Final answer:
In the Prisoner's Dilemma presented, both Jane and Bill have a dominant strategy to confess to avoid the worst personal outcome, despite a mutual silent approach being better collectively.
Step-by-step explanation:
The situation described in the question is an example of the classic Prisoner's Dilemma, a concept in game theory that demonstrates why two rational individuals might not cooperate even if it appears that it is in their best interest to do so.
If Jane trusts Bill to stay silent, her best move would be to also stay silent, incurring a lighter combined sentence. If Jane believes Bill will confess, she should also confess to avoid the longest sentence for herself. Analyzing the choices and resulting sentences, it is clear that both Jane and Bill have a dominant strategy: to confess. This strategy ensures they do not end up with the worst possible outcome for themselves, which is 35 years if the other confesses while they stay silent.
The dilemma exposes the tension between individual rationality and collective rationality, as cooperating (both staying silent) would lead to the best collective outcome.