Final answer:
In a Prisoner's Dilemma faced by Mary and Raj, the best choice for Raj, if he trusts Mary to cooperate, is to cheat and continue producing to potentially earn $200. If Mary thinks Raj will cheat, she should work independently to guarantee earning $100. Cooperation would be ideal, leading to $150 each, but the fear of betrayal may lead both to operate independently for a lower guaranteed income.
Step-by-step explanation:
The Prisoner's Dilemma is a fundamental problem in game theory that demonstrates why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so.
When analyzing the scenario presented for Mary and Raj, if Raj is confident that Mary will cooperate by lowering her output, Raj's best choice would be to cheat—meaning he would continue to produce his usual amount. This would lead to Raj earning $200, while Mary earns nothing ($0).
If Mary suspects that Raj might cheat, she should choose to work independently, thereby ensuring that she earns at least $100 rather than risking earning nothing at all. This decision is based on a defensive strategy to minimize potential loss due to a lack of trust.
The outcome of the Prisoner's Dilemma in this case suggests that both Mary and Raj would decide to work independently due to the risk associated with cooperation. However, the most favorable outcome for both parties, if they could ensure cooperation, would be to both agree to lower their output and increase their earnings to $150 each, as this would result in a higher combined payoff for the duo.