An optional question to give you more practice solving games. Consider the following one-shot simultaneous game: David K L 3, 1 0,0 2,8 4, 0 3, 2 1, 2 a. Before solving the game, put yourself in the position of Susan and write down your action. Then independent of that, put yourself in the position of David and write down your action. b. State all the dominated strategies in the full game, by which strategy they are dominated, 2,0 1, 1 2,2 Susan Y and whether weakly or strictly. c. Solve the game by dominance, what is the equilibrium outcome by dominance, if any? d. What are the pure strategy Nash equilibria of this game? e. Argue which NE is more likely and why. You can then relate this argument to your play in part a. f. Assume David is the leader and Susan the follower. Solve the game by backwards induction. What is the equilibrium outcome? Explain your steps. Is David's leadership and advantage to him compared to the simultaneous game? Is David's leadership advantage to Susan?

An optional question to give you more practice solving games. Consider the following one-shot simultaneous game: David K L 3, 1 0,0 2,8 4, 0 3, 2 1, 2 a. Before solving the game, put yourself in the position of Susan and write down your action. Then independent of that, put yourself in the position of David and write down your action. b. State all the dominated strategies in the full game, by which strategy they are dominated, 2,0 1, 1 2,2 Susan Y and whether weakly or strictly. c. Solve the game by dominance, what is the equilibrium outcome by dominance, if any? d. What are the pure strategy Nash equilibria of this game? e. Argue which NE is more likely and why. You can then relate this argument to your play in part a. f. Assume David is the leader and Susan the follower. Solve the game by backwards induction. What is the equilibrium outcome? Explain your steps. Is David's leadership and advantage to him compared to the simultaneous game? Is David's leadership advantage to Susan?

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 3MC

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on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.
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