### Game Theory Decision Tree AnalysisThe diagram above is a decision tree from a game theory scenario involving two players. This tree illustrates the strategic choices available to Player 1 and Player 2, along with their respective payoffs.#### Decision Tree Breakdown:1. **Player 1's Initial Choice**: - **Option: Up** - Player 1 can choose "Up," leading to Player 2's decision node. - If Player 2 chooses "Up": - **Payoff**: Player 1 gets $120; Player 2 gets $5. - If Player 2 chooses "Down": - **Payoff**: Player 1 gets $100; Player 2 gets $10. - **Option: Down** - Player 1 can choose "Down," leading to another decision node for Player 2. - If Player 2 chooses "Up": - **Payoff**: Player 1 gets $95; Player 2 gets $95. - If Player 2 chooses "Down": - **Payoff**: Player 1 gets $15; Player 2 gets $25.#### Question:In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium?#### Options:- [ ] (up, up)- [ ] (up, down)- [ ] (down, up)- [ ] (down, down)- [ ] No EFFICIENT equilibrium existsThis setup allows the players to determine their optimal strategies and identify the Nash equilibrium, where no player can benefit by changing their decision unilaterally.

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Up Down Player 1 Up Down Up Down Player 2 P1 gets $120 P2 gets $5 P1 gets $100 P2 gets $10 P1 gets $95 P2 gets $95 P1 gets $15 P2 gets $25 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No EFFICIENT equilibrium exists

Up Down Player 1 Up Down Up Down Player 2 P1 gets $120 P2 gets $5 P1 gets $100 P2 gets $10 P1 gets $95 P2 gets $95 P1 gets $15 P2 gets $25 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No EFFICIENT equilibrium exists

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

### Game Theory Decision Tree Analysis

The diagram above is a decision tree from a game theory scenario involving two players. This tree illustrates the strategic choices available to Player 1 and Player 2, along with their respective payoffs.

#### Decision Tree Breakdown:

1. **Player 1's Initial Choice**:
- **Option: Up**
- Player 1 can choose "Up," leading to Player 2's decision node.
- If Player 2 chooses "Up":
- **Payoff**: Player 1 gets $120; Player 2 gets $5.
- If Player 2 chooses "Down":
- **Payoff**: Player 1 gets $100; Player 2 gets $10.
- **Option: Down**
- Player 1 can choose "Down," leading to another decision node for Player 2.
- If Player 2 chooses "Up":
- **Payoff**: Player 1 gets $95; Player 2 gets $95.
- If Player 2 chooses "Down":
- **Payoff**: Player 1 gets $15; Player 2 gets $25.

#### Question:

In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium?

#### Options:
- [ ] (up, up)
- [ ] (up, down)
- [ ] (down, up)
- [ ] (down, down)
- [ ] No EFFICIENT equilibrium exists

This setup allows the players to determine their optimal strategies and identify the Nash equilibrium, where no player can benefit by changing their decision unilaterally.

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