Chapter 09 – Game Theory and Strategic Thinking
1. Muriel likes her job, but her boss gives lousy bonuses. Muriel was recently
offered a new job with better rewards, and her friend wants to know if she
intends to take it. “It depends on whether the bonus this year is generous.
Let’s wait and see. We’ll !nd out next week.” Explain why Muriel is likely to
be accepting the new job. How could she improve her strategy if she wants
to stay at her cur-rent job and be better rewarded? [LO 9.9]
Answer: Waiting to see what her bonus is this year is not a good strategy.
There is no reason she should expect her boss to behave differently than
2. Suppose you are moving out of the country and need to sell your car fast.
Explain why you are likely to get lower offers from used-car dealers if they
!nd out that you are moving away soon. [LO 9.10]
Answer: If dealers know you are moving soon, they know that you do not
3. Hal is negotiating his salary for a job offer. Hal’s potential employer moves
!rst by making an offer. Hal knows he will accept the offer but asks for a
couple of weeks to think it over. If the offer was acceptable to Hal, why did
he do this? [LO 9.10]
Answer: If Hal is not desperate to get paid right away, asking for more
time may increase his offer. Hal is hoping that by asking for time the
4. Many warrior cultures have codes of conduct that make retreat from
battle and other cowardly behaviors extremely dishonorable. Warriors are
expected to die bravely in battle rather than surrender; if they do retreat,
they face an enormous social stigma. Paradoxically, these codes could help
warriors to win their battles. Explain. [LO 9.11]
Answer: The cultural pressure and stigma essentially remove the option
for retreat. If a warrior knows that retreat is never going to be an
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Chapter 09 – Game Theory and Strategic Thinking
5. A town’s two gas stations are each considering lowering prices to attract
more sales. How this affects the pro!ts for each gas station depends on
whether the other station also lowers prices. The decision matrix in
Figure 9Q-4 shows the payoffs, depending on what each player decides to
do. Suppose both gas stations lower their prices, and they !nd themselves in
the worst-case scenario in which both have also lowered their pro!ts. Now
suppose gas station A announces in an advertisement that it is committed to
keeping the new low prices. Why would gas station A do this? What outcome
would you expect? [LO 9.11]
Answer: Gas station A is using a commitment strategy to signal to gas
station B that it won’t be returning to higher prices. Gas station A is best
off if it has low prices while gas station B has high prices. However, gas
Problems and Applications
1. Say whether each of the following is a rule, a strategy, or a payoff. [LO
9.1]
a. In chess, when you capture your opponent’s king, you win the game.
b. In Monopoly, players frequently mortgage their existing properties to raise
cash to buy new ones.
c. In chess, the rook piece can move any number of spaces directly forward,
back-ward, or to either side, but it cannot move diagonally.
d. In rock-paper-scissors, you might always play rock.
Answer: Rules de!ne the actions that are allowed in a game. Strategies
are the plans of action that players follow to achieve their goals. Payos
are the rewards that come from particular actions.
a. Payoff: In chess, when you capture your opponent’s king, you win the
game.
2. Sharon is going to an auction. Say whether each of the following is a rule,
a strategy, or a payoff. [LO 9.1]
a. Bids must increase in increments of $20.
b. The highest bid wins the item being auctioned.
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Chapter 09 – Game Theory and Strategic Thinking
c. Sharon waits until the bidding is just about to close before she enters a
bid.
d. The money raised from the auction goes to charity.
Answer: Rules de!ne the actions that are allowed in a game. Strategies
are the plans of action that players follow to achieve their goals. Payos
are the rewards that come from particular actions.
3. Two families are trying to decide whether to donate to a fund to build a
public park. The payoffs are shown in Figure 9P-1. [LO 9.2]
a. What is the mutually bene!cial outcome?
b. Acting in their best interests, what strategy will each family choose?
c. Explain why this game is or is not an example of a prisoners’ dilemma.
Answer: In the prisoners’ dilemma, noncooperation is the outcome. If
Family B donates, Family A is best off not donating. If Family B does not
donate, Family A is best off not donating. The same is true for Family B: If
4. In Figure 9P-2, what is the dominant strategy for Player A? What is the
dominant strategy for Player B? [LO 9.3]
Answer: A dominant strategy is a strategy that is the best one for a
player to follow no matter what strategy other players choose. Player A
should choose Strategy 1: If Player B chooses Strategy 1, Player A should
5. A town’s two gas stations are each considering lowering prices to attract
more sales. How this affects the pro!ts for each gas station depends on
whether the other also lowers prices. The decision matrix in Figure 9P-3
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Chapter 09 – Game Theory and Strategic Thinking
shows the payoffs, depending on what each player decides to do. Identify
any Nash equilibria. [LO 9.4]
Answer: A Nash equilibrium is an outcome in a game that is reached
when all players choose the best strategy they can, given the choices of
6. Consider again the two families trying to decide whether to donate to a
fund to build a public park. The payoffs are shown in Figure 9P–1. [LO 9.4,
9.5]
a. What is the Nash equilibrium?
b. Suppose Family A agrees to match the donation of Family B. Under these
new circumstances, what strategy will each family choose?
