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# Dominant Strategies and Nash Equilibrium of a Game

Dominant Strategies. Suppose two competitors each face 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 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 \$6million; \$1Million \$4million; \$3.5Million
Down \$2million; \$2Million \$3million; \$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?

#### Solution Preview

A. Is there a dominant strategy for Firm A? If so, what is it?
There is a dominant strategy for firm A: choosing up.
Because in the matrix, we find that A's ...

#### Solution Summary

This solution identifies and explains the Nash Equilibrium of this game.

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