Problem: 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
Firm A Low Price High Price
Low Price (1,1) (3, -1)
High Price (-1,3) (4,2)