Final answer:
The Prisoner's Dilemma for Jane and Bill illustrates that both have a dominant strategy to confess, which leads to a worse collective outcome than if both stayed silent. Regardless of the other's decision, confessing yields a lighter sentence for the one who confesses.
Explanation:'
The scenario presented for Jane and Bill is a classic example of the Prisoner's Dilemma, a fundamental concept in game theory, a field of study in economics and social science that analyzes strategic interactions between decision makers. If Jane trusts Bill to stay silent, her best move would be to stay silent also, hoping that loyalty prevails and they both receive a 20-year sentence. However, if Jane thinks Bill will confess, she should confess to minimize her sentence, as this would bring her sentence down to 30 years instead of the potential 35 years if only she remained silent.
If we analyze whether Jane has a dominant strategy, we see that no matter what Bill chooses, Jane gets a lighter sentence if she confesses (15 years if Bill stays silent, and 30 years if Bill confesses) compared to staying silent (20 years if Bill stays silent, and 35 years if Bill confesses). Therefore, Jane's dominant strategy is to confess. Bills situation is symmetrical; thus, he also has a dominant strategy to confess. The dilemma is that if both Jane and Bill choose their dominant strategy, they will end up with a worse outcome (30 years each) than if they both had stayed silent (20 years each).