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Friday, May 12, 2006

The prisoner's dilemma

In game theory, the prisoner's dilemma is a type of non-zero-sum game in which two players try to get rewards from a banker by cooperating with or betraying the other player. In this game, as in many others, it is assumed that the primary concern of each individual player ("prisoner") is self-regarding; i.e., trying to maximise his own advantage, with less concern for the well-being of the other players.
In the prisoner's dilemma, cooperating is strictly dominated by defecting (i.e., betraying one's partner), so that the only possible equilibrium for the game is for all players to defect. In simpler terms, no matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect.
The unique equilibrium for this game does not lead to a Pareto-optimal solution—that is, two rational players will both play defect even though the total reward (the sum of the reward received by the two players) would be greater if they both played cooperate. In equilibrium, each prisoner chooses to defect even though both would be better off by cooperating, hence the dilemma.

The classical prisoner's dilemma (PD) is as follows:
Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both stay silent, the police can sentence both prisoners to only six months in jail for a minor charge. If each betrays the other, each will receive a two-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So the question this dilemma poses is: What will happen? How will the prisoners act?

The dilemma arises when one assumes that both prisoners only care about minimising their own jail terms. Each prisoner has two options: to cooperate with his accomplice and stay quiet, or to betray his accomplice and give evidence. The outcome of each choice depends on the choice of the accomplice. However, neither prisoner knows the choice of his accomplice. Even if they were able to talk to each other, neither could be sure that he could trust the other.
Let's assume the protagonist prisoner is working out his best move. If his partner stays quiet, his best move is to betray as he then walks free instead of receiving the minor sentence. If his partner betrays, his best move is still to betray, as by doing it he receives a relatively lesser sentence than staying silent. At the same time, the other prisoner's thinking would also have arrived at the same conclusion and would therefore also betray.
If reasoned from the perspective of the optimal outcome for the group (of two prisoners), the correct choice would be for both prisoners to cooperate with each other, as this would reduce the total jail time served by the group to one year total. Any other decision would be worse for the two prisoners considered together. When the prisoners both betray each other, each prisoner achieves a worse outcome than if they had cooperated.

2 Comments:

Blogger Unknown said...

This is direct copy from wikipedia. That is not allowed. You must write what u understood from the topic in your own words.

12:46 AM  
Blogger Unknown said...

The topic is good btw. Nice writeup

10:29 AM  

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