1. Consider the car rental insurance scenario in Problem 8. Use the approach described in this chapter to develop your personal utility function for the payoffs associated with this decision. Determine the decision that would result using the utilities instead of the payoffs. Is the decision consistent with your choice? 2. A college football team is trailing 14–0 late in the game. The team is getting close to making a touchdown. If they can score now, hold the opponent, and score one more time, they can tie or win the game. The coach is wondering whether to go for an extra-point kick or a two-point conversion now, and what to do if they can score again. a. Develop a decision tree for the coach’s decision. Develop a utility function to represent the final score for each path in the tree. b. Estimate probabilities for successful kicks or two point conversions. (You might want to do this by some group brainstorming or by calling on experts, such as your school’s coach or a sports journalist.) Using the probabilities and utilities from part (a), determine the optimal strategy. c. Perform a sensitivity analysis on the probabilities to evaluate alternative strategies (such as when the starting kicker is injured).
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