CHAPTER 30: Game Applications
TRUE/FALSE
1. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
Under the circumstances, Alec should publicly announce at Thanksgiving that he is not buying a
Christmas gift for Kim.
2. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
Under the circumstances, Alec should publicly announce at Thanksgiving that he is not buying a
Christmas gift for Kim.
3. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
Under the circumstances, Alec should publicly announce at Thanksgiving that he is not buying a
Christmas gift for Kim.
4. In the classic 1960s macabre comedy Dr. Strangelove, the Soviet Union constructed a Doomsday
Machine which would end all life on earth if ever the Soviet Union were attacked. When playing
against a rational opponent, the existence of such a machine would be of great benefit to the Soviets.
5. In the classic 1960s macabre comedy Dr. Strangelove, the Soviet Union constructed a Doomsday
Machine which would end all life on earth if ever the Soviet Union were attacked. In the movie, the
existence of the Doomsday Machine was kept secret. This would enhance the effectiveness of such a
machine.
6. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
If Kim is worried that Alec is going to announce publicly what he is going to do at Thanksgiving, Kim
would definitely be made better off by announcing her action publicly at Halloween.
7. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
If Kim is worried that Alec is going to announce publicly what he is going to do at Thanksgiving, Kim
would definitely be made better off by announcing her action publicly at Halloween.
8. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
If Kim is worried that Alec is going to announce publicly what he is going to do at Thanksgiving, Kim
would definitely be made better off by announcing her action publicly at Halloween.
9. An equilibrium in a sequential game is always a Nash equilibrium in a simultaneous game with
equivalent payoffs.
1. Suppose Boeing and Airbus are both considering expanding their plant capacity as a strategic move
but can’t observe their opponent’s move until their own move has been determined. The following are
time-discounted values of all future profit streams in billions of dollars. Which of the following
strategies are Nash equilibria?
a.
(Expand, Expand)
b.
(Expand, Don’t)
c.
(Don’t, Expand)
d.
(Don’t, Don’t)
e.
(b) and (c)
f.
None are Nash equilibria.
2. Suppose Boeing and Airbus are both considering expanding their plant capacity as a strategic move
but can’t observe their opponent’s move until their own move has been determined. The following are
time-discounted values of all future profit streams in billions of dollars. Which of the following
strategies are Nash equilibria?
a.
(Expand, Don’t)
b.
(Don’t, Don’t)
c.
(Expand, Expand)
d.
(Don’t, Expand)
e.
(b) and (c)
f.
None are Nash equilibria.
3. Suppose Boeing and Airbus are both considering expanding their plant capacity as a strategic move
but can’t observe their opponent’s move until their own move has been determined. The following are
time-discounted values of all future profit streams in billions of dollars. Which of the following
strategies are Nash equilibria?
a.
(Expand, Don’t)
b.
(Don’t, Don’t)
c.
(Don’t, Expand)
d.
(Expand, Expand)
e.
(b) and (c)
f.
None are Nash equilibria.
4. In the little town of Gas Pump, South Dakota, there are two gas stations across the street from each
other, the East station and the West station. A local ordinance requires that they are permitted to
change the price of gasoline only once a week at precisely 8:00 a.m. on Monday and in 5 cent
increments. For some time, the price of gasoline has been stable at $1.50 per gallon, but midweek, the
price each station pays for gasoline changed to $1.50. Given the payoff matrix below, which of the
following strategies is a pure strategy Nash equilibrium?
a.
(raise, raise)
b.
(cut, cut) and (hold, hold)
c.
(hold, hold) and (raise, raise)
d.
(cut, cut), (hold, hold), and (raise, raise)
e.
No pure strategy Nash equilibrium exists.
5. In the little town of Gas Pump, South Dakota, there are two gas stations across the street from each
other, the East station and the West station. A local ordinance requires that they are permitted to
change the price of gasoline only once a week at precisely 8:00 a.m. on Monday and in 5 cent
increments. For some time, the price of gasoline has been stable at $1.50 per gallon, but midweek, the
price each station pays for gasoline changed to $1.49. Given the payoff matrix below, which of the
following strategies is a pure strategy Nash equilibrium?
a.
(hold, hold) and (raise, raise)
b.
(cut, cut) and (hold, hold)
c.
(cut, cut), (hold, hold), and (raise, raise)
d.
(raise, raise)
e.
No pure strategy Nash equilibrium exists.
