Suppose two airlines A and B must decide whether to discount a flight from Newark to...

Suppose two airlines A and B must decide whether to discount a flight from Newark to LA. If both firms don’t discount the flight each firm earns a profit of 20. If both firms discount the flight, each firm earns a profit of 10. If firm A discounts the flight while firm B doesn’t, firm A earns a profit of 100 while firm B has a loss of 20. If firm B discounts the flight while firm A doesn’t, firm B earns a profit of 100 while firm A has a loss of 20.

a. Use the information to construct a payoff matrix for firms A and B.

b. Does firm A have a dominant strategy?
c. Does firm B have a dominant strategy?
d. What is the Nash Equilibrium for this game?

Explain your answers.

Solutions

Expert Solution

A. In the following table the payoff matrix Is drawn with the first number in the bracket representing profit of A and second number representing profit of B

A\B	B discounts the flight	B doesn't discount the flight
A discounts the flight	(10,10)	(100,20)
A doesn't discount the flight	(-20,100)	(20,20)

B. The firm A has a dominant strategy of discounting the flight as it will always have a higher payoff than not discounting regardless of B's decision (since 10>-20 in case B discounts the flight) and 100 > 20 in case B doesn't discount

C. Similarly the firm B also has a dominant strategy of discounting the flight as it will always have a higher payoff with discounting regardless of A's decision.

D. Since both have their dominant strategies, they will each use their dominant strategy and the Nash equilibrium will be that both discount their flights and have a profit of 10 each. Neither one of them can increase their profit without the other changing their decision so there is no incentive for either of them to Change their decision and so it is a Nash equilibrium.

Hope it’s clear. Do ask for any clarifications if required.

Rahul Sunny answered 3 months ago

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