Introduction to Game Theory – Prisoners’ Dilemma (Part 1)

The prisoners’ dilemma is usually the first thing that people come across when they start to get interested in game theory. This post will give a (maths free) explanation of the idea.

It is called the prisoners’ dilemma because the standard example is one where two suspects have been arrested by the police and are being held in separate cells, there is no way for them to communicate. Both prisoners were involved in the same crime. There are three possible scenarios:

1 – If both prisoners keep quiet then the police will have limited evidence to convict them and they will both go to prison for two years.

2 – If one gives the police more evidence against the other then they will go free and the other will go to prison for ten years.

3 – If they both decide to give extra evidence about the other suspect to the police then they both get convicted for longer, but not as long as if there is evidence against just one of them, say five years each.

One of the basic elements to game theory is to take into account what you think the other person will do when you are working out your own strategy. In this case the first prisoner needs to think about what the second prisoner will do. There are two possibilities

a – if the second prisoner keeps quiet then the first should give evidence to the police as this will mean that they go free while the second prisoner gets convicted for 10 years.

b – if the second prisoner gives evidence then the first prisoner should also give evidence as this will mean a five year sentence rather than the 10 if they keep quiet.

We can see here that in both situations the prisoner should give evidence to the police as the outcome is better for them if they do that. This is the same for both players so the logical outcome of the game is that they both give evidence to the police and end up getting five years in jail. Although this is the outcome from the prisoners acting logically it is not the best outcome they could have achieved which would have been two years each in prison if they had both kept quiet.

The key thing to understand from the prisoners’ dilemma is that even though each person involved in a situation might act logically and in their own best interests the overall outcome might not be the best one for everyone.

There are lots of real situations where this can occur and I will look at a few of these in the second installment of this introduction to the prisoners’ dilemma (click here for part 2 of this post, and here for part 3)

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