GAME THEORY: INSIDE OLIGOPOLY
1. Use the following payoff matrix for a one-shot game to answer the accompanying questions
Player 2
Strategy
Player 1
X
Y
A
5, 5
0, -200
B
-200, 0
20,20
a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently,
simultaneously and without any communication. Which of these outcomes would you consider most likely?
Explain
b. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously
and independently make their decisions. What should player 1 utter, and what outcome do you think would
occur as a result
c. Suppose player 2 can choose her strategy before player 1, that player 1 observes player 2’s choice before
making her decision, and that this move structure is known to both players. What outcome would you
expect? Explain
2. Suppose GM and Ford must simultaneously decide whether to make side-impact airbags standard equipment on
all models. Side-impact airbags raise the price of each automobile by $500. If both Ford and GM make the
airbags standard equipment, each company will earn profits of $1.5billion. If neither company adopts the
airbags technology, each company will earn $0.5 billion. If one company adopts the technology as standard
equipment and the other does not, the adopting company will earn a profit of $2 billion and the other company
will lose $1 billion. If you were a decision maker at GM, would you make side-impact bags standard equipment?
Explain
3. You are a manager that manufactures front and rear windshields for the automobile industry. Due to
economies of scale in the industry, entry by new firms is not profitable. DaimlerChrysler has asked your
company and your only rival to simultaneously submit a price quote for supplying 100,000 front and rear
windshield for its new Jeep. If both of you and your rival submit a low price, each firm supplies 50,000 front and
rear windshields and earns zero profit. If one firm quotes a low price and the other a high price, the low-price
firm supplies 100,000 front and rear windshields and earns a profit of $9 million and the high priced firm
supplies no windshield and loses $1 million. If both firms quote a high price, each firm supplies half the total
amount and earns a $7 million profit. Determine your optimal pricing strategy if you and your rival believe that
the new Jeep is a “special edition” that will be sold only for one year. Would your answer differ if you and your
rival were required to submit price quotes year after year and if in any given year, there is a 50% chance that
DaimlerChrysler would discontinue the Jeep? Explain
4.
Coca-Cola and PepsiCo are the leading competitors in the market for cola products. In 1960 Coca-Cola
introduced Sprite, which today is the worldwide leader in the lemon-lime soft drink market and ranks fourth
among all soft drinks worldwide. Prior to 1999, PepsiCo did not have a product that competed directly against
Sprite and had to decide whether to introduce such a soft drink. By not introducing a lemon-lime drink, PepsiCo
would continue to earn a $200 million profit and Coca Cola would continue to earn a $300 million profit.
Suppose that by introducing a new lemon-line soft drink, one of two possible strategies could be pursued : (1)
PepsiCo could trigger a price war with Coca-Cola in both lemon-lime and cola markets or (2) Coca-Cola could
acquiesce and each firm maintains its current 50/50 split of the cola market and split the lemon-lime market
70/30 in favor of Coca-Cola. If Pepsi introduced a lemon-lime drink and a price war resulted, both companies
would earn profits of $100 million. Alternatively, Coca-Cola and PepsiCo would earn $275 million and $227
million, respectively, if PepsiCo introduce a lemon-lime drink and Coca-Cola acquiesced and split the markets as
listed above. If you were a manager of PepsiCo, would you try to convince your colleagues that introducing the
new soft drink is the most profitable strategy? Why or why not?
5.
What is the relation between a dominant strategy and a Nash equilibrium?
6.
Following our discussion of the ‘transient’ nature of groups and the possible ways to ensure that group
members do not shirk their responsibilities, use game theory to describe the problem of group work and the
suggested solutions to the problem. Make sure your answer contains terminologies and concepts used in game
theory. ?
7.
The following game matrix shows the strategies and payoffs to Sony and Philips as they choose what connection
technology to offer on their televisions. (12)
Philip’s Strategy
Sony’s Strategy
Offer HDMI
Offer S-video
a.
b.
c.
d.
8.
Offer HDMI
Offer S-video
Sony gets $22
Sony gets $22
Philips gets $33
Philips gets $13
Sony gets $10
Sony gets $30
Philips gets $17
Philips gets $20
What is the dominant strategy, if any, for Sony? Why?
What is the dominant strategy, if any, for Philips? Why?
Find the Nash equilibrium or Nash equilibria in this game. Explain.
Is this coordination or a prisoner’s dilemma game? Explain.
In the early 1990s, there was considerable uncertainty in the computer industry about whether the dominant
operating system for future personal computers would be IBM's OS/2 or Microsoft's Windows. Ultimately,
Windows emerged as the dominant system despite the fact that several trade publications viewed OS/2 as the
superior system. Why do you think this outcome prevailed?