Managerial Economics: Today’s Agenda
• Game Theory – Chapter 9
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“Strategery” – strategic interdependence
Cartels: Cooperation and Cheating
Auctions
Fun and Games
Sequential interactions
Holland Sweetener versus Monsanto, p. 245
Basic Ideas of Game Theory
• Game theory is the general theory of
strategic behavior.
· Generally depicted in mathematical form.
· Plays an important role in modern
economics.
Optimal decision making when
all decision agents are presumed rational
each attempts to anticipate actions of rivals
Rules, Strategies, Payoffs, and
Equilibrium
Economic situations are treated as games.
 The rules of the game state who can do what,
and when they can do it.
 A player's strategy is a plan for actions in
each possible situation in the game.
 A player's payoff is the amount that the
player wins or loses in a particular situation
in a game.
 A players has a dominant strategy if that
player's best strategy does not depend on
what other players do.
Nash Equilibrium
• Occurs when each player's strategy is
optimal, given the strategies of the other
players.
 A player's best response (or best strategy) is
the strategy that maximizes that player's
payoff, given the strategies of other players.
 A Nash equilibrium is a situation in which
each player makes his or her best response.
Prisoner’s Dilemma
Famous example of game theory.
• Strategies must be undertaken without the full knowledge
of what other players will do.
•Players adopt dominant strategies, but they don't necessarily
lead to the best outcome.
CLYDE
Confess
Not Confess
Confess
4 years each
1 year for Bonnie
and 8 years for
Clyde
8 years for Bonnie
and 1 year for Clyde
3 years each
BONNIE
Not
Confess
Bonnie’s Decision Tree
If Clyde Confesses
If Clyde Does Not Confess
Bonnie
Confess
4 Years in
Prison
Best
Strategy
Bonnie
Not Confess
8 Years in
Prison
Confess
1 Year in
Prison
Best
Strategy
Not Confess
3 Years in
Prison
•A cartel is a group of firms (members of the cartel)
that try to collude to act like a monopoly and share the
monopoly profit.
Problems Facing Cartels
• Members must be convinced to come to
coincidental interests.
• Production levels, or quotas, must be agreed upon.
• Profits must be divided to the cartel members’
satisfaction.
• Members who may cheat must be controlled.
P
Market Demand and Industry
Costs with Ten Firms
D
MR
Q
Market Demand and Industry
Costs with Ten Firms
P
AC
MC
AC
MC
D
MR
Q
Market Demand and Industry
Costs with Ten Firms
P
AC
MC
AC
$12
MC
D
MR
200
Q
Market Demand and Industry
Costs with Ten Firms
Competitive output
and price
P
AC
MC
AC
$12
MC
D
MR
200
Q
Market Demand and Industry
Costs with Ten Firms
Competitive output
and price
P
$18
AC
MC
AC
$12
MC
D
MR
120
200
Q
Market Demand and Industry
Costs with Ten Firms
$18
Competitive output
and price
Cartel output and price
P
AC
MC
AC
$12
MC
D
MR
120
200
Q
Firm A’s Output in the Cartel
P
MC
AC
Q
Firm A’s Output in the Cartel
P
MC
AC
$12
20
Q
Firm A’s Output in the Cartel
P
MC
AC
$12
Competitive quantity and price
20
Q
Firm A’s Output in the Cartel
P
MC
$18
AC
$12
Competitive quantity and price
12
20
Q
Firm A’s Output in the Cartel
Firm A’s output and price with cartel agreement
P
MC
$18
AC
$12
Competitive quantity and price
12
20
Q
Firm A’s Output in the Cartel
Firm A’s output and price with cartel agreement
P
MC
$18
AC
$12
Competitive quantity and price
12
20 24
Q
Firm A’s Output in the Cartel
Firm A’s output and price with cartel agreement
P
MC
$18
Firm A’s output and price if it
cheats on the cartel agreement
AC
$12
Competitive quantity and price
12
20 24
Q
Firm A’s Output in the Cartel
Firm A’s output and price with cartel agreement
P
MC
$18
Firm A’s output and price if it
cheats on the cartel agreement
AC
$12
Competitive quantity and price
12
20 24
Q
Firm A’s Output in the Cartel
Firm A’s output and price with cartel agreement
P
MC
$18
Firm A’s output and price if it
cheats on the cartel agreement
AC
$12
Extra profits earned by cheating
on cartel agreement
12
20 24
Q
Cheating on a Cartel
• Cartel members' possible strategies range from abiding by
their agreement to cheating.
 Cartel members can charge the monopoly price or a lower price.
 Cheating firms can increase profits.
 The best strategy is charging the low price.
