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 3, 3 -10, 20 Rooster 20, -10 -50, -50 a. State all the dominated strategies in the full 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? c. What are the pure strategy Nash equilibria of this game? (hint: there are two). Choose one of them and explain precisely why it is the Nash equilibrium (recall that two conditions need to be satisfied). Do you think one of them is more likely than the other?
(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 3, 3 -10, 20
Rooster 20, -10 -50, -50
a. State all the dominated strategies in the full 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?
c. What are the pure strategy Nash equilibria of this game? (hint: there are two). Choose one of them
and explain precisely why it is the Nash equilibrium (recall that two conditions need to be satisfied).
Do you think one of them is more likely than the other?
d. How would YOU play the game? If both players played the way you would, would such strategy profile
be a Nash equilibrium?
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