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.
Burger King and Mac Donald’s are situated on opposite corners of a downtown intersection. Burger King and
Mac Donald’s compete on the basis of the prices they set for their burger, fry, and soda combination meals.
Every Monday, Burger King and Mac Donald’s simultaneously choose their combo meal prices, which will remain
in effect for the rest of the week.
Burger King and MacDonald’s consider only two possible prices: a low price of $3.50 or a high price of
$4.50 for their combination meals. The weekly profit from each of the four possible combinations of decisions
are given in the following table:
Burger King’s price
Low ($3.50)
A
High ($4.50)
B
Low ($3.50)
$3,000, $5,500
Mac Donald’s
price
C
$6,500, $5,000
D
High ($4.50)
$2,000, $9,000
$5,000, $8,000
Payoffs in dollars of weekly profit.
a.
Is the pricing decision facing Burger King and Mac Donald’s a co-ordination game or a prisoners’’
dilemma.
b.
Cooperation between Burger King and Mac Donald’s occurs in cell ____ of the payoff table. The noncooperative outcome occurs in cell ______.
c.
Cell _____ represents cheating by Burger King, while cell _____ represents cheating by MacDonald’s.
d.
If Burger King and Mac Donald’s make their pricing decision just one time, they will likely end up in cell
_______.
e.
Burger King _____________ (can, cannot) credibly threaten to punish MacDonald’s with a retaliatory
price cut.
f.
MacDonald’s _____________ (can, cannot) credibly threaten to punish Burger King with a retaliatory
price cut.
Burger King and Mac Donald’s repeat their simultaneous pricing decisions every Monday and have been
cooperating for many weeks. Now, however, MacDonald’s is considering whether to cheat or to continue
cooperating. Mac’s manager believes that it can only get away with cheating for two weeks before Burger King’s
manager will decide to retaliate with a price cut of its own. The ensuing price war is expected to last for two
weeks and then the two restaurants typically return to period of cooperation again. MacDonald’s manager
employs a discount rate of 0.25 percent per week for the purpose of computing present values.
g.
The weekly (undiscounted) gain to MacDonald’s from cheating is $ ____________. The present value of
the benefits to MacDonald’s from cheating is $ ____________.
h.
The weekly (undiscounted) cost to MacDonald’s from cheating is $ ____________. The present value of
the costs to MacDonald’s from cheating is $ ____________.
i.
In order to maximize the value of the MacDonald’s restaurant, the manager ______________ (should,
should not) cheat.
5. Recently, there have been debates among both students and Faculty in the MBA program about the effectiveness of
group work. Some have called for the entire abolition of group work projects. Based on your knowledge of game
theory, advance an argument in support of this argument.
Others argue that the problems with group work arise because the groups are short lived (usually one semester) and
that to make group work effective, these groups should be maintained for the duration of the program (year or
two). . Would this solve the ‘problem’ of group work?
Suggest another option to deal with the ‘problem’?
6.
What is the relation between a dominant strategy and a Nash equilibrium?
7.
What is the grim trigger strategy, and how does it solve the Prisoner's Dilemma in repeated games? Under what
circumstances is it likely to fail?
8.
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.
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.