Session 19 Game Theory

Session 19 Game Theory - Transcript

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 1

Strategic Behavior
Decisions that take into account the predicted reactions of rival firms
Interdependence of outcomes

Game Theory
Players Strategies Payoff matrix

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

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
PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 3

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 4

Advertising Example 1

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 5

Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses to advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 6

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 B Advertise Don t Advertise 4 3 5 1 2 5 3 2

Firm A

Advertise Don t Advertise

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 7

Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses not to advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 8

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 B Advertise Don t Advertise 4 3 5 1 2 5 3 2

Firm A

Advertise Don t Advertise

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 9

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

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 10

Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses to advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 11

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 B Advertise Don t Advertise 4 3 5 1 2 5 3 2

Firm A

Advertise Don t Advertise

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 12

Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses not to advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 13

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 B Advertise Don t Advertise 4 3 5 1 2 5 3 2

Firm A

Advertise Don t Advertise

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 14

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

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 15

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

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 16

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 17

Advertising Example 2

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 6 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 18

Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses to advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 6 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 19

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 B Advertise Don t Advertise 4 3 5 1 2 5 6 2

Firm A

Advertise Don t Advertise

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 20

Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses not to advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 6 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 21

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 B Advertise Don t Advertise 4 3 5 1 2 5 6 2

Firm A

Advertise Don t Advertise

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 22

Advertising Example 2
The optimal strategy for Firm A depends on which strategy is chosen by Firm B Firm A does not have a dominant strategy

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 6 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 23

Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses to advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 6 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 24

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 B Advertise Don t Advertise 4 3 5 1 2 5 6 2

Firm A

Advertise Don t Advertise

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 25

Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses not to advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 4 3 5 1 2 5 6 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 26

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 B Advertise Don t Advertise 4 3 5 1 2 5 6 2

Firm A

Advertise Don t Advertise

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 27

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

Firm B Advertise Don t Advertise 4 3 5 1 2 5 6 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 28

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

Firm B Advertise Don t Advertise 4 3 5 1 2 5 3 2

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 29

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 If the evidence is not sufficient to convict them but found the crime of possessing stolen goods which carries a sentence of only 1 year The suspects who are interrogated separately 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 If you both do not confess you will both get 1 year in prison
PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 30

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 31

Prisoners Dilemma
Payoff Matrix negative values

Confess Individual A Don t Confess

Individual B Confess Don t Confess 5 5 0 10 10 0 1 1

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 32

Prisoners Dilemma
Dominant Strategy Both Individuals Confess Nash Equilibrium Individual B Confess Don t Confess 5 5 0 10 10 0 1 1

Confess Individual A Don t Confess

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 33

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 34

Prisoners Dilemma
Application Price Competition

Firm A

Low Price High Price

Firm B Low Price High Price 2 2 5 1 1 5 3 3

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 35

Prisoners Dilemma
Application Price Competition Dominant Strategy Low Price

Firm A

Low Price High Price

Firm B Low Price High Price 2 2 5 1 1 5 3 3

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 36

Prisoners Dilemma
Application Nonprice Competition

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 2 2 5 1 1 5 3 3

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 37

Prisoners Dilemma
Application Nonprice Competition Dominant Strategy Advertise

Firm A

Advertise Don t Advertise

Firm B Advertise Don t Advertise 2 2 5 1 1 5 3 3

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 38

Prisoners Dilemma
Application Cartel Cheating

Firm A

Cheat Don t Cheat

Firm B Cheat Don t Cheat 2 2 5 1 1 5 3 3

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 39

Prisoners Dilemma
Application Cartel Cheating Dominant Strategy Cheat

Firm A

Cheat Don t Cheat

Firm B Cheat Don t Cheat 2 2 5 1 1 5 3 3

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 40

Sequential Games
Decision trees
Decision nodes Branches alternatives

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 41

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 42

High Price Low Price Strategy Game
Firm A
ice h Pr Hig

Firm B

100 130 180 150

100 50 80 120

igh H

e ric P

B
Low P rice

A
Lo w Pri ce

e Pric High

B
Low P rice

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 43

High Price Low Price Strategy Game
Firm A
ice h Pr Hig

Firm B

100 130 180 150

100 50 80 120

igh H

e ric P

B

Low P

A
Lo w Pri ce

e Pric High

B

Low P

X X

rice

rice

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 44

High Price Low Price Strategy Game
Firm A
ice h Pr Hig

Firm B

100 130 180 150

100 50 80 120

igh H

A

X
Pri

e ric P

B

Low P

Lo w

ce

e Pric High

B

Low P

X X

rice

Solution Both firms choose low price

rice

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 45

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 46

Airbus and Boeing
Airbus
et bo J J um

Boeing

50 120 0 0

50 100 150 200

B
8 A3 0
Soni c Cr uiser

A
No A3 80
J

J m bo u

et

B
Soni c Cr uiser

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 47

Airbus and Boeing
Airbus
et bo J J um

Boeing

B
8 A3 0

Soni

X

50 120 0 0

50 100 150 200

A
No A3 80
J

c Cr uiser

J m bo u

B
Soni

X

et

c Cr uiser

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 48

Airbus and Boeing
Airbus
et bo J J um

Boeing

B
8 A3 0

Soni

X

50 120 0 0

50 100 150 200

A

c Cr uiser

No A3 80

X

J

J m bo u

B
Soni

X

et

c Cr uiser

Solution Airbus builds A380 and Boeing builds Sonic Cruiser
Slide 49

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc