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Finding dominant and optimal strategy

From the following payoff matrix, where the payoffs are the profits or losses of the two firms, determine (a) whether firm A has a dominant strategy, (b) whether firm B has a dominant strategy, (c) the optimal strategy for each firm, and (d) the Nash equilibrium, if there is one.

Firm B
___________
Low Price High Price
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Low Price (1,1) (3, -1)
Firm A
High Price (-1,3) (4,2)
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Solution:

(a) whether firm A has a dominant strategy

In case firm B charges a low price,
Firm A will earn a profit of 1 when it charges a low price
Firm A will earn a profit of -1(i.e. a loss of 1) when it charges a high price.

In case firm B charges a high price,
Firm A will make a profit ...

Solution Summary

Solution describes the steps to find out dominant and optimal strategy for each player.

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