Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and having separated both prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10 year sentence. If both remain silent, both prisoners are sentenced to only six months in jail on a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?
Assume that each prisoner prefers shorter sentences to longer ones, and that each gets no utility out of lowering the other prisoners sentence, and that there are no reputation effects from a prisoner’s decision.