Sophia and Dorcas are sisters who share the same room. The room can easily get messy, and their parents are always telling them to clean it up. If both Sophia and Dorcas clean, they each spend 2 hours and get a clean room. If Sophia decides not to clean and Dorcas does all the cleaning, Dorcas spends 10 hours cleaning and Sophia spends zero hours, and Dorcas is exhausted. The same would occur for Sophia if Dorcas decided not to clean Sophiaspends 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 Sophia and Dorcas?

b) What is the worst outcome?

c) Unfortunately, we know that the optimal outcome will most likely not happen and that the worst one would be chosen instead. Explain what about Sophia's and Dorcas'sreasoning thatwill lead them both to choose the worst outcome.