Question

GAME THEORY AND OLIGOPOLY. Profit payoff Matrix for Subways and Quiznos (Sandwich Style Resturants. Below is the profit payoff matrix for these two restaurants depending on whether they set their Chicken sandwich price HIGH or LOW

            

TABLE 1	Quiznos LOW price	Quiznos HIGH price
Subway LOW price	$7 million for Subway $7 million for Quiznos	$12 million for Subway $5 million for Quiznos
Subway HIGH price	$5 million for Subway $12 million for Quiznos	$9 million for Subway $9 million for Quiznos

a) Using Table, what if any is the collusive outcome? Explain whether it will occur.

b) Using Table, what if any is the Nash equilibrium? Explain whether it will occur.

TABLE 2	Quiznos LOW price	Quiznos HIGH price
Subway LOW price	$7 million for Subway $8 million for Quiznos	$12 million for Subway $6 million for Quiznos
Subway HIGH price	$10 million for Subway $12 million for Quiznos	$9 million for Subway $9 million for Quiznos

c) What is meant by a dominant strategy? Using Table 2, is there a dominant strategy? Explain, and determine which outcome will occur?

Answer 1

a) There is a collusive outcome when both charge a HIGH price. This is because the collective payoff is greater at 9 million for both which is highest of all options (HIGH, HIGH). No this is not likely to take place since both players have a dominant strategy of charging LOW price. This is because their profits are higher (7 million vs 5 million and 12 million vs 9 million) when they charge a LOW price.

b) Both players have a dominant strategy of charging LOW price. This is because their profits are higher (7 million vs 5 million and 12 million vs 9 million) when they charge a LOW price. This is the Nash equilibrium (LOW, LOW). It will occur because players will act independently and select their dominant strategies

c) This is the best possible response of a player given all the choices and it remains unchanged when the rival changes his own response. Subway has no dominant strategy because it charges HIGH price when Quiznos charge a LOW price but charges a HIGH price when Quiznos charges a HIGH price. However Quiznos charges a LOW price for any strategy selected by Subway. Hence, Quiznos has a dominant strategy of LOW price.