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 strictly dominant for firm A? 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 strictly dominant for firm A?
A) All x > 450
B) All x < 450
C) x = 450
D) x < 50

Quizplus · Accepted Answer

For strategy B to be strictly dominant for firm A, the payoff from choosing B must be greater than the payoff from choosing A, regardless of firm B's choice. 
From the given matrix, we can see that the payoff for firm A when choosing B is 100 if firm B chooses C, and 500-x if firm B chooses D. 
On the other hand, the payoff for firm A when choosing A is 50 if firm B chooses C, and 500-x if firm B chooses D. 
Therefore, to check if B is strictly dominant for A, we need to compare the two payoffs:
100 > 50 and 500-x > 200
The second inequality simplifies to x > 300. 
So, for all x > 300, strategy B is strictly dominant for firm A. Since the closest option is "all x > 450", that is our answer.

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