Suppose two companies, A and B, are the only two airlines operating in the same
ID: 1195095 • Letter: S
Question
Suppose two companies, A and B, are the only two airlines operating in the same market. Each airline decides whether to charge a high price (H) or a low price (L) for a ticket. In the table below, the dollar amounts (in millions of $) represent the annual profits of the two companies (the first number in each cell refers to Company B and the second number to company A):
Company A
High Price (H) Low Price (L)
High Price (H) 40, 40 0, 50
Company B
Low Price (L) 50, 0 20, 20
a) Does either player have a dominant strategy? Therefore, does the game have a dominant strategy solution? Explain.
b) Does this game have a Nash equilibrium? Explain.
c) Consider what would happen if Company B were able to make its price choice first, before Company A is able to set its price (assume that A is able to observe B’s choice once made).
Would Company B choose the same price as in part a)? Would Company A choose the same price as in part a)? Explain why or why not.
Suppose two companies, A and B, are the only two airlines operating in the same market. Each airline decides whether to charge a high price (H) or a low price (L) for a ticket. In the table below, the dollar amounts (in millions of $) represent the annual profits of the two companies (the first number in each cell refers to Company B and the second number to company A):
Company A
High Price (H) Low Price (L)
High Price (H) 40, 40 0, 50
Company B
Low Price (L) 50, 0 20, 20
a) Does either player have a dominant strategy? Therefore, does the game have a dominant strategy solution? Explain.
b) Does this game have a Nash equilibrium? Explain.
c) Consider what would happen if Company B were able to make its price choice first, before Company A is able to set its price (assume that A is able to observe B’s choice once made).
Would Company B choose the same price as in part a)? Would Company A choose the same price as in part a)? Explain why or why not.
Explanation / Answer
a) When both companies A & B choose high price, they both have a dominant strategy. This game have a dominant strategy because each company has the same optimal choice independent of the other company.
b) The Nash equilibrium for this game is for both companies to choose high price. If company A decides to choose low price, then company B is certainly better off choosing high price, since then B will make greater profits. Similarly, if company A chooses high price, then B will be better off choosing high price, since then B will get a payoff of 40 rather than a payoff of 0. Thus, whatever company A does, company B is better off choosing high price. The same thing goes for company A, it is better off choosing high price as well .
c) Company B would choose the same price as in part a) because by choosing high price he will make greater profits as choosing high price for both the companies is a dominant strategy.
Company A would choose the same as in a part a) because if company B chooses high price, then A will be better off choosing high price, since then A will get a payoff of 40 rather than a payoff of 0.
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