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Line 1: − + − The game is usually phrased in terms of two suspects, both of whom have been arrested, and offered a bargain. If neither of them confess, they will both serve 6 months in prison for a minor crime. If one of them confesses, this provides evidence of a major crime. The confessor is rewarded by being let off, and the other suspect serves ten years in prison. If both confess, they both serve two years.+ + + + + + + + + + + + + + + + + + + + + + + + + − + − Thus, the situation leads to both prisoners confessing, and serving a two year prison term. However, this is worse for both prisoners than if they both kept quiet, and served only six months. The prisoners would benefit if they could co-operate, but in the usual phrasing of the problem, neither player knows what the other will do. The situation with both prisoners confessing is a Nash equilibrium, and is in fact the only such equilibrium that exists in the problem.+ + + + + + + + + +
Rewrite of the main part. I think it's a bit easier to understand this way.
The Prisoner's Dilemma is a classic problem in [[Game Theory]]. It seems paradoxical, in that the [[Nash equilibrium]] is not the best solution for both players.
The '''Prisoner's Dilemma''' is a classic problem in [[Game Theory]]. It has the paradoxial outcome that members of a group will consciously steer towards a sub-optimal outcome in certain scenarios.
<div style=float:right; padding: 20px">
{|style="border-collapse:collapse"
|
|
!colspan=2 style="padding:10px"|''B''
|-
|
|
|style="border-style:solid; border-width:1px; padding:10px"|don't confess
|style="border-style:solid; border-width:1px; padding:10px"|confess
|-
!rowspan=2 style="padding:10px"|''A''
|style="border-style:solid; border-width:1px; padding:10px"|don't confess
|style="border-style:solid; border-width:1px; padding:10px"|A: 6 months
B: 6 months
|style="border-style:solid; border-width:1px; padding:10px"|A: 10 years
B: free
|-
|style="border-style:solid; border-width:1px; padding:10px"|confess
|style="border-style:solid; border-width:1px; padding:10px"|A: free
B: 10 years
|style="border-style:solid; border-width:1px; padding:10px"|A: 2 years
B: 2 years
|}
</div>
If each prisoner only cares about their own jail term, then the best choice for each prisoner would be to confess. Confession is what is known as a [[Strictly Dominant Strategy]], as whatever one suspect chooses to do, Confess is the best choice. If Prisoner B confesses, then Prisoner A's best response is to confess, to avoid the ten year prison term. If Prisoner B does not confess, then Prisoner A's best response is still to confess, to get the reward of not going to prison.
The game is usually phrased in terms of two suspects, both of whom have been arrested, and offered a bargain. If both stay silent, they will both serve 6 months in prison for a minor crime. If one of them confesses, this provides evidence of a major crime. The confessor is rewarded by being let off, and the other suspect will serve ten years in prison. If both confess, they will both serve two years.
It is obvious that the best outcome (the [[Pareto optimum]]) for the group would be if both prisoners cooperated and stayed silent: Six months for both prisoners. However, in the "default" setting of the Prisoner's dilemma, we assume that the prisoners are not given the chance to work out such a strategy and that they are interested in their own wellbeing first.
Prisoner A will now analyze his options:
*If Prisoner B chooses "don't confess", Prisoner A's best choice will be "confess": A gets out of prison immediately.
*If Prisoner B chooses "confess", Prisoner A's best choice will be "confess", too: 2 years is better than 10 years.
(The case for Prisoner B is symmetric.)
Using this reasoning, both prisoners will choose "confess", even though it is not best result.
The strategy "confess" is a strictly [[dominant strategy]]: The choice of the Prisoner B does not change the way Prisoner A will act. The "confess/confess" scenario is also the only [[Nash equilibrium]] in this problem.
==Iterated Prisoner's Dilemma==
==Iterated Prisoner's Dilemma==