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5) The following set of (extensive form) games represent two firms who are attempting to form a cartel. The firms are called "A" and "B". The moves each can make are "Increase output" (1) and "don't increase output" (X). The first game (shown below) represents their behavior in a single period where they act simultaneously, unaware of what their opponent is doing.

5) The following set of (extensive form) games represent two firms who are attempting to form a cartel. The firms are called "A" and "B". The moves each can make are "Increase output" (1) and "don't increase output" (X). The first game (shown below) represents their behavior in a single period where they act simultaneously, unaware of what their opponent is doing.

Exploring Economics
Exploring Economics
8th Edition
ISBN:9781544336329
Author:Robert L. Sexton
Publisher:Robert L. Sexton
Chapter15: Oligopoly And Strategic Behavior
Section: Chapter Questions
Problem 17P
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This is a 2-part question that requires the answer before in order to answer the next one. Thank you for your time.

5) The following set of (extensive form) games represent two firms who are attempting to form a cartel. The firms are called "A" and "B". The moves each can make are "Increase output" (1) and “don't increase output" (X). The first game (shown below) represents their behavior in a single period where they act simultaneously, unaware of what their opponent is doing. Nash Equilibrium (NE) A: B: A: 3 A: 1 A: 4 A: 2 B: 3 B: 4 B: 1 B: 2 a. Solve the game by the Rollback (backward induction) method by identifying the dominant strategies (the ones that the players choose), and circle the Nash Equilibrium (for the entire game) and write it above the starting node. X X A X
Transcribed Image Text:5) The following set of (extensive form) games represent two firms who are attempting to form a cartel. The firms are called "A" and "B". The moves each can make are "Increase output" (1) and “don't increase output" (X). The first game (shown below) represents their behavior in a single period where they act simultaneously, unaware of what their opponent is doing. Nash Equilibrium (NE) A: B: A: 3 A: 1 A: 4 A: 2 B: 3 B: 4 B: 1 B: 2 a. Solve the game by the Rollback (backward induction) method by identifying the dominant strategies (the ones that the players choose), and circle the Nash Equilibrium (for the entire game) and write it above the starting node. X X A X
The second game (shown below) is a repeated game. It represents their behavior in two successive periods. Within each period they act simultaneously, but recall what has happened previously. In the second period, In the second period, the players acquire the same payoffs they did in the first, while retaining the payoffs received in the first. The figure below shows only two of the four possible subgames for the second period. Nash Equilibrium (NE) A: Period 1 B: A Period 2 Nash Equilibrium (NE) A: B: X X X X A: 4 B: 1 X ↑ X A: 6 A: 4 A: 7 A: 5 A: 4 A: 2 A:5 A: 3 B: 6 B: 7 B: 4 B: 5 B: 7 B: 8 B:5 B: 6 a. Solve the game by the Rollback method. Identify the dominant strategies and circle the Nash Equilibrium for each subgame and write it above its starting node. Has the player's behavior changed significantly? Why or why not? A: 2 B: 2 Nash Equilibrium (NE) A: B:
Transcribed Image Text:The second game (shown below) is a repeated game. It represents their behavior in two successive periods. Within each period they act simultaneously, but recall what has happened previously. In the second period, In the second period, the players acquire the same payoffs they did in the first, while retaining the payoffs received in the first. The figure below shows only two of the four possible subgames for the second period. Nash Equilibrium (NE) A: Period 1 B: A Period 2 Nash Equilibrium (NE) A: B: X X X X A: 4 B: 1 X ↑ X A: 6 A: 4 A: 7 A: 5 A: 4 A: 2 A:5 A: 3 B: 6 B: 7 B: 4 B: 5 B: 7 B: 8 B:5 B: 6 a. Solve the game by the Rollback method. Identify the dominant strategies and circle the Nash Equilibrium for each subgame and write it above its starting node. Has the player's behavior changed significantly? Why or why not? A: 2 B: 2 Nash Equilibrium (NE) A: B:
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