Module
32
Game Theory
Module Objectives
Students will learn in this module:
• How our understanding of oligopoly can be enhanced by using game theory.
• The concept of the prisoners’ dilemma.
• How repeated interactions among oligopolists can result in collusion in the
absence of any formal agreement.
Module Outline
I.Games Oligopolists Play
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A.Definition: The study of behavior in situations of interdependence is known as
game theory.
B.The prisoners’ dilemma
1. Definition: The reward received by a player in a game, such as the profits
earned by an oligopolist, is that player’s payoff.
2. Definition: A payoff matrix shows how the payoff to each of the participants in a two-player game depends on the actions of both. This is illustrated in text Figure 32-1, shown on the next page.
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game theory
A Payoff Matrix
Ajinomoto
Produce 30
million pounds
ADM
Produce
30 million
pounds
Produce
40 million
pounds
Ajinomoto makes
$180 million
profit.
ADM makes
$180 million
profit.
Ajinomoto makes
$150 million
profit.
ADM makes
$200 million
profit.
Produce 40
million pounds
Ajinomoto makes
$200 million
profit.
ADM makes
$150 million
profit.
Ajinomoto makes
$160 million
profit.
ADM makes
$160 million
profit.
a.In a prisoners’ dilemma game, each player has an incentive, regardless of what the other player does, to cheat, to take an action that
benefits it at the other’s expense.
b.When both players in the prisoners’ dilemma cheat, both are worse off
than they would have been if neither had cheated.
c.Definition: An action is a dominant strategy when it is a player’s best
action regardless of the action taken by the other player.
d.Definition: A Nash equilibrium, also known as a noncooperative
equilibrium, is the result when each player in a game chooses the
action that maximizes his or her payoff given the actions of the other
players, ignoring the effects of that action on the payoffs received by
those other players.
C. Overcoming the prisoners’ dilemma: Repeated interaction and tacit collusion
1. Oligopolists in the real world play repeated games.
2. Definition: A firm engages in strategic behavior when it attempts to
influence the future behavior of other firms.
3. Definition: A strategy of tit for tat involves playing cooperatively at first,
then doing whatever the other player did in the previous period. Doing
this, a firm can punish another firm for cheating.
4. Definition: When firms limit production and raise prices in a way that
raises each others’ profits, even though they have not made any formal
agreement, they are engaged in tacit collusion.
5. When oligopolists expect to compete with each other over an extended
period, each individual firm will often find it in its own best interests to
help other firms in the industry, and so there will be tacit
collusion.
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game theory
Teaching Tips
Games Oligopolists Play
Creating Student Interest
Tell students that you are going to give them a pop quiz. The only question on the quiz
is, “What grade would you like to receive on this quiz?” The two permitted answers
are “A” or “C” (though those are not the only possible grades they may receive). Then
explain that the grade they will actually receive on the quiz depends on their answer and
the answer of another student in the class. (Each student will be randomly paired with
another student. If there is an odd number of students in the class, the remaining student will be paired with the instructor.) Tell the students that the grade assigned for the
quiz will be determined by the following payoff matrix:
You
A
C
You: F
You: F
A
Them: F
Other Student
Them: A
You: A
You: C
C
Them: F
Them: A
Have students write their name and their choice (A or C) on a small slip of paper and
collect all the decisions and put them in a hat. Draw two names at a time and inform
the students what grade they receive, based on the payoff matrix. After assigning all the
grades, ask the students what they think. You will likely get comments like “It’s not fair!”
You can also repeat the exercise and/or change the payoffs.
Presenting the Material
Use the payoff matrix below. In this game, there are two airlines, Sky World and Bay City
Airlines, and they have the choice of pricing high or low. Each company’s profit depends
on how the other company responds to its pricing strategy. If both firms collude and
agree on a high price, they each earn $30 in profit. If one prices low and the other prices
high, the low-price firm earns $50 (grabbing market share), while the high price firm
earns only $4. Because of the risk of retaliation, the likely outcome is that both firms
will price low and earn only $10 each. The dominant strategy in this game is to choose
a low price.
