Up Down Up Down Up gets P2 gets $15 P1 gets $10 P2 gets $10 P1 gets $85 P2 gets $85

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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### 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
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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