Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter10: Monopolistic Competition And Oligopoly
Section: Chapter Questions
Problem 13PAE
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Question
Transcribed Image Text:### Efficient Sub-game Perfect Nash Equilibrium in the Given Game
#### Game Structure
The game depicted above involves two players, Player 1 and Player 2, who choose between two options: "Up" and "Down." The decision tree branches out based on these choices.
Here's a detailed breakdown of the game structure:
#### Decision Points:
1. **Player 1 Choices:**
- **Up**
- **Down**
2. **Player 2 Choices (conditional upon Player 1's choice):**
- If Player 1 chooses **Up**:
- Player 2 chooses **Up**
- Result: Player 1 gets $45, Player 2 gets $155
- Player 2 chooses **Down**
- Result: Player 1 gets $100, Player 2 gets $10
- If Player 1 chooses **Down**:
- Player 2 chooses **Up**
- Result: Player 1 gets $85, Player 2 gets $85
- Player 2 chooses **Down**
- Result: Player 1 gets $95, Player 2 gets $95
#### Payoff Outcomes:
- If Player 1 -> Up, Player 2 -> Up:
- **Player 1**: $45
- **Player 2**: $155
- If Player 1 -> Up, Player 2 -> Down:
- **Player 1**: $100
- **Player 2**: $10
- If Player 1 -> Down, Player 2 -> Up:
- **Player 1**: $85
- **Player 2**: $85
- If Player 1 -> Down, Player 2 -> Down:
- **Player 1**: $95
- **Player 2**: $95
#### Efficient Sub-game Perfect Nash Equilibrium
In the given game, the question is to identify the efficient sub-game perfect Nash equilibrium. The efficient equilibrium is where both players receive optimal payoffs, considering the strategy combinations.
- (up, up)
- (up, down)
- (down, up)
- **(down, down)**
#### Correct Answer:
- **(down, down)**
This outcome is efficient since it provides both players with equal payoffs of $95 each, which is higher than the other potential payoffs they could receive in different strategy
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