Dominant Strategies. Conceive of two competitors facing important strategic deci

Question

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 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

Competitive Strategy

Left

Right

Firm A

Up

$5 million, $10 million

$7.5 million, $4 million

Down

$1 million, $3.5 million

$5 million, $5 million

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

                Firm B

Competitive Strategy

Left

Right

Firm A

Up

$5 million, $10 million

$7.5 million, $4 million

Down

$1 million, $3.5 million

$5 million, $5 million

Explanation / Answer

First we will find out Firm A’s best response to all of Firm B’s actions -

For A-

Since Firm A can go only Up and down

so 5>1 and 7.5>5 so A will have two options 5 (UP-Left)& 7.5 (UP & RIght)

Now For B

Since Firm B can go only Left and RIght-

So, 10>4 & 5>3.5 so B have Options 10 (left Up) and (5 Left- Down)

so we have two nash eqilibrium @ {5(A),10(B)} & {5(A),5(B)}

Firm B has dominant Strategy because in any case Whatever firm A action is Firm B will always have better pay off ($10&$5)

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