(KEY QUESTION) Consider the following one-shot simultaneous game (three actions for each player is the maximum we will consider in this subject, but once you get on top of this, you will see that even large games are equally easy to solve): Phil A B D 6,4 5,8 6,-2 Cindy E 1,2 4,8 2,0 F 5,5 6,2 5,-1 a. Before solving the game, put yourself in the position of Phil and write down your action. Then independent of that, put yourself in the position of Cindy and write down your action. b. State all the dominated strategies in the full game, by which strategy they are dominated, and whether weakly or strictly. c. What is the equilibrium outcome by dominance (by elimination of dominated strategies), if any? d. What are the pure strategy Nash equilibria of this game? Pick one and explain precisely (prove) why it is the Nash equilibrium. e. Argue which NE is more likely and why. You can then relate this argument to your play in part a. f. Prove that the (C, D) outcome is not a NE. g. Assume Phil is the leader and Cindy the follower. Solve the game by backwards induction. What is the equilibrium outcome? Explain your steps.

(KEY QUESTION) Consider the following one-shot simultaneous game (three actions for each player is the maximum we will consider in this subject, but once you get on top of this, you will see that even large games are equally easy to solve): Phil A B D 6,4 5,8 6,-2 Cindy E 1,2 4,8 2,0 F 5,5 6,2 5,-1 a. Before solving the game, put yourself in the position of Phil and write down your action. Then independent of that, put yourself in the position of Cindy and write down your action. b. State all the dominated strategies in the full game, by which strategy they are dominated, and whether weakly or strictly. c. What is the equilibrium outcome by dominance (by elimination of dominated strategies), if any? d. What are the pure strategy Nash equilibria of this game? Pick one and explain precisely (prove) why it is the Nash equilibrium. e. Argue which NE is more likely and why. You can then relate this argument to your play in part a. f. Prove that the (C, D) outcome is not a NE. g. Assume Phil is the leader and Cindy the follower. Solve the game by backwards induction. What is the equilibrium outcome? Explain your steps.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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