Question

Consider the following game between passengers options for a route for a quarter of the year between American and United Airlines where quantities are in thousands of passengers and payoffs are in millions of dollars. American Airlines QA = 192 QA = 128 OA = 96 United Airlines Qu = 192 4.0 6.2 9.2 Qu = 128 6.2 8.2 10.2 Qu = 96 9.2 4.6 0 8.2 4.0 10.2 7.6 a. (7 points) Determine the Nash Equilibrium and explain how you got to that conclusion. b. (4 points) Is there any dominant strategy in this game? If so, which one?

Answer 1

a) There is only one Nash equilibrium, where both firms produce a quantity of 128. This implies, Nash equilibrium is (QU = 128, QA = 128)

This is found using the best responses which are shown below as circled choices. For example, when American Airlines select QA = 192, United Airlines will select QU = 96 because it has highest payoff of 4.6. Similarly, when United Airlines select QU = 192, American Airlines will select QA = 96 because it has highest payoff of 4.6

b) No. There is no one choice that proves to be the best for one firm irrespective of what the rival firm is selecting. This can be seen from the figure below where no single strategy has all circles for one player for different choices by rival

PUYOLIS DIL MITTUI American Airlines QA = 192 QA = 128 QA=96 United Airlines Qu = 192 0 4.0 9.2 Qu = 128 6.2 Qu = 96 10.2 9.2 4.6 76 9.2