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600 CHAPTER 14 GAME THEORY AND STRATEGIC BEHAVIOR
14.17. In the mid-1990s, Value Jet wanted to enter the modest expansion). What is the equilibrium in this
market serving routes that would compete head to head sequential-move capacity game?
with Delta Airlines in Atlanta. Value Jet knew that Delta Braeutigam
might respond in one of two ways: Delta could start a
price war or it could be “accommodating,” keeping the No Modest
price at a high level. Value Jet had to decide whether it Expansion Expansion
would enter on a small scale or on a large scale. The No Expansion $1,013, $1,013 $844, $1,125
annual profits (in zillions of dollars) associated with each Besanko Modest Expansion $1,125, $844 $900, $900
strategy are summarized in the following table (where $1,013, $506 $675, $450
the first number is the payoff to Value Jet and the second Major Expansion
the payoff to Delta): 14.19. Boeing and Airbus are competing to fill an
order of jets for Singapore Airlines. Each firm can offer a
Delta price of $10 million per jet or $5 million per jet. If both
Accommodate Price Low firms offer the same price, the airline will split the order
(Price High) (Price War)
between the two firms, 50–50. If one firm offers a higher
Enter on Small Scale 8, 40 2, 32 price than the other, the lower-price competitor wins the
Value Jet entire order. Here is the profit that Boeing and Airbus
Enter on Large Scale 16, 20 4, 24
expect they could earn from this transaction:
a) If Value Jet and Delta choose their strategies simulta- Boeing
neously, what strategies would the two firms choose at P $5m P $10m
the Nash equilibrium, and what would be the payoff for P $5m 30, 30 270, 0
Value Jet? Explain. Airbus
P $10m 0, 270 50, 50
b) As it turned out, Value Jet decided to move first, en-
tering on a small scale. It communicated this information (payoffs are in millions of dollars)
by issuing a public statement announcing that it had lim-
ited aspirations in this marketplace and had no plans to a) What is the Nash equilibrium in this game?
grow beyond its initial small size. Analyze the sequential b) Suppose that Boeing and Airbus anticipate that they
game in which Value Jet chooses “small” or “large” in the will be competing for orders like the one from Singapore
first stage and then Delta accommodates or starts a price Airlines every quarter, from now to the foreseeable future.
war in the second stage. Did Value Jet enhance its profit Each quarter, each firm offers a price, and the payoffs are
by moving first and entering on a small scale? If so, how determined according to the table above. The prices
much more did it earn with this strategy? If not, explain offered by each airline are public information. Suppose
why not? (Hint: Draw the game tree.) that Airbus has made the following public statement:

14.18. Besanko, Inc. and Braeutigam, Ltd. compete in To shore up profit margins, in the upcoming quarter we
the high-grade carbon fiber market. Both firms sell iden- intend to be statesmanlike in the pricing of our aircraft
tical grades of carbon fiber, a commodity product that and will not cut price simply to win an order. However,
will sell at a common market price. The challenge for if the competition takes advantage of our statesmanlike
each firm is to decide upon a capacity expansion strategy. policy, we intend to abandon this policy and will compete
The following problem pertains to this choice.
all out for orders in every subsequent quarter.
a) Suppose it is well known that long-run market demand
in this industry will be robust. In light of that, the payoffs Boeing is considering its pricing strategy for the
associated with various capacity expansion strategies that upcoming quarter. What price would you recommend that
Besanko and Braeutigam might pursue are shown in the Boeing charge? Important note: To evaluate payoffs,
following table. What are the Nash equilibrium capacity imagine that each quarter, Boeing and Airbus receive
choices for each firm if both firms make their capacity their payoff right away. (Thus, if in the upcoming quar-
choices simultaneously? ter, Boeing chooses $5 million and Airbus chooses
b) Again, suppose that the table gives the payoffs to each $10 million, Boeing will immediately receive its profit of
firm under various capacity scenarios, but now suppose $270 million.) Furthermore, assume that Boeing and
that Besanko can commit in advance to a capacity strat- Airbus evaluate future payoffs in the following way: a
egy. That is, it can choose no expansion, modest expan- stream of payoffs of $1 starting next quarter and received
sion, or major expansion. Braeutigam observes this in every quarter thereafter has exactly the same value as a
choice and makes a choice of its own (no expansion or one-time payoff of $40 received immediately this quarter.