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16) Convert the following extensive form game into a normal form game. Solve the gam find all pure strategy Nash equilibria. 1 A В 2 2 W X 3. 3 1. 2 2, 1

16) Convert the following extensive form game into a normal form game. Solve the gam find all pure strategy Nash equilibria. 1 A В 2 2 W X 3. 3 1. 2 2, 1

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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**Problem 16: Conversion and Solution of Extensive Form Game** The task is to convert the given extensive form game into a normal form game and identify all pure strategy Nash equilibria. **Description of the Extensive Form Game:** - **Players:** The game involves two players, labeled as Player 1 and Player 2. - **Structure:** The game tree has two stages: - At the first stage, Player 1 makes a move with two possible actions, labeled A and B. - At the second stage, Player 2 makes a move after observing Player 1's action. After action A, Player 2 chooses between W and X. After action B, Player 2 chooses between Y and Z. - **Outcomes and Payoffs:** - For action pair (A, W), the payoff is (3, 3). - For action pair (A, X), the payoff is (1, 2). - For action pair (B, Y), the payoff is (4, 4). - For action pair (B, Z), the payoff is (2, 1). **Objective:** - Convert this extensive form representation into a normal form matrix. - Determine all pure strategy Nash equilibria from the normal form representation.
Transcribed Image Text:**Problem 16: Conversion and Solution of Extensive Form Game** The task is to convert the given extensive form game into a normal form game and identify all pure strategy Nash equilibria. **Description of the Extensive Form Game:** - **Players:** The game involves two players, labeled as Player 1 and Player 2. - **Structure:** The game tree has two stages: - At the first stage, Player 1 makes a move with two possible actions, labeled A and B. - At the second stage, Player 2 makes a move after observing Player 1's action. After action A, Player 2 chooses between W and X. After action B, Player 2 chooses between Y and Z. - **Outcomes and Payoffs:** - For action pair (A, W), the payoff is (3, 3). - For action pair (A, X), the payoff is (1, 2). - For action pair (B, Y), the payoff is (4, 4). - For action pair (B, Z), the payoff is (2, 1). **Objective:** - Convert this extensive form representation into a normal form matrix. - Determine all pure strategy Nash equilibria from the normal form representation.
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