Question

Assume Continental and United are the only airlines servicing several routes in the Midwest. Both are contemplating on whether or not to raise their prices on these routes. Also assume that both airliners announce their decision at the same time and that there will be no communication between them prior to making the announcement. If both increase their fares, then Continental will make $15 million profit and United will make $10 million profit. If both keep their fares unchanged, then Continental will lose $10 million and United will make $3 million profit. If one raises its fares and the other does not, then the one that increased its fares will lose $5 million and the other will have a profit of $12 million.
a) Set up the payoff matrix for the decision strategy (to increase fares vs. to keep fares unchanged).
b) What is the dominant strategy for Continental?
c) What is the dominant strategy for United?
d) Is there a dominant equilibrium? If yes, what is it; if not why?.

Answer 1

(a) The payoff matrix is shown as follows:

(b) If United raise prices, then the best strategy for Continental is to Raise prices because of the higher payoff i.e. 15 > 12.

If United keep the prices unchanged, then best strategy for Continental is to Raise prices because of the higher payoff i.e. (- 5) > (-10).

Therefore, the dominant strategy for the Continental is to Raise prices because Continental choose to raise prices irrespective of the decision of United.

(c) If Continental raise prices, then the best strategy for United is to keep the prices unchanged because of the higher payoff i.e. 12 > 10.

If Continental keep the prices unchanged, then best strategy for United is to keep the prices unchanged because of the higher payoff i.e. 3 > (-5).

Therefore, the dominant strategy for the United is to keep the prices unchanged because United choose to keep the prices unchanged irrespective of the decision of Continental.

(d) Yes, there is a dominant equilibrium. Dominant strategy equilibrium refers to the equilibrium at which each player chooses their own dominant strategy.

Dominant equilibrium = (Raise prices, Unchanged prices)

= (-5, 12)