Assume two competitors every face important strategic decisions where payoff to each decision depends upon reactions of the competitor. Company A can select either row in the payoff matrix defined below, whereas firm B can choose either column. For firm A the choice is either "up" or "down;" for firm B the choice is either "left" or "right". notice that neither firm can unilaterally choose a given cell in the profit payoff matrix. The ultimate result of this one-shot, simultaneous-move game depends upon the choices made by both competitors. In this payoff matrix, strategic decisions made by firm A or firm B could signify decisions to offer a money-back guarantee, lower prices, offer free shipping, and so on. The first number in each cell is the profit payoff to firm A; the second number is the profit payoff to firm B.

Firm B
Firm A Competitive Strategy Left Right
UP $6 million; $1 Million $4 million; $3.5 Million
Down $2 million; $2 Million $3 million; $3 million

A. Is there a dominant strategy for firm A? If so, what is it?
B. Is there a dominant strategy for firm B? If so, what is it?