Managerial Economics in a
Global Economy, 5th Edition
by
Dominick Salvatore
Chapter 10
Game Theory and
Strategic Behavior
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 1
Strategic Behavior
• Decisions that take into account the
predicted reactions of rival firms
– Interdependence of outcomes
• Game Theory
– Players
– Strategies
– Payoff matrix
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 2
Strategic Behavior
• Types of Games
– Zero-sum games
– Nonzero-sum games
• Nash Equilibrium
– Each player chooses a strategy that is
optimal given the strategy of the other
player
– A strategy is dominant if it is optimal
regardless of what the other player does
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 3
Advertising Example 1
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 4
Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses to
advertise?
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 5
Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses to
advertise?
If Firm A chooses to advertise, the payoff is 4. Otherwise,
the payoff is 2. The optimal strategy is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 6
Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses
not to advertise?
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 7
Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses
not to advertise?
If Firm A chooses to advertise, the payoff is 5. Otherwise,
the payoff is 3. Again, the optimal strategy is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 8
Advertising Example 1
Regardless of what Firm B decides to do, the optimal
strategy for Firm A is to advertise. The dominant strategy
for Firm A is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 9
Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses to
advertise?
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 10
Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses to
advertise?
If Firm B chooses to advertise, the payoff is 3. Otherwise,
the payoff is 1. The optimal strategy is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 11
Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses
not to advertise?
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 12
Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses
not to advertise?
If Firm B chooses to advertise, the payoff is 5. Otherwise,
the payoff is 2. Again, the optimal strategy is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 13
Advertising Example 1
Regardless of what Firm A decides to do, the optimal
strategy for Firm B is to advertise. The dominant strategy
for Firm B is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 14
Advertising Example 1
The dominant strategy for Firm A is to advertise and the
dominant strategy for Firm B is to advertise. The Nash
equilibrium is for both firms to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 15
Advertising Example 2
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 16
Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses to
advertise?
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 17
Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses to
advertise?
If Firm A chooses to advertise, the payoff is 4. Otherwise,
the payoff is 2. The optimal strategy is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 18
Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses
not to advertise?
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 19
Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses
not to advertise?
If Firm A chooses to advertise, the payoff is 5. Otherwise,
the payoff is 6. In this case, the optimal strategy is not to
advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 20
Advertising Example 2
The optimal strategy for Firm A depends on which strategy
is chosen by Firms B. Firm A does not have a dominant
strategy.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 21
Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses to
advertise?
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 22
Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses to
advertise?
If Firm B chooses to advertise, the payoff is 3. Otherwise,
the payoff is 1. The optimal strategy is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 23
Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses
not to advertise?
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 24
Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses
not to advertise?
If Firm B chooses to advertise, the payoff is 5. Otherwise,
the payoff is 2. Again, the optimal strategy is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 25
Advertising Example 2
Regardless of what Firm A decides to do, the optimal
strategy for Firm B is to advertise. The dominant strategy
for Firm B is to advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(6, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 26
Advertising Example 2
The dominant strategy for Firm B is to advertise. If Firm B
chooses to advertise, then the optimal strategy for Firm A
is to advertise. The Nash equilibrium is for both firms to
advertise.
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(4, 3)
(5, 1)
(2, 5)
(3, 2)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 27
Prisoners’ Dilemma
Two suspects are arrested for armed robbery. They are
immediately separated. If convicted, they will get a term
of 10 years in prison. However, the evidence is not
sufficient to convict them of more than the crime of
possessing stolen goods, which carries a sentence of
only 1 year.
The suspects are told the following: If you confess and
your accomplice does not, you will go free. If you do not
confess and your accomplice does, you will get 10
years in prison. If you both confess, you will both get 5
years in prison.
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 28
Prisoners’ Dilemma
Payoff Matrix (negative values)
Confess
Individual A
Don't Confess
Prepared by Robert F. Brooker, Ph.D.
Individual B
Confess
Don't Confess
(5, 5)
(0, 10)
(10, 0)
(1, 1)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 29
Prisoners’ Dilemma
Dominant Strategy
Both Individuals Confess
(Nash Equilibrium)
Confess
Individual A
Don't Confess
Prepared by Robert F. Brooker, Ph.D.
Individual B
Confess
Don't Confess
(5, 5)
(0, 10)
(10, 0)
(1, 1)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 30
Prisoners’ Dilemma
Application: Price Competition
Firm A
Low Price
High Price
Prepared by Robert F. Brooker, Ph.D.
Firm B
Low Price
High Price
(2, 2)
(5, 1)
(1, 5)
(3, 3)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 31
Prisoners’ Dilemma
Application: Price Competition
Dominant Strategy: Low Price
Firm A
Low Price
High Price
Prepared by Robert F. Brooker, Ph.D.
Firm B
Low Price
High Price
(2, 2)
(5, 1)
(1, 5)
(3, 3)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 32
Prisoners’ Dilemma
Application: Nonprice Competition
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(2, 2)
(5, 1)
(1, 5)
(3, 3)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 33
Prisoners’ Dilemma
Application: Nonprice Competition
Dominant Strategy: Advertise
Firm A
Advertise
Don't Advertise
Prepared by Robert F. Brooker, Ph.D.
Firm B
Advertise
Don't Advertise
(2, 2)
(5, 1)
(1, 5)
(3, 3)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 34
Prisoners’ Dilemma
Application: Cartel Cheating
Firm A
Cheat
Don't Cheat
Prepared by Robert F. Brooker, Ph.D.
