Matrix Games and Nash Equilibrium

A crime has been committed for which two prisoners are held incommunicado. The district attorney is assigned to question the prisoners. He designs the following incentive structure to induce the prisoners to talk. If neither prisoner talks, both prisoners automatically receive mild sentences (payoff 4). But if exactly one prisoner squeals on the other, the squealer is let off scot free (payoff 5), while the “squealee” is subject to a severe sentence (payoff 0). Finally, if both prisoners squeal, they share the severe punishment (payoff 1).