Final answer:
The best outcome for Becky and Sarah is mutual cleaning, resulting in a clean room with equitable effort, but the worst outcome is neither cleaning, leading to a dirty room. These situations present a classic prisoner's dilemma, where individual reasoning may lead to non-cooperation and a suboptimal outcome.
Step-by-step explanation:
The best outcome for Becky and Sarah is to share the cleaning duties, so they each spend two hours and enjoy a clean room, which fosters cooperation and equitable distribution of labor. This outcome is modeled on the concept of the prisoner's dilemma in game theory, where mutual cooperation results in the best collective outcome. The worst outcome would occur if both Becky and Sarah decide not to clean, resulting in a dirty room and showing a breakdown in cooperation.
Individual reasoning based on self-interest can lead both Becky and Sarah to choose not to clean, expecting the other to do it. This type of reasoning is often influenced by the desire to avoid effort at the cost of another's labor, which can lead to the suboptimal outcome of a dirty room.