Prisoner’s Dilemma — Recollections and Observations

Two prisoners accused of the same crime are kept in separate cells. Only a confession by one or both can lead to conviction. If neither confesses, they can be convicted of a lesser offense, incurring a penalty of one month in prison. If both plead guilty of the major crime, both receive a reduced sentence, five years. If one confesses and the other does not, the first goes free (for having turned State’s evidence), while the other receives the full sentence, ten years in prison. Under the circumstances is it rational to admit guilt or to deny it?