Refer to the normal-form game of price competition shown below. For what values of x is strategy D strictly dominant for firm B? A) All x 450 B) All x

Question

Refer to the normal-form game of price competition shown below.  For what values of x is strategy D strictly dominant for firm B?
A) All x > 450 
B) All x < 450 
C) x = 450 
D) x < 50

Quizplus · Accepted Answer

For strategy D to be strictly dominant for firm B, it should give a higher payoff to firm B than its other strategies for any choice of firm A.

Suppose firm A chooses strategy C. Then, firm B's payoff from choosing strategy D is 1000 - x, which is greater than its payoff from choosing strategy C (which is only 800).

Now suppose firm A chooses strategy A. Then, firm B's payoff from choosing strategy D is 800 - x, which is greater than its payoff from choosing strategy B (which is only 700).

Since firm B's payoff is higher for strategy D than its other strategies for any choice of firm A, strategy D is strictly dominant for firm B when all x > 450.

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