Firm B
Cheat
Don't Cheat
(2, 2)
(5, 1)
(1, 5)
(3, 3)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 35
Prisoners’ Dilemma
Application: Cartel Cheating
Dominant Strategy: Cheat
Firm A
Cheat
Don't Cheat
Prepared by Robert F. Brooker, Ph.D.
Firm B
Cheat
Don't Cheat
(2, 2)
(5, 1)
(1, 5)
(3, 3)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 36
Extensions of Game Theory
• Repeated Games
– Many consecutive moves and
countermoves by each player
• Tit-For-Tat Strategy
– Do to your opponent what your
opponent has just done to you
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 37
Extensions of Game Theory
• Tit-For-Tat Strategy
– Stable set of players
– Small number of players
– Easy detection of cheating
– Stable demand and cost conditions
– Game repeated a large and
uncertain number of times
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 38
Extensions of Game Theory
• Threat Strategies
– Credibility
– Reputation
– Commitment
– Example: Entry deterrence
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 39
Entry Deterrence
No Credible Entry Deterrence
Firm A
Low Price
High Price
Credible Entry Deterrence
Firm A
Low Price
High Price
Prepared by Robert F. Brooker, Ph.D.
Firm B
Enter
Do Not Enter
(4, -2)
(6, 0)
(7, 2)
(10, 0)
Firm B
Enter
Do Not Enter
(4, -2)
(6, 0)
(3, 2)
(8, 0)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 40
Entry Deterrence
No Credible Entry Deterrence
Firm A
Low Price
High Price
Credible Entry Deterrence
Firm A
Low Price
High Price
Prepared by Robert F. Brooker, Ph.D.
Firm B
Enter
Do Not Enter
(4, -2)
(6, 0)
(7, 2)
(10, 0)
Firm B
Enter
Do Not Enter
(4, -2)
(6, 0)
(3, 2)
(8, 0)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 41
International Competition
Boeing Versus Airbus Industrie
Boeing
Produce
Don't Produce
Prepared by Robert F. Brooker, Ph.D.
Airbus
Produce
Don't Product
(-10, -10)
(100, 0)
(0, 100)
(0, 0)
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 42
Sequential Games
• Sequence of moves by rivals
• Payoffs depend on entire sequence
• Decision trees
– Decision nodes
– Branches (alternatives)
• Solution by reverse induction
– From final decision to first decision
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 43
High-price, Low-price
Strategy Game
Firm A
Firm B
Pr
High
$100
$100
Low
P
$130
$50
$180
$80
$150
$120
ice
gh
i
H
c
Pri
e
B
rice
A
Lo
w
Pri
ric
P
h
g
Hi
ce
e
B
Low
P
rice
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 44
High-price, Low-price
Strategy Game
ice
Pr
High
gh
i
H
c
Pri
e
B
rice
A
Lo
w
X
X
Low
P
Pri
ric
P
h
g
Hi
ce
B
Low
P
e
rice
Prepared by Robert F. Brooker, Ph.D.
Firm A
Firm B
$100
$100
$130
$50
$180
$80
$150
$120
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 45
High-price, Low-price
Strategy Game
ice
Pr
High
A
e
B
X
igh
H
c
Pri
Lo
w
Pri
X
X
Low
P
rice
ric
P
h
g
Hi
ce
B
Low
P
e
rice
Prepared by Robert F. Brooker, Ph.D.
Firm A
Firm B
$100
$100
$130
$50
$180
$80
$150
$120
Solution:
Both firms
choose low
price.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 46
Airbus and Boeing
Airbus
J
oJ
b
m
u
et
Boeing
$50
$50
$120
$100
$0
$150
$0
$200
B
Soni
0
8
A3
c Cr
uiser
A
No
A3
80
J
oJ
b
m
u
et
B
Soni
Prepared by Robert F. Brooker, Ph.D.
c Cr
uiser
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 47
Airbus and Boeing
Airbus
J
oJ
b
m
u
B
X
Soni
0
8
A3
et
c Cr
uiser
Boeing
$50
$50
$120
$100
$0
$150
$0
$200
A
No
A3
80
J
oJ
b
m
u
B
X
Soni
Prepared by Robert F. Brooker, Ph.D.
et
c Cr
uiser
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 48
Airbus and Boeing
Airbus
J
oJ
b
m
u
B
A
X
No
A3
80
X
Soni
0
8
A3
J
et
c Cr
uiser
oJ
b
m
u
B
X
Soni
Prepared by Robert F. Brooker, Ph.D.
et
c Cr
uiser
$50
Boeing
$50
$120
$100
$0
$150
$0
$200
Solution:
Airbus builds
A380 and
Boeing builds
Sonic Cruiser.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 49
Integrating
Case Study
Firm A
Firm B
60
70
100
50
40
60
Adv
er
75
70
tise
r
e
v
Ad
70
50
90
40
80
50
Adv
ertis 60
e
30
tise
r
e
v
Ad
gh
Hi
c
Pri
e A
Not
A
dver
tise
B
Pri
gh
P
ric
e
Lo
w
ce
tise
r
e
v
Ad
A
Hi
Not
tise
A
w
Lo
ic
Pr
e
Hi
gh
c
Pri
e A
Not
B
Lo
w
Pri
ce
Adv
ertis
e
e
ertis
v
d
A
A
Not
Prepared by Robert F. Brooker, Ph.D.
Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.
Slide 50