Refer to the game. $\begin{array}{c}
\text { Player 2 }\
\text { Player 1}
\begin{array}{|l|l|l|l|}
\hline & \mathrm{t} 1 & \mathrm{t} 2 & \mathrm{t} 3 \
\hline & & & \
\mathrm{S} 1 & 10,0 & 5,1 & 4,-200 \
\hline & & & \
\mathrm{S} 2 & 10,100 & 5,0 & 0,-100 \
\hline
\end{array}\end{array}$ Which of the following pairs of strategies constitute a Nash equilibrium of the game?
A) S1, t1
B) S1, t2
C) S2, t1
D) S1, t2 and S2, t1

Question

Refer to the game. $\begin{array}{c}
\text { Player 2 }\
\text { Player 1}
\begin{array}{|l|l|l|l|}
\hline & \mathrm{t} 1 & \mathrm{t} 2 & \mathrm{t} 3 \
\hline & & & \
 \mathrm{S} 1 & 10,0 & 5,1 & 4,-200 \
\hline & & & \
\mathrm{S} 2 & 10,100 & 5,0 & 0,-100 \
\hline
\end{array}\end{array}$ Which of the following pairs of strategies constitute a Nash equilibrium of the game?
A) S1, t1
B) S1, t2
C) S2, t1
D) S1, t2 and S2, t1

Quizplus · Accepted Answer

A Nash equilibrium is a situation where neither player can improve their payoff by unilaterally changing their strategy.

If Player 1 chooses S1, Player 2's best response is to choose t2 (which gives a payoff of 1 instead of 0). 
If Player 1 chooses S2, Player 2's best response is to choose t1 (which gives a payoff of 10 instead of 0).

Therefore, there are two Nash equilibria in the game: 
1. Player 1 chooses S1 and Player 2 chooses t2 
2. Player 1 chooses S2 and Player 2 chooses t1

So, the correct answer is D, which includes both of these Nash equilibria.

Refer to the Game Which of the Following Pairs of Strategies Constitute a Nash