Question 2. Airfare Game. Consider the following airfare game between Qantas and Virgin. Suppose Qantas and Virgin are the only two airlines flying from Melbourne to Sydney. The capacity is 150 passengers for each airline. Each airline has two pricing strategies: charge a regular airfare at $300 or charge a discount airfare at $200. The market demand is uncertain and could be either high or low with equal probability. When demand is high, 260 people would like to take the Melbourne- Sydney trip when the airfare is $300, and additional 120 people (so 380 people in total) would like to take the trip when the airfare is $200. When demand is low, 220 people would like to take the trip when the airfare is $300, and additional 100 people (so 320 people in total) would like to take the trip when the airfare is $200. To make our life easier, we assume that discount air tickets always go to the passengers with highest willingness to pay first. Both airlines have to simultaneously set their airfare before demand is realized. When both airlines set the same airfare, they share the market equally. Moreover, both airlines have the same cost structure with TC(q) = 19000 + 70q. Calculate the expected profit for each airline when both airlines set the airfare at Calculate the expected profit for each airline when both airlines set the airfare at Calculate the expected profit for each airline when the two airlines set different (a) $300. (b) $200. (c) airfares.
Question 2. Airfare Game. Consider the following airfare game between Qantas and Virgin. Suppose Qantas and Virgin are the only two airlines flying from Melbourne to Sydney. The capacity is 150 passengers for each airline. Each airline has two pricing strategies: charge a regular airfare at $300 or charge a discount airfare at $200. The market demand is uncertain and could be either high or low with equal probability. When demand is high, 260 people would like to take the Melbourne- Sydney trip when the airfare is $300, and additional 120 people (so 380 people in total) would like to take the trip when the airfare is $200. When demand is low, 220 people would like to take the trip when the airfare is $300, and additional 100 people (so 320 people in total) would like to take the trip when the airfare is $200. To make our life easier, we assume that discount air tickets always go to the passengers with highest willingness to pay first. Both airlines have to simultaneously set their airfare before demand is realized. When both airlines set the same airfare, they share the market equally. Moreover, both airlines have the same cost structure with TC(q) = 19000 + 70q. Calculate the expected profit for each airline when both airlines set the airfare at Calculate the expected profit for each airline when both airlines set the airfare at Calculate the expected profit for each airline when the two airlines set different (a) $300. (b) $200. (c) airfares.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 2. Airfare Game. Consider the following airfare game between Qantas and Virgin.
Suppose Qantas and Virgin are the only two airlines flying from Melbourne to Sydney. The capacity
is 150 passengers for each airline. Each airline has two pricing strategies: charge a regular airfare at
$300 or charge a discount airfare at $200. The market demand is uncertain and could be either high
or low with equal probability. When demand is high, 260 people would like to take the Melbourne-
Sydney trip when the airfare is $300, and additional 120 people (so 380 people in total) would like
to take the trip when the airfare is $200. When demand is low, 220 people would like to take the
trip when the airfare is $300, and additional 100 people (so 320 people in total) would like to take
the trip when the airfare is $200. To make our life easier, we assume that discount air tickets always
go to the passengers with highest willingness to pay first. Both airlines have to simultaneously set
their airfare before demand is realized. When both airlines set the same airfare, they share the
market equally. Moreover, both airlines have the same cost structure with TC(q) = 19000 + 70q.
Calculate the expected profit for each airline when both airlines set the airfare at
Calculate the expected profit for each airline when both airlines set the airfare at
$200.
Calculate the expected profit for each airline when the two airlines set different
(c)
airfares.
(d)
Construct the payoff matrix for this airfare game between Qantas and Virgin.
Find all Nash equilibria of the game.
(a)
$300.
(b)
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