Final answer:
The prisoners in the given scenario face the Prisoner's Dilemma, where remaining silent would result in a minimal two-year sentence for each, but confessing could lead to longer sentences depending on the other's decision.
Step-by-step explanation:
The scenario presented is an example of the Prisoner's Dilemma, a common situation in game theory. If both prisoners remain silent, they will each get a shorter sentence because the evidence against them is not strong. However, if one confesses and the other does not, the confessor will receive a lighter sentence while the silent partner will face a more severe penalty. The offer presented to each prisoner by the police is designed to incentivize self-interested behavior that, unfortunately, results in a worse outcome for both if they both choose to confess. To achieve the best collective outcome, both prisoners should remain silent, resulting in a lower sentence of two years each, compared to the higher sentences if they betray one another.