Original Question: Delta Airlines and American Airlines compete on the route bet
ID: 1197865 • Letter: O
Question
Original Question:
Delta Airlines and American Airlines compete on the route between Indianapolis
and New York City. Every year, they have to decide what price to charge for holiday season
tickets. Tickets go on sale on the same day, therefore both companies have to make their
decisions independently and simultaneously.
The profits in each possible outcome are given by the following table, the Delta figure listed
first.
American
High Price
Low Price
High Price
10, 8
-5, 17
Delta
Low Price
20, -7
6, 4
-
In a one-shot version of the game, does any of the airlines have a dominant strategy?
If so, explain what those are. Answer:The dominant strategy for both the firm is to charge low price, as the maximum Delta can earn is 20 when it charges low prices. Similarly American will get a payoff of 17 when it charges low prices. Thus low price strategy is the dominant strategy
b. What is the Nash equilibrium of this game?
Answer: The Nash Equilibrium of this game is charging low price i.e. (6,4)
C If the two airlines collude, trying to maximize their combined profits, which strategy
should each of them play? Explain
ANSWER: The combined profit for each strategy is as follows
(H,H) = 10+8 = 18
(H,L) = -5+17 = 12
(L,H) = 20-7 = 13
(L,L) = 6+4 = 10
Thus it two airlines collude, then both should opt for (H,H) strategy
c. Formulate a trigger strategy that may help support collusion if the game specified
above is played repeatedly. ANSWER:A player using a trigger strategy initially cooperates but punishes the opponent if a certain level of defection (i.e., the trigger) is observed. That means if any one deviates from the cooperation then the other player will never cooperate in the future games. Thus when initially Delta and American collude and play (H,H) then if any one of the two tries to lower the price then the other will not also lowers its prices in all the future games. Therefore, if the game has to be played repeatedly then one should not deviates from cooperative position.
NEED THIS ANSWER:
d. Suppose the game is infinitely repeated.
Delta discounts payoffs in future periods at the 10 rate.
American is experiencing some cash flow problems due to its merger with US Airways and is
much more concerned with immediate profit. Because of that, the rate of discounting for
American is 20 per period.
Under these circumstances, if American follows the collusive agreement, the present value of
its profits is :
If American cheats, the present value of its profits is :
If Delta follows the collusive agreement, the present value of its profits is :
If Delta cheats, the present value of its profits is :
Based on your findings above, can collusion in the repeated game be sustained? Explain
American
High Price
Low Price
High Price
10, 8
-5, 17
Delta
Low Price
20, -7
6, 4
-
Explanation / Answer
Present value of profits= profits/(1-discount factor)
Under these circumstances, if American follows the collusive agreement, the present value of
its profits is : 10
If American cheats, the present value of its profits is : 21.25
If Delta follows the collusive agreement, the present value of its profits is : 11.11
If Delta cheats, the present value of its profits is : 22.22
Yes collusion can sustain. With collusion both earn higher profits. And as it is infinitely repeated game and if anyone cheats, the other player will respond to it similarly. This inturn it would lower the profits. So they would not try to cheat and collusion is sustainable
American High price Low price High price (11.11,10.00) (-5.56,21.25) Delta Low price (22.22,-8.75) (6.67,5.00)Related Questions
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