Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Suppose player 1 plays a mixed strategy in which she plays U 25% of the time and D 75% of the time, and player 2 plays a mixed strategy in which she plays L 25% of the time and R 75% of the time. This pair of strategies ✓a Nash equilibrium. Player 1's expected payoff from playing U (when player 2 plays the mixed strategy above) is
Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Suppose player 1 plays a mixed strategy in which she plays U 25% of the time and D 75% of the time, and player 2 plays a mixed strategy in which she plays L 25% of the time and R 75% of the time. This pair of strategies ✓a Nash equilibrium. Player 1's expected payoff from playing U (when player 2 plays the mixed strategy above) is
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:**Simultaneous Game Analysis**
Consider the following simultaneous game matrix involving two players:
| | Player 2 L | Player 2 R |
|---------------|------------|------------|
| **Player 1 U** | (30, 20) | (-10, -10) |
| **Player 1 D** | (-10, -10) | (20, 30) |
Each cell contains the payoff for each player in the format (Player 1 payoff, Player 2 payoff).
**Scenario:**
- Player 1 uses a mixed strategy: plays U (Up) 25% of the time and D (Down) 75% of the time.
- Player 2 uses a mixed strategy: plays L (Left) 25% of the time and R (Right) 75% of the time.
**Analysis Tasks:**
1. Determine whether this pair of strategies forms a Nash equilibrium.
2. Calculate Player 1's expected payoff from playing U, given Player 2's mixed strategy.
*Note:*
- A Nash equilibrium is a strategy profile where no player can benefit by unilaterally changing their strategy.
- Expected payoff for Player 1 when playing U is computed using the probabilities given for Player 2's actions.
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