The prisoners dilemma

The situation• Imagine … – You live in a totalitarian regime where opposition to the government is repressed. – Walking home from work you are arrested and immediately taken to a police station for interrogation. – You are accused of plotting, with a man called Smith, to overthrow the government. – You profess your innocence and maintain that you don’t know Smith. However it soon becomes clear to you that the regime is more interested in extracting a confession than in the truth. – You are very scared. – The chief interrogator offers you a deal:

The deal• If Smith doesn’t confess, but you confess against him, they will release you. You’ll go free, whereas Smith, who did not cooperate, will be put away for 10 years.• If Smith confesses and you don’t, the situation will be reversed – he will go free while you get 10 years.• If you both confess, you will be each sentenced to 5 years.• If neither of you confess, there won’t be enough evidence to convict either of you. They can hold you for a year; but then they’ll have to let you go.

The dilemmaWHAT SHOULD YOU DO?CONFESS OR NOT CONFESS?

Remember to the deal• If Smith doesn’t confess, but you confess against him, they will release you. You’ll go free, whereas Smith, who did not cooperate, will be put away for 10 years.• If Smith confesses and you don’t, the situation will be reversed – he will go free while you get 10 years.• If you both confess, you will be each sentenced to 5 years.• If neither of you confess, there won’t be enough evidence to convict either of you. They can hold you for a year; but then they’ll have to let you go.

Why you should confess.• Either Smith will confess or he won’t.• Suppose Smith confesses. The, if you confess you’ll get 5 years, whereas if you don’t confess you’ll get 10 years. Therefore, if he confesses you’re better off confessing.• Suppose Smith doesn’t confess. Then: if you confess you’ll go free; if you don’t confess you’ll spend a year in prison. So if he doesn’t confess, you’re still better off.• So you must confess – it’ll get you out of jail the quickest.

But …• Smith is being offered the same deal.• Therefore, following his logic (the same logic as yours), he will confess.• So you’ll both get 5 years.• But if you had both done the opposite, each of you would have got out of prison in only 1 year.

So …• By rationally pursuing your own interests you will both end up worse off than if you’d acted differently.• If you simultaneously do what is not in your best interests, you will both be better off.

The prisoners dilemma

by Clive McGoun on Nov 20, 2011

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