Final answer:
The scenario describes the Prisoner's Dilemma, where two prisoners each face varying prison sentences based on their cooperation or confession. There is no third prisoner involved; the question seems to be misinterpreted the scenario. The best collective outcome for both prisoners is if they remain silent, resulting in a two-year sentence for each.
Step-by-step explanation:
The scenario provided is based on the classic example of the Prisoner's Dilemma, a concept in game theory that demonstrates why two completely rational individuals might not cooperate, even if it appears that it is in their best interest to do so. The third prisoner, mentioned in the question, seems to be a misinterpretation, as the scenario only discusses two prisoners, Prisoner A and Prisoner B. If both prisoners had cooperated by remaining silent, they would have each received a sentence of two years, based on the premise that the evidence against them was not strong.
The outcome of this dilemma varies depending on the actions of the prisoners: If both remain silent, each serves two years. If one confesses and the other remains silent, the confessor receives one year while the silent prisoner receives eight years. If both confess, they each receive five years. However, the officers are attempting to manipulate each prisoner into confessing by implying that the other is already doing so. The officers do not reveal that silence from both parties would lead to the lightest collective sentence. This situation demonstrates the challenges of trust and cooperation in the face of individual incentives.