Exam 11: Game Theory and Strategic Behavior

A Nash equilibrium results when every firm in an industry chooses a strategy that is optimal given the strategies chosen by its competitors.

Two grocery stores compete against each other in a community. Both are considering an increase in advertising expenditures. Their interdependent alternatives are described by the payoff matrix. Firm 2 Advertise Don't Advertise Firm 1 Advertise (3,7) (5,3) Don'tAdvertise (4,5) (3,3) (i) Determine whether each firm has a dominant strategy and, if it does, identify the strategy. (ii) Determine the optimal strategy for each firm. (iii) Determine the Nash equilibrium. (iv) Is this a prisoners' dilemma? How do you know?

Oligopolistic firms often sacrifice profits in order to gain an advantage over competitors in the long run.

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 percent increase in profits. If both firms charge a low price, then each firm will experience a 3 percent decrease in profits. If Firm 1 charges a high price and Firm 2 charges a low price, then Firm 1 will experience a 4 percent decrease in profits and Firm 2 will experience a 6 percent increase in profits. If Firm 2 charges a high price and Firm 1 charges a low price, then Firm 2 will experience a 5 percent decrease in profits and Firm 1 will experience a 7 percent increase 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?

Two car dealerships compete against each other in a small city. Both are considering an increase in marketing expenditures. Their interdependent alternatives and outcomes are described by the decision tree. What is each firm's optimal strategy and anticipated payoff?