6. In the little town of Gas Pump, South Dakota, there are two gas stations across the street from each
other, the East station and the West station. A local ordinance requires that they are permitted to
change the price of gasoline only once a week at precisely 8:00 a.m. on Monday and in 5 cent
increments. For some time, the price of gasoline has been stable at $1.50 per gallon, but midweek, the
price each station pays for gasoline changed to $1.44. Given the payoff matrix below, which of the
following strategies is a pure strategy Nash equilibrium?
a.
(cut, cut), (hold, hold), and (raise, raise)
b.
(cut, cut) and (hold, hold)
c.
(hold, hold) and (raise, raise)
d.
(raise, raise)
e.
No pure strategy Nash equilibrium exists.
7. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
If Alec commits at Thanksgiving time not to buy a gift for Kim, Kim will find it in her best interest
a.
to buy a gift for Alec to spite him.
b.
not to buy a gift for Alec.
c.
to buy a gift for Alec with probability 2/7.
d.
to buy a gift for Alec with probability 4/9.
e.
to buy a gift for Alec with probability 4/6.
8. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
If Alec commits at Thanksgiving time not to buy a gift for Kim, Kim will find it in her best interest
a.
to buy a gift for Alec to spite him.
b.
not to buy a gift for Alec.
c.
to buy a gift for Alec with probability 2/7.
d.
to buy a gift for Alec with probability 4/9.
e.
to buy a gift for Alec with probability 4/6.
9. Alec and Kim used to be much better friends than they are now. The problem is what to do about
Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is
If Alec commits at Thanksgiving time not to buy a gift for Kim, Kim will find it in her best interest
a.
not to buy a gift for Alec.
b.
to buy a gift for Alec to spite him.
c.
to buy a gift for Alec with probability 1/6.
d.
to buy a gift for Alec with probability 4/9.
e.
to buy a gift for Alec with probability 4/5.
10. Consider the goalie’s anxiety at the penalty kick. Let the kicker’s payoffs below represent the kicker’s
probability of success and the goalie’s payoffs the probability of failure.
The goalie should defend left with probability
a.
.60.
b.
.20.
c.
.40.
d.
.80.
e.
1.
11. Consider the goalie’s anxiety at the penalty kick. Let the kicker’s payoffs below represent the kicker’s
probability of success and the goalie’s payoffs the probability of failure.
The goalie should defend left with probability
a.
.50.
b.
.38.
c.
.63.
d.
.50.
e.
1.
12. Consider the goa lie’s anxiety at the penalty kick. Let the kicker’s payoffs below represent the kicker’s
probability of success and the goalie’s payoffs the probability of failure.
The goalie should defend left with probability
a.
.38.
b.
.63.
c.
.13.
d.
.88.
e.
1.
13. In a small isolated town, there are two types of people, saints and crooks. In business dealings between
any two residents of this town, the payoffs are below.
What percentage of this town’s residents would be saints in an evolutionary stable strategy?
a.
100%
b.
33.33%
c.
83.33%
d.
28.51%
e.
0%
14. In a small isolated town, there are two types of people, saints and crooks. In business dealings between
any two residents of this town, the payoffs are below.
What percentage of this town’s residents would be saints in an evolutionary stable strategy?
a.
40.42%
b.
50%
c.
100%
d.
87.50%
e.
0%
15. In a small isolated town, there are two types of people, saints and crooks. In business dealings between
any two residents of this town, the payoffs are below.
What percentage of this town’s residents would be saints in an evolutionary stable strategy?
a.
62.50%
b.
100%
c.
87.50%
d.
15.30%
e.
0%
16. Suppose AMD is considering cloning Intel’s latest CPU chip. If AMD enters Intel’s market, Intel can
play Mean, expand its output, drop prices, and try to make AMD’s profit as small as possible or play
Nice by cutting back its output and sharing the market. AMD and Intel both know that after all moves
are complete, the time-discounted profits of future chip production in billions of dollars are
Assuming AMD moves first, which of the following is the Nash equilibrium for sequential play?
a.
c.
(Out, Mean)
b.
d.
(Out, Nice)
17. Suppose AMD is considering cloning Intel’s latest CPU chip. If AMD enters Intel’s market, Intel can
play Mean, expand its output, drop prices, and try to make AMD’s profit as small as possible or play
Nice by cutting back its output and sharing the market. AMD and Intel both know that after all moves
are complete, the time-discounted profits of future chip production in billions of dollars are
Assuming AMD moves first, which of the following is the Nash equilibrium for sequential play?
a.
c.
