Final answer:
The best outcome for Becky and Sarah is to collaborate on cleaning, while the worst is if neither cleans, resulting in a messy room. This situation resembles a prisoner's dilemma, leading to mutual defection due to lack of trust and communication.
Step-by-step explanation:
The best outcome for Becky and Sarah cleaning their room would be both chicas cooperating and cleaning together, spending two hours each, resulting in a clean room without exhaustion. The worst outcome is if both decided not to clean at all, leaving them with a dirty room. This scenario is akin to a prisoner's dilemma, a concept in game theory.
In a prisoner's dilemma, the optimal collective result is for both parties to cooperate, but due to the lack of communication and trust, the expected result is mutual defection. This will lead both Becky and Sarah to the worst outcome because each sister may independently conclude that they are better off not cleaning, regardless of the other's decision. Rational thinking, aimed at personal cost-benefit analysis without cooperation, leads to a scenario where both end up in a less desirable situation.