978-1260152616 Chapter 9 Solution Manual Part 1

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Chapter 09 – Game Theory and Strategic Thinking

CHAPTER 9

GAME THEORY AND STRATEGIC THINKING

Chapter Overview

This chapter introduced the concept of strategic games. Many real-life

situations can be analyzed as if they were strategic games, with associated

rules, strategies, and potential payoffs.

Game theory can explain the logic behind outcomes that might not seem

intuitive at “rst. Sometimes, for example, both players in a simultaneous

game may choose to behave in a way that makes both worse off. When

games are played in turns rather than simultaneously, the “rst mover’s

decision can dictate the outcome of the entire game. With repeated play,

however, the “rst mover’s advantage weakens. Players who can

communicate with each other and agree on a strategy can often secure a

better outcome than if they acted alone. Such agreements may break down

if one side tries to get ahead by defecting.

Backward induction is another useful analytical tool; it allows you to break

down your decisions and predict how they will affect others’ decisions and

shape the “nal payoff.

When trying to solve a real-life problem, whether societal, personal, or

business, it helps to think through these strategic issues. Doing so can help

you see how to “play” the game given the rules and constraints. It also can

help you see how to change the rules and constraints, if possible, to help get

to a better outcome.

Much of the analysis in this chapter involved one player guessing what the

other will do and acting accordingly. In the next chapter, we’ll see that

knowing what one player is planning to do isn’t always easy, and that a lack

of information can have real economic consequences.

Learning Objectives

LO 9.1: Understand strategic behavior and describe the components of a

strategic game.

LO 9.2: Explain why noncooperation is always the outcome in the prisoners’

dilemma.

LO 9.3: Identify whether or not a player has a dominant strategy in a one-

time game.

LO 9.4: Identify whether or not a Nash equilibrium will be reached in a one-

time game.

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Chapter 09 – Game Theory and Strategic Thinking

LO 9.5: Explain how a commitment strategy can be used to achieve

cooperation in a one-time game.

LO 9.6: Explain how repeated play can enable cooperation.

LO 9.7: Explain how backward induction can be used to make decisions.

LO 9.8: Use a decision tree to solve a sequential game.

LO 9.9: De”ne “rst-mover advantage and identify it in practice.

LO 9.10: Explain why patient players have more bargaining power in

repeated games.

LO 9.11: Explain how a commitment strategy can allow players to achieve

their goals by limiting their options.

Chapter Outline

OPENING STORY: LITTERBUGS BEWARE

Games and Strategic Behavior (LO 9.1)

Rules, Strategies, and Payoffs

One-Time Games and the Prisoner’s Dilemma

Prisoner’s Dilemma (LO 9.2)

Finding the Dominant Strategy (LO 9.3)

Reaching Equilibrium (LO 9.4)

Avoiding Competition through Commitment (LO 9.5)

Promoting Competition in the Public Interest

Repeated Play in the Prisoners’ Dilemma (LO 9.6)

The Tit-for–Tat Strategy

BOX FEATURE: REAL LIFE – WHAT DO PRICE-MATCHING GUARANTEES

GUARANTEE?

BOX FEATURE: FROM ANOTHER ANGLE – TIT-FOR–TAT AND HUMAN EMOTIONS

Sequential Games

Think Forward, Work Backward (LO 9.7)

Deterring Market Entry: A Sequential Game (LO 9.8)

BOX FEATURE: WHAT DO YOU THINK? – SURVIVING WITH STRATEGIC

THINKING

First-Mover Advantage in Sequential Games (LO 9.9)

Repeated Sequential Games (LO 9.10)

Commitment in Sequential Games (LO 9.11)

BOX FEATURE: REAL LIFE – DR. STRANGELOVE, OR HOW WE LEARNED TO

LOVE THE COMMITMENT DEVICE

Beyond the Lecture

Class Discussion: Games and Strategic Behavior (LO 9.1)

Consider showing students this brief interview with Vanessa Rousso, a

professional poker player brieJy discussing the use of game theory in poker.

1. What strategic behavior occurs in poker (or similar games)?

2. How can game theory be applied in poker?

3. Can game theory give someone an advantage in poker?

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Chapter 09 – Game Theory and Strategic Thinking

Class Activity: Games, Strategic Behavior, and the Prisoner’s

Dilemma (LO 9.1, LO 9.2)

Consider placing students in groups and having them work through a game

theory problem. A simple prisoner’s dilemma works well with the class. You

can set up a number of scenarios for students to discuss. Additionally,

consider having students attempt one of the free game theory applets

available here.