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game theory
Sky World
High
Low
+30
+50
High
Bay City
+30
+4
+4
+10
Low
+50
+10
Students should be able to grasp the concept of a dominant strategy from the matrix
provided. They should also be able to understand why a firm would have an incentive to
break an agreement to collude, based on the example from the previous section. These
are all one-period examples. Now that students have mastered one-period games, introduce the concept of a repeated game. Discuss tit for tat and explain that tacit collusion
is a likely outcome.
Case Studies in the Text
Economics in Action
Prisoners of the Arms Race—This EIA looks at the arms race between World War II and the
late 1980s as an example of the application of game theory.
Activities
Tit for Tat? (30–45 minutes)
Organize students into teams of three, with each team representing a specific oligopoly
industry. Each student represents a specific company within the oligopoly. Make this
clear by standing by one team and indicating that one student may play the role of
Kellogg’s, the second Quaker Oats, and the third student General Mills. The goal of each
company is to maximize profits for their corporation.
Explain that during this experiment, each firm must decide whether to choose a high
price for their product (H = $8) or a low price (L = $6). (In this game, oligopolists are
competing on price alone, not on quantities.) If a student is operating as the price leader,
she will signal a high price by thumbs up and a low price by thumbs down.
Before the experiment begins, distribute the following chart for students to fill out.
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Prices
(possible Total sales
Total outcomes of in the Firm’s sales revenue each round)
market
Price
(quantity)
(P x Q)
HHH
60,60,60
Total cost
($110 fixed
and
$2 variable)
Profit
180
H = $8
HHL
20,20,160
200
H = $8
L = $6
HLL
10,100,100
210
H = $8
L = $6
LLL
216
L = $6
72,72,72
During the game, students track their pricing and profits with the form below:
Profit or Loss Statement form (extend this form to show 15 rounds):
Round
Industry situation
(HHH,HHL,HLL,LLL)
Your firm’s price (H or L)
Profit
Loss
1
2
3
4
5
• Tell students that any verbal discussion on pricing strategy during the game will be
punished under antitrust laws: a team can be thrown out into the hall. Optional:
Remind students that the most profitable strategy for the industry as a whole is to
collude.
• To start the experiment, ask each team to choose a price leader for the first round; the student taking this role changes each round. Ask the price leader to choose
a high or low price and signal to the team his or her choice. Then have the two
other students choose their prices and secretly record them on the firm’s profit
sheet, covering their prices with their hands. Now it is time for them to reveal
their pricing decisions to the industry. The oligopoly determines the outcome:
HHH, HHL, HLL, LLL, etc. Then each firm records its individual profit or loss for
this first round.
• Teams continue this process until they have played all 15 rounds: The new price
leader shows the choice of his or her firm’s price, and the two other firms secretly
respond. The two firms show their choice, the oligopoly determines the outcome,
and individual firms record their profit or loss for that round.
• Observe the teams during the game to see if any are able to achieve tacit collusion
and agree on a high price. Because leading with a high price risks rivals
undercutting the price, the least risky strategy is to lead with a low price. Students
tend to use a tit for tat strategy in this game.
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game theory
To Collude or Not? (5–10 minutes)
Use the payoff matrix shown previously for the two airlines to play the following game.
Pair students and tell them that each student in a pair represents an airline in a duopoly. On the count of three, each student chooses a high or a low price by signaling
thumbs up or thumbs down. Students then record their profits based on the payoff
matrix.
Round
Your price
Your payoff
1
2
3
4
5
6
Profit
Debrief the game by pointing out that the dominant strategy in this game is to choose
a low price.
Oligopoly (10 minutes)
The “Classroom Expernomics” website has a variety of classroom experiments that can
be used to teach about oligopoly. Go to http://www.marietta.edu/~delemeeg/expernom.
html and type in oligopoly, collusion or cartel to find interesting activities.
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