# 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?

https://brainmass.com/economics/game-theory/dominant-strategies-and-nash-equilibrium-of-a-game-134779

#### 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.