A market has only two sellers. They are both trying to decide on a pricing strategy. If both firms charge a high price, then each firm will experience a 10% increase in profits. If both firms charge a low price, then each firm will experience a 5% decrease in profits. If Firm 1 charges a low price and Firm 2 charges a high price, then Firm 1 will experience a 6% increase in profits and Firm 2 will experience a 2% decrease in profits. If Firm 2 charges a low price and Firm 1 charges a high price, then Firm 2 will experience a 7% increase in profits and Firm 1 will experience a 3% decrease in profits.
(i) Construct a payoff matrix for this game.
(ii) Determine whether each firm has a dominant strategy and, if it does, identify the strategy.
(iii) Determine the optimal strategy for each firm.
(iv) Determine the Nash equilibrium.
(v) Is this a prisoners' dilemma? How do you know?
Firm A and Firm B operate retail malls. Both are trying to determine whether to increase advertising budgets during the holiday season or to keep them constant. Because of contract cycles, Firm A will have to make a commitment regarding an advertising budget before Firm B. Their alternatives and payoffs are displayed in the decision tree diagram. Use this information to determine each firm's optimal strategy and anticipated payoff.
Game theory computations shown for you.