1. Your Decision: Think of a simple decision you face regularly and formalize it as a decision problem, carefully listing the actions and outcomes without the preference relation. Then assign payoffs to the outcomes and draw the decision tree.
2. Going to the Movies: There are two movie theaters in your neighborhood: Cineclass, which is located one mile from your home, and Cineblast, located three miles from your home. Each is showing three films. Cineclass is showing Casablanca, Gone with the Wind, and Dr. Strangelove, while Cineblast is showing The Matrix, Blade Runner, and Aliens. Your problem is to decide which movie to go to.
a. Draw a decision tree that represents this problem without assigning payoff values.
b. Imagine that you don't care about distance and that your preferences for movies are alphabetic (i.e., you like Aliensthe most and The Matrix the least). Using payoff values 1 through 6 complete the decision tree you drew in part (1). Which option would you choose?
c. Now imagine that your car is in the shop and that the cost of walking each mile is equal to one unit of payoff. Update the payoffs in the decision tree. Would your choice change?