Solution to Prisoner's Dilemma

Proof
From the payoff table:

Each player gains by cooperating, and the best outcome is for neither player to confess.

However, because each player then has the opportunity to improve his position by changing his strategy to confessing, $\left({\text{Don't Confess}, \text{Don't Confess} }\right)$ is not a Nash equilibrium.

Thus there is a single Nash equilibrium:
 * $\left({\text{Confess}, \text{Confess} }\right)$