Refer to the normal-form game of price competition shown below. $\begin{array}{l} \quad\quad\quad\quad\quad\quad\text { Firm B}\ \text { Firm A} \begin{array}{|l|l|l|} \hline & \text { C } & \text { D }\ \hline & & \ \text { A } & 50,50 & 500-x, 200 \ \hline & & \ \text { B } & 100,500-x & 50,50 \ \hline \end{array}\end{array}$ For what values of x is strategy (B,D)the only Nash equilibrium of the game? A) All x 450 B) All x

Question

Refer to the normal-form game of price competition shown below. $\begin{array}{l}
\quad\quad\quad\quad\quad\quad\text { Firm B}\
\text { Firm A}
\begin{array}{|l|l|l|} 
\hline & \text { C } & \text { D }\
\hline & & \
 \text { A } & 50,50 & 500-x, 200  \
\hline & & \
\text { B } & 100,500-x & 50,50 \
\hline
\end{array}\end{array}$ For what values of x is strategy (B,D)the only Nash equilibrium of the game?
A) All x > 450
B) All x < 450
C) x = 450
D) x < 50

Quizplus · Accepted Answer

For (B,D) to be a Nash equilibrium, firm B must have no incentive to deviate from D given that firm A is playing B. In other words, firm B must earn at least 50 by playing D rather than C. 
From the payoffs in the table, we see that 50 ≥ 500 - x, or x ≥ 450. Therefore, (B,D) is a Nash equilibrium for all x > 450. Hence, the answer is (A).

Refer to the Normal-Form Game of Price Competition Shown Below