Becky and Sarah are sisters who share a room. Their room can easily get messy, and their parents are always telling them to tidy it. Here are the costs and benefits to both Becky and Sarah, of taking the time to clean their room: If both Becky and Sarah clean, they each spends two hours and get a clean room. If Becky decides not to clean and Sarah does all the cleaning, then Sarah spends 10 hours cleaning (Becky spends 0) but Sarah is exhausted. The same would occur for Becky if Sarah decided not to clean-Becky spends 10 hours and becomes exhausted. If both girls decide not to clean, they both have a dirty room.

a. What is the best outcome for Becky and Sarah? What is the worst outcome? (It would help you to construct a prisoner's dilemma table.)

b. Unfortunately, we know that the optimal outcome will most likely not happen, and that the sisters probably will choose the worst one instead. Explain what it is about Becky's and Sarah's reasoning that will lead them both to choose the worst outcome.