5) (KEY QUESTION) In the movie Rebel Without a Cause, James Dean and Buzz Gunderson compete for the favours of sixteen year old Judy. Buzz's gang members steal two cars. The group of teenagers gathers on a Los Angeles lookout, with a cliff that drops down to the Pacific Ocean. James and Buzz are to drive the stolen cars toward the cliff. The first person to jump from his car is declared the chicken (which is bad). The last person to jump is the hero (which is good), capturing Judy's affection and the gang's respect. The driverless cars continue over the cliff and plunge to the rocks at its base. Each driver can make two possible actions. Jump when he feels endangered (be a chicken) or jump AFTER the other driver jumps (be a rooster). Assuming that both feel endangered at the same moment, the following matrix represents the payoffs for James and Buzz for each choice of strategy. Buzz Chicken Rooster James Chicken 30, 30 2, 50 Rooster 50, 2 0,0 a. State all the dominated strategies in the game, by which strategy they are dominated, and whether weakly or strictly. b. Solve the game by elimination of dominated strategies. What is the equilibrium outcome by dominance, if any