Question:
In a two-player game, player 1 can choose either U or D as strategies. Player 2 can choose either L or R as strategies. Let π be a real number such that $0 < π < 1$. If the payoff matrix is L R U 0, 0 0, βc D βc, 0 1 β c, 1 β c
then the number of pure strategy Nash Equilibria in the game equals
In a two-player game, player 1 can choose either U or D as strategies. Player 2 can choose either L or R as strategies. Let π be a real number such that $0 < π < 1$. If the payoff matrix is
then the number of pure strategy Nash Equilibria in the game equals
| L | R | |
| U | 0, 0 | 0, βc |
| D | βc, 0 | 1 β c, 1 β c |
Updated On: Feb 10, 2025
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The Correct Option is B
Solution and Explanation
Analyzing Best Responses and Nash Equilibria
Step 1: Best Responses for Player 1
- Player 1 chooses between strategies U (Up) and D (Down).
- Choosing D is a best response to both L and R since it yields higher payoffs compared to U.
Step 2: Best Responses for Player 2
- Player 2 chooses between strategies L (Left) and R (Right).
- Choosing L is a best response when Player 1 chooses U.
- Choosing R is a best response when Player 1 chooses D.
Step 3: Identifying Nash Equilibria
A Nash equilibrium occurs when both players are playing best responses to each other.
- Since U is a best response to L and L is a best response to U, (U, L) is a Nash equilibrium.
- Since D is a best response to R and R is a best response to D, (D, R) is also a Nash equilibrium.
Final Answer:
The two Nash equilibria are:
- (U, L)
- (D, R)
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