Final answer:
The prisoner's dilemma scenario presented shows Jane should stay silent if she trusts Bill, but if she thinks he will confess, then she should confess as well making confession her dominant strategy, which is also true for Bill.
Step-by-step explanation:
The classic scenario similar to the prisoner's dilemma, a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. In this case, if Jane trusts Bill to stay silent, the optimal choice for her is to also stay silent, hoping that trust is honored, resulting in both receiving 20-year sentences.
However, if Jane believes Bill will confess, to minimize her potential sentence, she should also confess, resulting in both receiving 30-year sentences. Jane's dominant strategy is to confess, as it always results in a lesser sentence for her regardless of Bill's decision. This is also Bill's dominant strategy. The prisoner's dilemma highlights the difficulties in achieving the best outcome when individuals cannot trust each other to cooperate.