Class Discussion: One-Time Games and the Prisoner’s Dilemma [LO

9.2]

Consider showing this clip from the British game show Golden Balls. The

players must simply decide to split or steal. If they both choose split, they

split a sum of money. If one person splits and one steals, the person who

steals gets all of the money. If they both steal, they get nothing. You can use

well-timed pauses while showing the video to ask students if they

understand and what they think is going to happen. It’s a great example of

the prisoner’s dilemma, attempts at cooperative game theory, and [Spoiler

Alert] a player defecting from the cooperation strategy. Students really

respond well to the “surprise” ending in this clip.

Class Discussion: One-Time Games and the Prisoner’s Dilemma [LO

9.2]

For a short comic relief, you can show this clip from the cartoon Dilbert.

Keep in mind that games only work if we assume everyone understands the

game, strategies, payoffs, and rules. If we begin to include outside

inJuence, the strategies and payoffs can change.

Clicker Questions

There are three main purposes to clicker questions. First, they are a great

way to do a quick and instant “on demand” test of student understanding of

the material. You can cover material, and instantly get feedback on student

comprehension. You can see whether you need to explain certain topics

again, or move on to the next subject. Second, they are a great method to

break up the class and take a moment away from lecture. It gets the

students actively involved. Finally, certain clicker questions can be framed in

a “discussion” manner, in which you can invite students to talk about the

possible right answer with their peers. You can instruct students to convince

their classmate of a right or wrong answer.

1. What does it mean for a strategy to be dominant? [LO 9.1, LO 9.2]

A. The strategy provides the highest payoffs most of the time

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Feedback: Dominant strategies are best for you no matter the choice of the

other players.

2. Players will be more likely to cooperate in simultaneous games when [LO

9.3]

D. The rules and payoffs of the game aren’t understood by one of the players

3. In sequential games, backwards induction means that? [LO 9.4]

A. The game is played in reverse and the last player chooses “rst

4. The prisoners’ dilemma is a famous game, and has many real-life

applications. What is true about this type of game? [LO 9.2]

A. The Nash equilibrium is not a result of dominant strategies

Feedback: The Nash equilibrium leads to worse payoffs for both players

compared to a cooperative outcome. However, it is the dominant strategy of

both players to NOT cooperate!

5. Which of the following could most likely turn into a prisoner’s dilemma

game? [LO 9.2]

A. A husband and wife each deciding how much spending money to bring on

vacation

Feedback: Perhaps a student discussion question. [C] and [D] could both

be correct. For the boys, the strategies are “embarrass” or “not embarrass”

their friend, with a dominant strategy for each being “embarrass”, even

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Chapter 09 – Game Theory and Strategic Thinking

though it makes them both look bad. For the two countries, the dominant

strategy could be “get more nukes”.

Solutions to End-of–Chapter Questions and Problems

Review Questions

1. Taking an exam can be considered a game. Describe a rule, a strategy,

and payoff for this game. [LO 9.1]

Answer: Rule: The exam might have a time limit, such as one hour.

Another rule could be that you have to show your work when solving a

2. Why is strategic behavior required to win a presidential election? Describe

some of the rules, strategies, and payoffs that de”ne this game in the real

world. [LO 9.1]

Answer: Strategic behavior is about thinking about what your opponent

is likely to do and letting this inform your own choices. Elections involve a

3. Felix and Sam are roommates. They both want the dishes to be washed,

but each would prefer that the other person do it. Use the decision matrix in

Figure 9Q-1 to explain why Felix and Sam are likely to end up with a sink full

of dirty dishes. Their preferences are ranked from 1 (lowest) to 4 (highest).

[LO 9.2]

Answer: If Sam does dishes, Felix prefers not do the dishes (4) rather

than to help Sam (2). If Sam does not do dishes, Felix prefers not to do

dishes either (3) rather than do all the dishes himself (1). No matter what

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Chapter 09 – Game Theory and Strategic Thinking

4. Two neighbors share a pond they have stocked with cat”sh. They have

agreed upon the amount of “shing each can do in order for the stock of

cat”sh to replenish itself. If one neighbor increases the amount he “shes a

little bit, the cat”sh stock could still replenish itself. If both neighbors

increase their “shing, the stock will not be sustainable. Both neighbors would

like to cheat and increase the amount they “sh, but want the other neighbor

to stick to the agreement. [LO 9.2]

a. What is the noncooperative outcome, and why does it occur?

b. What is the cooperative outcome, and how could the neighbors achieve

this outcome?

