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 𝑐 be a real number such that $0 < 𝑐 < 1$. If the payoff matrix is

	L	R
U	0, 0	0, −c
D	−c, 0	1 − c, 1 − c

then the number of pure strategy Nash Equilibria in the game equals

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The Correct Option is B

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)