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.
Low Price High Price
Low Price (1,1) (3, -1)
High Price (-1,3) (4,2)
(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 describes the steps to find out dominant and optimal strategy for each player.