The classical prisoner's dilemma (PD)* is as follows:
Two suspects A, B are arrested by the police. The police have insufficient evidence for a conviction, and having separated both prisoners, visit each of them and offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the silent accomplice receives the full 10-year sentence and the betrayer goes free. If both stay silent, the police can only give both prisoners 6 months for a minor charge. If both betray each other, they receive a 2-year sentence each.
It can be summarized thus:
| | Prisoner A Stays Silent | Prisoner A Betrays |
| Prisoner B Stays Silent | Both serve six months | Prisoner B serves ten years; Prisoner A goes free |
| Prisoner B Betrays | Prisoner A serves ten years; Prisoner B goes free | Both serve two years |
The dilemma arises when one assumes both prisoners are selfish enough to want to minimize their own jail term. 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 they could trust the other.
Let's assume the protagonist prisoner is rationally 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 thinking rationally would also have arrived at the same conclusion and therefore will betray.
It would be rational then for a prisoner to decide to cooperate if only he could be sure that the other player would not betray, and thus achieve a better result than in mutual betrayal. However, such a cooperation is then rationally vulnerable to the treachery of selfish individuals, which we assumed our prisoners to be. Therein lies the paradox of the game.
If reasoned from the perspective of the optimal interest of the group (of two prisoners), the correct outcome 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. However by each following their individual interests, the two prisoners each receive a lengthy sentence, which in fact hurts both the interest of the group and that of the individuals.
*Source: Wikipedia, www.wikipedia.com
2 comments:
However, if the prisoner's dilemma is iterated, there is a solution: tit-for-tat. If your default strategy is cooperation, and this turns to betrayal only on turns after your opponent betrays, you induce your opponent to cooperate!
This is the mechanism nature has evolved for us humans. Hooray!
P.S. This is Leo.
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