5. American Airlines (AA) and United Airlines (UA) are engaging into the following one-shot simultaneous game:...

5. American Airlines (AA) and United Airlines (UA) are engaging into the following one-shot simultaneous game: if AA advertises for a fair from Newark to Chicago and UA does not, AA will make $20 million in profits and UA will make $6 million. If UA advertises and AA does not, AA will make $2 million and UA will make $6 million. If AA advertises and UA advertises, each firm earns $10 million. If neither firm advertises, UA will make $8 million and AA will make $4 million.

(a) Write the payoff matrix for the above game.

(b) Does AA have a dominant strategy?

(c) Does UA have a dominant strategy?

(d) What is the Nash equilibrium for the one-shot game?

Expert Solution

5)a)

		United airlines	united airlines
		Advertise	do not advertise
American airlines	advertise	10,10	20,6
American airlines	do not advertise	2,6	4,8

b) American airlines has a dominant strategy. Dominant strategy is the one that the player chooses irrespective of what the other player choOSes.

AA will choose Advertise no matter what UA does. If UA , advertises then it is best for AA to advertise and if UA chooses not to advertise, it is best for AA to advertise.

c) UA will not have a dominant strategy. UA will oscillate between advertising and not advertising depending on the where he receives the maximum payoff.

d) Nash equilibrium is at advertise,advertise ie (10,10) would be the profits. If AA advertises and UA doesn't, he would receive a lesser payoff than when both of them would have advertised.

Similarly AA will advertise no matter what UA chooses. So the Nash equilibrium is (advertise ,advertise)

(You can comment for doubts)

Rahul Sunny answered 2 years ago

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