# The Emerging Revolution in Game Theory

by James Furbush
on September 7, 2012

The prisoner’s dilemma has been studied for decades because it is essentially a thought experiment about how to achieve the best outcome for yourself when you have to rely on the variable of someone else and you can’t necessarily predict what they will choose to do. It’s about collaboration and blind trust dominated by betrayal and selfishness.

The setup goes like this: two people have committed a crime and are arrested. They are told by police in separate holding cells that if they snitch on the other person they will go free while their partner does six months in jail. If both snitch they get three months in jail. If neither snitches they each get one month in jail.

The best strategy is to snitch because it guarantees that you don’t get the maximum jail term. Now, there’s a previously unknown strategy for the game that guarantees one player a better outcome than the other.

The new approach is called the zero determinant strategy (because it involves the process of setting a mathematical object called a determinant to zero).

It turns out that the tit-for-tat approach is a special case of the zero determinant strategy: the player using this strategy determines that the other player’s time in jail is equal to theirs. But there are a whole set of other strategies that make the other player spend far more time in jail (or far less if you’re feeling generous).

The one caveat is that the other player must be unaware that they are being manipulated. If they discover the ruse, they can play a strategy that results in the maximum jail time for both players: ie both suffer.

Game theorists call this the Ultimatum Game. It’s equivalent to giving Alice £100 and asking her to divide it between her and Bob. Bob can accept the division or refuse it if he thinks the division is unfair, in which case both players get nothing. The refusal is Bob’s way of punishing Alice for her greed.

The interesting thing here is that when both players are aware of the zero determinant ruse, the prisoner’s dilemma turns into a different game.

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