(In, Mean)
b.
d.
(Out, Nice)
18. Suppose AMD is considering cloning Intel’s latest CPU chip. If AMD enters Intel’s market, Intel can
play Mean, expand its output, drop prices, and try to make AMD’s profit as small as possible or play
Nice by cutting back its output and sharing the market. AMD and Intel both know that after all moves
are complete, the time-discounted profits of future chip production in billions of dollars are
Assuming AMD moves first, which of the following is the Nash equilibrium for sequential play?
a.
c.
(Out, Nice)
b.
d.
(In, Nice)
19. Suppose AMD is considering cloning Intel’s latest CPU chip. If AMD enters Intel’s market, Intel can
play Mean, expand its output, drop prices, and try to make AMD’s profit as small as possible or play
Nice by cutting back its output and sharing the market. AMD and Intel both know that after all moves
are complete, the time-discounted profits of future chip production in billions of dollars are
Assuming AMD moves first, which of the following is the Nash equilibrium for sequential play?
a.
c.
(Out, Mean)
b.
d.
(Out, Nice)
20. Suppose AMD is considering cloning Intel’s latest CPU chip. If AMD enters Intel’s market, Intel can
play Mean, expand its output, drop prices, and try to make AMD’s profit as small as possible or play
Nice by cutting back its output and sharing the market. AMD and Intel both know that after all moves
are complete, the time-discounted profits of future chip production in billions of dollars are
Assuming AMD moves first, which of the following is the Nash equilibrium for sequential play?
a.
c.
(Out, Nice)
b.
d.
(In, Nice)
21. Suppose AMD is considering cloning Intel’s latest CPU chip. If AMD enters Intel’s market, Intel can
play Mean, expand its output, drop prices, and try to make AMD’s profit as small as possible or play
Nice by cutting back its output and sharing the market. AMD and Intel both know that after all moves
are complete, the time-discounted profits of future chip production in billions of dollars are
Assuming AMD moves first, which of the following is the Nash equilibrium for sequential play?
a.
c.
(Out, Nice)
b.
d.
(Out, Mean)
PROBLEM
1. In the movie Dr. Strangelove, crazed U.S. General Jack Ripper orders his B-52 bomber wing to launch
a preemptive nuclear attack on the Soviet Union. General Ripper believes the payoffs for a U.S. first
strike to be as follows
The U.S.S.R. has a little surprise of its own in the movie. It has constructed a Doomsday Machine,
which will automatically destroy all life on earth if the U.S.S.R. is attacked. With the Doomsday
Machine operational, the payoffs for a U.S. first strike are as follows:
a. Prior to the building of the Doomsday Machine, would a Soviet threat to retaliate be
credible? Explain.
b. How does the construction of the Doomsday Machine change this?
c. What purpose did keeping construction of the Doomsday Machine secret serve?
d. In the movie, the Soviet ambassador announced the existence of the Doomsday Machine only after
the attack on the Soviet Union was in progress. Did this serve any useful strategic purpose? Why?
2. Recall from the movie Dr. Strangelove, General Turgison (played by George C. Scott) remarks, “Boy,
I sure wish we had one of those Doomsday Machines.” If both the United States and the Soviet Union
possess a Doomsday Machine, the payoffs for a simultaneous attack are as follows:
Would it be desirable from the U.S. perspective to have its own Doomsday Machine? Explain why or
why not?
3. For the following scenarios, state whether the strategic effect of the firm’s action will cause
competitors to behave more or less aggressively, and why.
a. Sleep Country USA announces that it will beat any competitor’s advertised price by 5%.
b. Termite Woods, a local, new home development, unexpectedly announces that it will decrease by
50% the number of homes it had planned to build in the coming year.
c. Used car dealership Roach Motors announces a 25% price cut on its entire stock.
4. The February 24, 1997, issue of Forbes has an article about a private Belgian utility company which is
aggressively expanding its overseas holdings. Loosely quoting from Forbes, “At least one of the
Belgian utility’s foreign moves was inspired by game theory. Last year, the Belgian utility paid $141
million for 49% of a Hungarian power station. The firm’s CEO figured that if French utilities
threatened to dump cheap power into the Belgian market, he could retaliate by dumping cheap
Hungarian power into France.”
a. What is this CEO trying to accomplish?
b. What is necessary for this plan to be successful?