but Henry pleads guilty, Dave get 5 years in jail but Henry only gets 1.
If both plead not guilty each get 2 years in jail

There is now a risk element in playing the game; there is no optimal solution. If I choose to stay silent there is a 50% chance that I could end up with a paltry sentence of just a year but equally I run the risk of going to jail for 5 years. If I choose to confess I have a 50% chance of going free or receiving 3 years in jail.

In this game, it is assumed that there cannot be any cooperation between the two players.

Cooperation would imply that the best option is for us both to stay silent and take the lesser sentence of 2 years.

Without the option of cooperating, the prisoners have to think about what they would least like - that seems to be the idea of spending 5 years in jail. I don't want to spend any time in jail but 3 years is preferable to 5 years but not as preferable as only 2 years.

Given this logic, therefore, my best option is to confess. I have a 50% chance of going free or facing 3 years in jail. If I chose to stay silent there is a 50% chance I could end up in jail for 5 years!