Answer: Each family has a dominant strategy to not donate. Thus, the
Nash equilibrium is where neither family donates. When both players have
a dominant strategy, playing the dominant strategy will always result in a
7. In which of the following situations, a or b, is a tit-for–tat strategy more
likely to be successful at maintaining cooperation? [LO 9.6]
a. An agreement of mutual support between players on a reality television
show, in which the relatively worst-off player is eliminated every episode.
b. A peace treaty between neighboring countries.
Answer: A tit-for-tat strategy is one in which a player in a repeated game
8. Which of the following are examples of tit-for-tat strategies? [LO 9.6]
a. A friend forgets to send you a birthday card this year, so you decide not to
send one to her on her next birthday.
b. Your friend let you borrow her class notes last week, so you decide to skip
class again this week.
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Chapter 09 – Game Theory and Strategic Thinking
c. You and your roommate take turns buying toilet paper, milk, and other
shared items.
d. Your book club chooses a book you don’t want to read, so you decide not
to go this month.
Answer: a and c. A tit-for-tat strategy is one in which a player in a
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Chapter 09 – Game Theory and Strategic Thinking
9. Using backward induction in Figure 9P-4, decide which class a
hypothetical college student should take her freshman and sophomore years,
assuming that she wants to be an economics major. [LO 9.7]
Answer: Backward induction is the process of analyzing a problem in
reverse, starting with the last choice, then the second-to-last choice, and
10. You need to travel from Minneapolis to Copenhagen; it’s now Tuesday
morning. You know you need to arrive in Copenhagen no later than 4 pm on
Wednesday. Using backward induction in Table 9P–1, choose your travel
itinerary. Enter the Kight numbers for each leg of your trip. [LO 9.7]
803
11. In the sequential game shown in Figure 9P-5, what choice should Player
A make now to achieve the highest payoff at the end of the game? [LO 9.8]
Answer: Player A should choose Strategy 2. Even though the highest
payoff for Player A is if Player A chooses Strategy 1 and Player B chooses
Strategy 4, Player B will not choose Strategy 4 if Player A chooses
12. Company A is considering whether to invest in infrastructure that will
allow it to expand into a new market. Company B is considering whether to
enter the market. Assume the companies know each other’s payoffs. Using
Figure 9P-6, choose the outcome that will occur from the list below. [LO 9.8]
a. A invest, B enter.
b. A invest, B don’t enter.
c. A don’t invest, B enter.
d. A don’t invest, B don’t enter.
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Chapter 09 – Game Theory and Strategic Thinking
13. In the sequential game shown in Figure 9P-7, does Player A have a
!rst-mover advantage? [LO 9.9]
Answer: Yes. If Player A chooses Strategy 1, Player B is better off to
choose Strategy 1. This will leave player A with a payoff of 4 while Player
14. Which of the following are examples of !rst-mover advantage? [LO
9.9]
a. You make an offer on a house. The seller can only accept or reject the
offer.
b. You and your roommate are dividing chores. The chores are written on
slips of paper and drawn from a hat. You get to draw !rst.
c. You are !rst in line to buy a raLe ticket.
d. You can take vacation whenever you like, as long as no other employees
are also scheduled to take vacation. You submit your vacation requests !rst
this year.
15. Which player is likely to have higher bargaining power: a city
government responding to angry citizens’ demands that the trash be
collected regularly or the sanitation workers’ union? Explain your answer.
[LO 9.10]
Answer: The sanitation workers’ union has higher bargaining power
16. Which player is likely to have higher bargaining power: a large,
established company shopping around for a new parts supplier, or a start-up
company trying to sell its parts? Explain your answer. [LO 9.10]
Answer: The established company shopping around for a new parts
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Chapter 09 – Game Theory and Strategic Thinking
17. Figure 9P-8 shows a sequential game in which one player decides
whether to injure another player. The injured player can then choose whether
to sue, which involves costly legal fees. [LO 9.11]
a. What is the predicted outcome in this “game”?
b. The injured party threatens to always sue when injured. Is this a credible
threat? What is the predicted outcome if the injured party has threatened to
always sue when injured?
c. What is the predicted outcome if the injured party has made a binding
commitment to always sue when injured?
Answer:
a. The injurer gets the highest payout if he does harm and does not get
b. Even if the injured party threatens to sue, the injurer knows that the
c. Now that the injured party has made a binding commitment to always
18. Two companies are considering whether to enter a new market. The
decision matrix in Figure 9P-9 shows each company’s payoff, depending on
whether one, both, or neither enters the market. Company A is in Costa Rica.
Company B is in Nicaragua. [LO 9.8]
a. If Company A enters, what should Company B do?
b. If Company B enters, what should Company A do?
c. Suppose the Nicaraguan government releases a press statement that it
will cover any pro!t losses for Company B. How much will this policy cost the
Nicaraguan government? (Hint: Think carefully about what Company A’s best
choice would be.)
Answer:
a. Company B should not enter, to avoid losing $1M.
b. Company A should not enter, to avoid losing $3M.
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