What is... | July 21, 2017

What is the prisoner’s dilemma?

How the best strategy for individuals, separately, can result in a poor outcome, collectively.

The prisoner’s dilemma is a type of game theory. These are mathematical representations of situations where decisions depend on the actions of others.

It goes like this: two thieves – let’s call them Albert and Barbara – burgle a jewellery store. They're brought in to the police station and placed in separate cells for questioning. The police have some evidence to charge the pair with previous petty crime but need a confession to charge them for the jewellery heist.

The jail sentences handed down to each will depend on the outcome of the questioning. If neither Albert nor Barbara confesses to the heist, they will each get one year in jail for their previous minor misdeeds. 

If both confess, they will each be given five years in jail for theft. 

If one confesses that the pair committed the crime, but the other doesn’t, the confessor will be granted amnesty but the other will face eight years in jail: five for the crime plus three extra for obstructing justice.

What happens?
Albert considers what Barbara will do. If she keeps quiet, he can confess and avoid prison. But if she confesses, he should confess too, to avoid getting stuck with eight years in jail. Barbara goes through the same thought process.

So they each confess and are locked up for five years. But both could have been much better off (if we leave truth and ethics to one side) if they had kept quiet and received a sentence of just one year each (the “cooperation” strategy).

The prisoner’s dilemma shows that each person following their dominant strategy - in this case confessing - doesn’t always lead to the best outcome.

Split or steal?
The UK TV show Golden Balls uses the prisoner’s dilemma in the game, Split or Steal. There is a pot of money and each of the two players has to choose whether to split, i.e. cooperate, or steal, i.e. confess.

The two players can discuss with each other what they are going to do. But of course they can say one thing and do another.  If both players choose to split, then they will split the pot equally.

If one chooses to split and the other chooses to steal, the stealer gets everything. If both choose to steal, neither gets anything.

Persuading the other contestant to split is the aim, but of course, if they think you’re going to do the same, they have an incentive to choose steal. But in one memorable episode, one of the players cleverly tells the other that he is going to choose steal, but that he will share the pot of money after the show. He is adamant that this is what he will do. 

The other player therefore knows that, if he chooses to steal too, they will both walk away with nothing, so he has no choice but to “split”. Find out what happens in the video clip here.

This can affect a range of business-related or money decisions. Read more about game theory, and how it can affect personal finance, here.


eZonomics team
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