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# Finding dominant strategies given a payoff matrix.

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Dominant Strategies
Suppose two competitors each face important strategic decisions where the payoff to each decision depend 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, 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 \$ 75,000; \$ 10,000 \$ 50,000; \$ 40,000

Down \$ 25,000; \$ 25,000 \$ 80,000; \$ 30,000

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/finding-dominant-strategies-given-a-payoff-matrix-229918

#### Solution Preview

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Dominant Strategies
Suppose two competitors each face important strategic decisions where the payoff to each decision depend 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 ...

#### Solution Summary

In the problem I provide a method for determining if a firm has a dominant strategy. I also provide the equilibrium outcome.

\$2.19

## Dominant strategy & nash equilibrium

Suppose two competitors, Coa, Inc., and Han, Inc., are locked in a bitter pricing struggle in the aluminum industry. In the limit pricing payoff matrix, Coa can choose a given row of outcomes by offering a limit price ("up") or monopoly price ("down"). Han can choose a given column of outcomes by choosing to offer a limit price ("left") or monopoly price ("right"). Neither firm can choose which cell of the payoff matrix to obtain; the payoff for each firm depends upon the pricing strategies of both firms.

Han
Coa Pricing Strategy Limit Price Monopoly Price
Limit Price \$1.5 bil, \$3 bil \$2.5 bil, \$2 bil
Monopoly Price \$1 bil, \$4 bil \$1.75 bil, \$3 billion

a. Is there dominant strategy equilibrium in this problem? If so, what is it?

b. Is there Nash equilibrium in this problem? If so, what is it?

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