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Nau: Game Theory 1 Updated 8/25/11 Homework Problem 2.1 : Consider the game shown here: (a) What are all the Pareto optimal action profiles? (b) What are all of the Nash equilibria? Problem 2.2. Suppose we modify the Battle of the Sexes by changing both of the “2” payoffs to “3” (a) Is this a positive affine transformation of the utilities? Why or why not? (b) Find all of the Nash equilibria. (c) Is this game equivalent to the unmodified version? Why or why not?
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Unformatted text preview: Continued on next page Husband Wife Opera Football Opera 3, 1 0, 0 Football 0, 0 1, 3 C D C 3, 3 0, 5 D 5, 0 1, 1 E 3, 3 1, 3 Nau: Game Theory 2 Updated 8/25/11 More Homework Problem 2.3: Ø Find the Nash equilibria for each of the following road networks, under the same assumptions as in Braess’s paradox • e.g., 1000 drivers going from S to D S D t = 50 t = cars/25 t = cars/25 t = 50 B A t = 0 S D t = cars/25 t = cars/25 t = 50 t = 50 B A t = 5...
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