Problem: 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 5% increase in profits. If both firms charge a low price, then each firm will experience a 3% increase in profits. If Firm 1 charges a high price and Firm 2 charges a low price, then Firm 1 will experience a 1% increase in profits and Firm 2 will experience a 6% increase in profits. If Firm 2 charges a high price and Firm 1 charges a low price, then Firm 2 will experience a 2% increase in profits and Firm 1 will experience a 7% increase in profits.
(a) Construct a payoff matrix for this game.
(b) Determine whether each firm has a dominant strategy and, if it does, identify the strategy.
(c) Determine the optimal strategy for each firm.
(d) Determine the Nash equilibrium.
(e) Is this a prisoners' dilemma? How do you know?