PROBLEM SET #8 (ALMOST THERE!!!)
Q.1 (1 word or 1 line answers)
(i)
Game theory is best applied to analysis of _______________
(ii)
A coordination problem arises whenever there are ___________
(iii) Game theory suggests that, in the absence of patents, the privately motivated
innovation decisions of firms might lead to ________
(iv)
If you advertise and your rival advertises, you each will earn $5 million in profits.
If neither of you advertise, you will each earn $10 million in profits. However, if one of
you advertises and the other does not, the firm that advertises will earn $15 million and
the non advertising firm will earn $1 million. A dominant strategy of your rival is
_______
(v)
Consider the following innovation game. Firm A must decide whether or not to
introduce a new product. Firm B must decide whether or not to clone firm A's product. If
firm A introduces and B clones, then firm A earns $1 and B earns $10. If A introduces
and B does not clone, then A earns $10 and B earns $2. How many Nash equilibria are
there for this game?
(v)
Q.2
If you advertise and your rival advertises, you each will earn $3 million in profits. If
neither of you advertise, you will each earn $7 million in profits. However, if one of you
advertises and the other does not, the firm that advertises will earn $10 million and the
non-advertising firm will earn $1 million.
a. Create the normal form game
b. Do you have a dominant strategy? If so, what is it?
c. Does your rival have a dominant strategy? If so what is it?
d. Do you and your rival have a secured strategy?
e. If you and your rival plan to be in business for only one year, what is the Nash
equilibrium is for your firm
f. If you and your rival plan to be in business for 15 years, then what is the Nash
equilibrium?
g. . If you and your rival plan to hand your business down to your children, and this
"bequest" goes on forever, then what is the Nash equilibrium when the interest
rate is zero?
Q.3 Two firms produce identical products at zero cost, and they compete by setting
prices. If each firm charges a low price, the both firms earn profits of zero. If each firm
charges a high price, then each firm earns profits of $30. if one firm charges a high price
and the other firm charges a low price, the firm that charges the lowest price earns profits
of $50 and the firm charging the highest price earns profits of zero.
a. Which oligopoly model best describes this situation?
b. Write this game in normal form.
c. Suppose the game is infinitely repeated. Can the players sustain the "collusive
outcome" as a Nash equilibrium if the interest rate if 50 percent? Explain.
Q.4. Would collusion be more likely in the shoe industry or in the airline industry? Why?
Q.5.You are the owner-operator of the Better Gas Station in a small southeastern town.
Over the past 20 years, you and your rival have successfully kept prices at a very high
level. You recently learned that your competitor is retiring and closing his station in two
weeks. What should you do today? Why?
Q.6. What is the difference between a ‘tit for tat’ trigger strategy and a grim trigger
strategy? Which would you use to solve the Prisoner's Dilemma in repeated games?
Explain. Under what circumstances is it likely to fail?
Q.7 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.
Q.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
Offer HDMI
Offer S-video
Sony’s
Strategy
Offer HDMI
Offer S-video
a.
b.
c.
d.
Sony gets $22
Philips gets $33
Sony gets $10
Philips gets $17
Sony gets $22
Philips gets $13
Sony gets $30
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.
Q.9
‘Mafioso Al’ visits merchants in downtown Nanaimo and threatens every merchant with
violent reprisal if they do not pay a certain sum for “protection services.” A journalist
visiting Nanaimo asks a merchant what the merchant is going to do about “Mafioso Al”
and the merchant says “Nothing. I am actually happy Al is threatening me with breaking
my legs if I don’t pay”. Surprised by the answer, the journalist goes to other merchants.
However, the other merchants have the same opinion about “Mafioso Al” and his
extortion practices. What is going on?