General Electric
Cheat on Cartel
(Charge Low Price)
Westing
- house
Cheat on
Cartel
$3 million each
Don’t Cheat
Westinghouse earns $2
million
G.E. earns $8 million
Don’t Cheat
(Charge Monopoly Price)
Westinghouse earns $8
million
G.E. earns $2 million
$6 million each
Restraint of Trade and the Antitrust Laws
• Antitrust laws make it illegal to restrain
trade or attempt to monopolize a market.
– Sherman Antitrust Act of 1890
– Clayton Act of 1914
• Executives face jail time
for fixing prices or agreeing
to limit competition.
Auctions
• Oral versus sealed bid
• First Price Auction
– highest bidder pays his bid and receives object
• Second Price Auction
– highest bidder pays the 2nd highest bid and receive
object
• First and second price Auction
– First and second bidders pay, high bid wins object
Rock, Paper, Scissors
• What are the elements of a
game?
• What are elements of the rock
paper scissors game?
• What is the Nash equilibrium
strategies in this game?
Rock, Paper, Scissors
Knowing this, we can see without the
complex math that to be indifferent to
all 3 options both players should play
Rock, Paper and Scissors in 1/3 of their
games.
Normal form of Rock Paper
Scissors
Seinfeld plays Kramer’s Rock, Paper, Scissors
• Payoffs:
–
–
–
–
Scissors cut paper (Scissors wins)
Rock smashes scissors (Rock wins)
But, rock flies straight through paper (Rock wins)
Both players play the same object results in a tie
• What are elements of Kramer’s rock paper scissors
game?
• What is the Nash equilibrium strategies in this game?
• What does the rock paper scissors game teach us about
baseball? Pitching? Hitting? Sitting “dead red?”
The Auditing Game is like Rock, Paper, Scissors
• Auditing and malfeasance
• Employees determine whether and when to “Enron”
by cooking the books or “Rigas,” the corporation and
take a ”five-finger discount?”
• Auditors determine what receives higher or lower
levels of scrutiny.
• Why is nobody steals and nobody audits not a Nash
equilibrium?
• What are the key features of a Nash equilibrium in the
auditing game?
An Advertising Game
Marlboro’ s Decision
Advertise
Marlboro gets $3
billion profit
Don’t Advertise
Marlboro gets $2
billion profit
Advertise
Camel’s
Decision
Don’t
Advertise
Camel gets $3
billion profit
Marlboro gets $5
billion profit
Camel gets $2
billion profit
Camel gets $5
billion profit
Marlboro gets $4
billion profit
Camel gets $4
billion profit
Does this game explain why Phillip Morris was so happy for
the federal government to restrict tobacco advertising?
A Common-Resource Game
Exxon’s Decision
Drill Two Wells
Drill Two
Wells
Exxon gets $4
million profit
Texaco gets $4
million profit
Texaco’s
Decision
Exxon gets $6
million profit
Drill One
Well
Texaco gets $3
million profit
Drill One Well
Exxon gets $3
million profit
Texaco gets $6
million profit
Exxon gets $5
million profit
Texaco gets $5
million profit
Why People Sometimes Can Cooperate
• Firms that care about future profits will
cooperate in repeated games rather than
cheating in a single game to achieve a onetime gain.
• Will ECON 600 students successfully form
a cartel against Professor Spry? Will they
all agree to turn in poor final exams, so that
he will have to give everyone a large curve?
– FYI, there is a reason past cartels to turn in
blank exams have failed.
Sequential interactions
• Boeing & Airbus communications
technology choice
– Boeing chooses first
• Analyze with backward induction
– Boeing must take Airbus’s best response into
account in making its choice
– Boeing has first mover advantage
• Credible commitment by second mover
can alter first mover choice
Extensive form
sequential game
Holland Sweetener versus Monsanto, p. 245
• Construct the strategic-form payoff matrix or this strategic
pricing problem. Find the Nash equilibrium.
• Now assume that the interaction is sequential where Holland
Sweetner chooses to enter and if so they face the pricing
problem in the second stage. Should Holland Sweetner enter?
• Why do you think Holland Sweetner entered? Were they just
dumb or were there other potential considerations?
• Prior to Holland Sweetner’s entry into the US market, Pepsi
and Coke began deemphasizing the NutraSweet label on their
cans and bottles. Why do you think they did this?
• Explain how Monsanto had a “first-mover’s advantage.”
• Pepsi and Coke were the big winners in this case. Explain why.
Looking Forward
• Assignment 3 due
Oct. 28, Nov. 1 or 2
• Readings:
– Managerial Economics Chapters 10
and 18 (pages 503-513)
• eBay.com, p. 275.