Question

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

i.     Construct a payoff matrix for this game.

                        Firm 2

                        High Price       Low Price

Firm 1 High Price       ______, ______

            ______, ______

            Low Price       ______, ______

            ______, ______

(ii)     Determine whether each firm has a dominant strategy and, if it does, identify the strategy.

            Firm 1: ______________

            Firm 2: ______________

(iii)     Determine the optimal strategy for each firm.

Firm 1: ______________

            Firm 2: ______________

(iv)     Determine the Nash equilibrium.

___________________________________________________________

Answer 1

(i)   

	Firm 2: High price	Firm 2: Low price
Firm 1: High Price	(10, 10)	(-3, 7)
Firm 1: Low Price	(6, -2)	(-5, -5)

(ii)
When Firm 1 choose high price, Firm 2's best response is High price (10).
When Firm 1 choose low price, Firm 2's best response is High price (-2).
So, Firm 2's dominant strategy is to choose High price as it always gives higher payoff irrespective of firm 1's strategy.

When Firm 2 choose high price, Firm 1's best response is High price (10).
When Firm 2 choose low price, Firm 1's best response is High price (-3).
So, Firm 1's dominant strategy is to choose High price as it always gives higher payoff irrespective of firm 2's strategy.

(iii) Optimal strategy:
Firm 1: High price
Firm 2: High price
(Optimal strategy is the strategy which gives best payoff given other player's strategy. So, high price is the optimal strategy of both firms.)

(iv) The Nash Equilibrium is (High price, High price) or (10, 10) as best response of both firms occur simultaneously when they choose high price.