Answer:

a. The noncooperative outcome is for both neighbors to increase “shing,

which will make them both worse off. This outcome occurs because

b. The cooperative outcome is to stick to the original agreement about

the amount of “shing that is sustainable without having to restock the

5. You have been texting with your friends trying to make plans for this

evening. Your best friend Jocelyn is not sure if she will “nish her homework in

time to come out, but if she does, she wants to go to a new restaurant on the

north end of town that you’ve both been wanting to try. Another group of

friends is going to a restaurant on the south end of town, but you’ve already

been to this restaurant and it was only okay. No one is returning your calls,

but you need to get on the subway and head into town if you want to do

anything this evening. You have to decide whether to head north or south.

Do you have a dominant strategy? Explain why or why not.

Answer: Something can only be a dominant strategy if you want to

6. You have just played rock, paper, scissors with your friend. You chose

scissors and he chose paper, so you won. Is this a Nash equilibrium? Explain

why or why not.

Answer: Even though you don’t regret your choice, your friend regrets his

choice. A Nash equilibrium is reached when all players choose the best

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7. Two “rms each have the option of polluting during production or cleaning

up their production process such that they don’t pollute. Of course, polluting

is cheaper than not polluting. The payoffs for each of the choice

combinations are shown in the decision matrix in Figure 9Q-2. The

government would like to stop pollution by making it illegal and charging a

“ne if a “rm is found polluting. How large does the “ne need to be to keep a

“rm from polluting?

Answer: If the government charges a “ne for pollution, this changes the

8. Explain how you could use a tit-for-tat strategy to motivate your

roommate to do his share of the cleaning. [LO 9.6]

Answer: Tit-for-tat involves taking the same action (or inaction) as the

other player. If your roommate does not pull his weight on cleaning, tit-for–

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Chapter 09 – Game Theory and Strategic Thinking

9. Toni and Kala are new coworkers. They make a plan to go out together

every Thursday night. On their “rst Thursday night out, Toni buys a pitcher of

beer and shares it with Kala. Kala is excited to discover that her Thursday

night outings will include free beer as well as a way to have fun with her new

coworker. Explain why Kala is likely to be disappointed. [LO 9.6]

Answer: It is unlikely that Toni was signaling that she will always buy the

10. Suppose your goal is to be promoted at your job. Use backward

induction to determine what you should do to work toward that goal right

now, and describe each step in your logic. [LO 9.7]

Answer: If your goal is to be promoted, you would start by “nding out the

requirements and preferred quali”cations of the job you want. Next, you

11. You are playing a game with a friend. It’s your move but you don’t have

a dominant strategy. Your payoff depends on what your friend does after your

move. You consider Jipping a coin to decide what to do. You are about to

reach for a coin, but then you realize that your friend has a dominant

strategy. Explain how using backward induction (rather than a coin toss) will

now determine your next move. [LO 9.7]

Answer: If you don’t have a dominant strategy because your payoff

depends on what your friend does after your move, it’s unclear how you

12. Melissa let Jill cheat off of her during a history exam last week. Now

Melissa is threatening to tell on Jill unless Jill pays her $50. Use the decision

tree in Figure 9Q-3 to explain whether Jill will pay Melissa to keep her quiet.

[LO 9.8]

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Answer: Jill will not pay Melissa. Jill knows that Melissa will also be

13. Nicolas has asked for a raise. His boss must decide whether to approve

his request. If Nicolas doesn’t get the raise, he will have to decide whether to

stay at his job or quit. Construct a decision tree for these sequential

decisions and choose a payoff structure where Nicolas has a dominant

strategy to stay at his job even without getting the raise. [LO 9.8]

Answer: Numbers are arbitrary, but students should choose a payoff

14. Job offers could be considered a one-round bargaining game with a

“rst-mover advantage: The company offers you a job at a certain salary, and

you can take it or leave it. Explain why the company might not capture all

the surplus in this game, even if you can’t make a counteroffer. [LO 9.9]

Answer: Even if you cannot make a counteroffer, you do still have

options. Presumably, you have applied to more than one place. At least

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