13 Apr 2006

The Prisoner’s dilemma

I came across this queer part mathematical, part psychological, part philosophical problem.

Two criminals are arrested under the suspicion of having committed a crime together. However, the police do not have enough evidence to convict the suspects. The two prisoners are kept isolated, and the police interrogate them separately.

If one of the criminals decides to confess (i.e betray the other suspect) to the police, while the other does not, the defector will gain, as by offering evidence against the other suspect he will be freed. The one who was silent would be duly punished.

If both of them choose not to confess, then they will both gain, and be freed, due to the lack of evidence to convict them.

However, if both betray, both will be punished, but less severely than if they had refused to talk.

The dilemma for a prisoner here is to decide whether he should trust his accomplice or not. The prisoner has only two options: Confess or remain silent. Whichever option he chooses, his fate his also dependent on his accomplice’s action.

The safest option in the game is to perhaps choose to confess to the police, because, when you do that, regardless of whatever the other guy does, you will not face a severe penalty. But then again, if you do trust your mate and decide to remain silent, then you can either go scott-free or be severely punished (the extremes). Well, if the luck indeed favors the brave, then it would not be an bad idea to remain silent right?

On digging further, I found out that The Prisoner’s Dilemma was originally formulated by mathematician Albert W. Tucker and has since become the classic example of a “non-zero sum” game.

A “zero sum” game is simply a win-lose game such as tic-tac-toe. For every winner, there’s a loser. If one player wins, the other loses.

Non-zero sum games allow for cooperation. The games would have moves that benefit both players, and this makes these games a lot more interesting.

You can play the game, The Prisoner’s Dilemma, here.

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