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P14.2 Dominant Strategies. Conceive of two competitors facing important strategic decisions where the payoff to each decision depends upon the reactions of the competitor. Firm A can choose either row in the payoff matrix shown here, 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 $5 million, $10 million $7.5 million, $4 million
Down $1 million, $3.5 million $5 million, $5 million

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

Answer:
Up

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

Answer:
No

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1) There is a dominant strategy for firm A: choosing up.
Because in the matrix, we find that A's payoff by choosing up is ...

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