Final answer:
In the Prisoner's Dilemma, Jane and Bill each have a dominant strategy to confess, which would lead to a higher prison sentence for both compared to if they cooperated and stayed silent.
Step-by-step explanation:
The situation described is a classic example of the Prisoner's Dilemma in game theory. Jane and Bill, having been apprehended for bank robbery, face the dilemma: if Jane trusts Bill to stay silent (B), she should also stay silent to achieve the best joint outcome. However, if she believes Bill will confess (A), her best response is also to confess to minimize her prison time. This scenario reveals that the dominant strategy for both Jane and Bill is to confess, as it is the best course of action regardless of the other's decision. This leads to a less favorable outcome for both, compared to if they had both stayed silent.
From the perspective of game theory, when two parties are in a situation where their best individual strategies lead to a worse collective outcome, they are trapped in a Prisoner's Dilemma. Both parties have the incentive to pick the dominant strategy, leading to a suboptimal outcome if they do not find a way to enforce cooperation, such as staying silent.