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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 seems paradoxical, in that the [[Nash equilibrium]] is not the best solution for both players.

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.

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.

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.

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.

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.

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.

==Iterated Prisoner's Dilemma===

==Iterated Prisoner's Dilemma===

The Iterated Prisoner's dilemma is when the basic game is played multiple times (sometimes infinitely many times). Here, co-operation can be a Nash equilibrium. This requires that each player pays attention to what the other player does on previous "rounds", and punish or reward the other player as appropriate.

The Iterated Prisoner's dilemma is when the basic game is played multiple times (sometimes infinitely many times). Here, co-operation can be a Nash equilibrium. This requires that each player pays attention to what the other player does on previous "rounds", and punish or reward the other player as appropriate.