(d) (5 points) Explain how this implies that the utility representation of preferences is not unique; that is, there can be several different ways to represent a person's preferences. (e) (2 points) Does your answer above depend on the fact that the person is indifferent between their outcomes? Explain why or why not. Total for Question 3: 4. (10 points) Suppose I know you place a value of 100 utility on winning a game, while I place a utility of only 50. Can we say that you value winning more than I do? Why or why not? (Hint: what if I had said you value winning at $100 while I only valued it at $50). 5. (10 points) Model the following situation as a strategic game, being careful to (i) outline and describe explicitly the different parts of a strategic game and, (ii) justify your choices: A group of ten astronauts has to vote on which one amongst them is a murderer! They all must cast their votes secretly, without seeing how the others have voted; only once all of the ballots are cast are the results revealed. They can vote for any (or none) of the astronauts, but can't change their vote once it has been cast. If any astronaut gets 5 or more votes, they are thrown out the airlock. Obviously, no one wants to get thrown out of an airlock, and the non-murderers would prefer to catch the guilty party. Note that guilt is revealed after vote regardless of what happens - since if they tossed the murderer, the murders will stop, and if they didn't, someone else will be murdered next! Oh no