5. Dominant Strategies. Conceive of two competitors facing important strategic d

Question

5. 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.

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?

Explanation / Answer

(a) Yes there is a Dominant Strategy for Firm A

Dominant strategy occurs when a player is choosing a strategy irrespective of what strategy other player chooses

In the case of Firm A,

When Firm B chooses "left" then Firm A chooses "up"

When Firm B chooses "right" then Firm A chooses "up"

It means decision of Firm A is "up" irrespective of what the decision of Firm B is. Hence "up" is the dominant strategy of Firm A

(b) No, there is no dominant strategy for Firm B

When Firm A chooses "up", Firm B chooses "left"

When Firm B chooses "down", Firm A chooses " right"

This means decision of Firm B is changing withe change in decision of Firm A and hence Firm B has no dominant strategy.

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