Setup and payoffs

In the classic presentation of the Prisoner's Dilemma, you and your fellow bank robber have been arrested and imprisoned. You cannot communicate with each other. You are facing a prison sentence of one year each. Both of you have been offered a chance to betray the other (Defect); someone who Defects gets one year off their own prison sentence, but adds two years onto the other person's prison sentence. Alternatively, you can Cooperate with the other prisoner by remaining silent.

So:

If you both Cooperate (refuse to testify), you each get 1 year in prison.
If one Defects and the other Cooperates, they go free and the other gets 3 years in prison.
If you both Defect (testify), you each get 2 years in prison.

Or in the form of an outcome matrix where $(o_{1}, o_{2})$ is the outcome for Player 1 and Player 2 respectively:

$\begin{matrix} Player 2 Defects: & Player 2 Cooperates: Player 1 Defects: & (2 years, 2 years) & (0 years, 3 years) Player 1 Cooperates: & (3 years, 0 years) & (1 year, 1 year) \end{matrix}$

As usual, we assume:

(For scenarios that would reproduce the resulting ideal structure with more realistic human motives and situations, see True_prisoners_dilemma.)

Then we can rewrite the Prisoner's Dilemma as a game with moves $D$ and $C,$ and positive payoffs where $X denotes "X utility":

$\begin{matrix} D_{2} & C_{2} D_{1} & ($ 1, $ 1) & ($ 3, $ 0) C_{1} & ($ 0, $ 3) & ($ 2, $ 2) \end{matrix}$

Significance

In the Prisoner's Dilemma, each player is individually better off Defecting, regardless of what the other player does. However, both players prefer the outcome of mutual Cooperation to the outcome from mutual Defection; that is, the game's only Nash equilibrium is not Pareto optimal. The Prisoner's Dilemma is therefore an archetypal example of a coordination problem.

The Prisoner's Dilemma provoked an enormous amount of debate, mainly due to the tension between those who accepted that it was reasonable or 'rational' to Defect in the Prisoner's Dilemma, and those who found it hard to believe that two reasonable or 'rational' agents would have no ...