How much to Produce
Simple Business Games
Firm A
Firm B B
1
Firm A
1
π
2
2
π
πA = 18 πA = 10
πB = 10 πB = 11
Model
Change
Styling
Model
Change
Firm 2’s choices
Technical
Styling
model
model
change
change
π2 =20
Firm 1’s
choices
Styling
Model
Change
2
Firm 1 has a
dominant strategy:
technical change.
Firm 1’s
choices
π2 = 15
π2 =20
π2 = 15
π1 = 40 π1 = 60
π2 = 16 π2 = 18
Simple Business Games
Firm 2’s choices
Technical
Styling
model
model
change
change
Technical
Model
Change
Styling
Model
Change
π2 =20 π2 = 15
π 1 = 40 π 1 = 60
π2 = 16 π2 = 18
π1 = 8
π1 = 12
Simple Business Games
Firm 2’s choices
Technical
Styling
model
model
change
change
π1 = 8
πA = 11
π1 = 12
Do all Games Have Dominant
Strategies?
Technical
Model
Change
πA = 18 πA = 10
πB = 10 πB = 11
Do all Games Have Dominant
Strategies?
π1 = 40 π1 = 60
π2 = 16 π2 = 18
π1 = 8
2
πB = 20
Simple Business Games
Simple Business Games
Firm 2 does not
have a dominant
strategy.
1
πA = 20
Do all Games Have Dominant
Strategies?
Firm 1’s
choices
1
πB =18
πA = 11
Lectures in Microeconomics-Charles W. Upton
Automotive Firm 1
has great
engineering skills.
Firm 2 has good
designers and does
great styling.Technical
Firm B B
πB = 20
πB =18
πA = 20
Dominant
Strategy
Nash Equilibrium
π1 = 12
Do all Games Have Dominant
Strategies?
Firm 2’s choice is
still obvious:
assume #1 acts
rationally. Adopt a
technical change.
Firm 1’s
choices
Technical
Model
Change
Styling
Model
Change
Firm 2’s choices
Technical
Styling
model
model
change
change
π2 =20
π2 = 15
π1 = 40 π1 = 60
π2 = 16 π2 = 18
π =8
1
Simple Business
Games
π1 = 12
1
Do all Games Have Dominant
Strategies?
The lesson:
assume your
opponent will act
rationally.
Firm 1’s
choices
Technical
Model
Change
Styling
Model
Change
Firm 2’s choices
Technical
Styling
model
model
change
change
Early entry
π1 = 40 π1 = 60
π2 = 16 π2 = 18
π =8
1
Simple Business
Games
π1 = 12
Firm 1’s
choices of
When to
extend the
brand
π1 = 45
π2 = 80
Late entry
π1 = 95
π2 = 55
π1 = 35
Technical
Model
Change
Styling
Model
Change
π2 = 55
π1 = 35
Stodgy pays.Early entry
Firm 1’s
choices of
When to
extend the
brand
Firm 2’s choices of when to
enter the new brand
Early entry
Late entry
π2 =60
π2 = 20
π1 = 40
π1 = 45
π2 = 80
Late entry
π1 = 95
π2 = 55
π1 = 35
Simple Business Games
Multiple Nash Equilibria
Firm 1’s
choices
π1 = 45
π2 = 80
π1 = 95
Moral of the story.
Let the new guys try
the gutsy strategies.
Simple Business Games
This is the styling
problem with a new
payoff matrix.
π1 = 40
Late entry
Early and Late Entry
Firm 2’s choices of when to
enter the new brand
Early entry
Late entry
π2 =60
π2 = 20
π1 = 40
Firm 2’s choices of when to
enter the new brand
Early entry
Late entry
π2 =60
π2 = 20
Simple Business Games
Early and Late Entry
The existing firm does
not have a dominant
strategy but it can rely
on the new firm’s
strategy Early entry
The new firm has a
dominant strategy
Firm 1’s
choices of
When to
extend the
brand
π2 = 15
π2 =20
Early and Late Entry
Multiple Nash Equilibria
Now there are two
Nash Equilibria
Firm 2’s choices
Technical
Styling
model
model
change
change
π2 =20
π2 = 55
π1 = 20
π2 = 55
π1 = 60
Simple Business Games
π1 = 60
π2 = 25
π1 = 25
Firm 1’s
choices
Technical
Model
Change
Styling
Model
Change
Firm 2’s choices
Technical
Styling
model
model
change
change
π2 = 55
π2 =20
π1 = 20
π2 = 55
π1 = 60
π1 = 60
π2 = 25
π1 = 25
Simple Business Games
2
Early
Late Entry
New entrant
canand
enter
either new or wait.
Established Firm can
Firm 2’s choices of when to
extend early or late.
enter the new brand
Early entry
Late entry
π2 =60
Early entry
Firm 1’s
choices of
when to
extend the
brand
π1 = 95
Look at the first Nash
Equilibrium. Neither
firm has reason to
change
π2 = 20
π1 = 40
π1 = 45
π2 = 55
π2 = 80
Late entry
Multiple Nash Equilibria
Firm 1’s
choices
Styling
Model
Change
π1 = 35
Simple Business Games
Firm 1’s
choices
Technical
Model
Change
Styling
Model
Change
Firm 2’s choices
Technical
Styling
model
model
change
change
π2 =20
π2 = 55
π1 = 20 π1 = 60
π2 = 55 π2 = 25
π1 = 60
π1 = 25
Multiple Nash Equilibria
This is an introduction.
It shows how to get
going. There is more to Firm 2’s choices
Technical
Styling
come.
π2 = 55
π1 = 20 π1 = 60
π2 = 55 π2 = 25
π1 = 60
π2 =20
Simple Business Games
Multiple Nash Equilibria
Ditto for the second
equilibrium
Technical
Model
Change
Firm 2’s choices
Technical
Styling
model
model
change
change
π1 = 25
Simple Business Games
Firm 1’s
choices
Technical
Model
Change
Styling
Model
Change
model
change
π2 =20
π1 = 20
π2 = 55
π1 = 60
model
change
π2 = 55
π1 = 60
π2 = 25
π1 = 25
Simple Business Games
End
©2003 Charles
W. Upton
Simple Business Games
3