Matakuliah : J0434/EKONOMI MANAJERIAL
Tahun
: 2008
Game Theory: Inside Oligopoly
Pertemuan 19 - 20
Managerial Economics & Business
Strategy
Chapter 10
Game Theory: Inside Oligopoly
Overview
I. Introduction to Game Theory
II. Simultaneous-Move, One-Shot Games
III. Infinitely Repeated Games
IV. Finitely Repeated Games
V. Multistage Games
Elements of Games
•
•
•
•
•
Environment
Rules
Players
Strategies
Payoffs
Some Possible Game Structures
• 0-sum vs. variable sum
• co-operative vs. non-cooperative
• simultaneous mover vs. alternating mover
Important Strategic Considerations
• Credible vs. non-credible threats (strategies)
• Equilibria:
– Nash
– Sub-game Perfect
Normal Form Game
(Simultaneous Movers - Prisoner’s Dilemma)
• Environment - Police station after a crime wave. Police have
evidence on a minor crime. Police have insufficient evidence on
major crime
•
•
•
•
Players - Bonnie and Clyde
Rules - no escape is possible
Strategies - Rat or not rat
Payoffs – No one rats: both get 3 years
– One rats and the other stays quiet: rat gets 1 year, Silent
partner gets 23 years
– Both rat: both get 16 years
Resolving Bonnie & Clyde
• If Bonnie Rats and
– Clyde doesn’t rat, then Bonnie gets 1 year
– Clyde rats, then Bonnie gets 16 years
• If Bonnie doesn’t Rat and
– Clyde doesn’t rat, then Bonnie gets 3 years
– Clyde rats, then Bonnie gets 23 years
• If Clyde Rats and
– Bonnie doesn’t rat, then Clyde gets 1 year
– Bonnie rats, then Clyde gets 16 years
• If Clyde doesn’t Rat and
– Bonnie doesn’t rat, then Clyde gets 3 years
– Bonnie rats, then Clyde gets 23 years
The Normal Form of Prisoner’s Dilemma
Bonnie
Clyde
Strategy
Rat
Don't Rat
Rat
Don't Rat
16,16
1, 23
23,1
3,3
A Market Share Game
• Two managers want to maximize market share (0sum game)
• Strategies are pricing decisions
– Customers move to low priced product
– Limits?
• Capacity
• Loyalty
• Heterogeniety and preferences
• Simultaneous moves
• One-shot game
The Market-Share Game
in Normal Form
Manager 1
Manager 2
Strategy
P=$10
P=$5
P=$1
P=$10
.5, .5
.8, .2
.9, .1
P=$5
.2, .8
.5, .5
.8, .2
P = $1
.1, .9
.2, .8
.5, .5
Key Insight:
• Game theory can be used to analyze situations
where “payoffs” are non monetary!
• We will, without loss of generality, focus on
environments where businesses want to maximize
profits.
– Hence, payoffs are measured in monetary units.
No and multiple equilibria
• Not all games will have a single equilibrium
– Scissors, rock, paper
– Battle of the Sexes
Child’s play
Player 2
Strategy
Scissors
Player 1
Rock
Paper
Scissors
0, 0
1, -1
-1, 1
Rock
-1, 1
0, 0
1, -1
Paper
1, -1
-1, 1
0, 0
Multiple Equilibria Battle of the Sexes
Him
Her
Strategy
Ballet
Boxing
Ballet
4, 5
1, 1
Boxing
0,0
5, 4
Gain Coordination in a non-cooperative
environment
• Find a coordinating device
• Repeat the game finitely
• Repeat the game infinitely using
– Grim-trigger strategy
– Tit-for-tat strategy
Developing a Coordination Device
• Environment - Pulling groceries to market. Pulling harder
yields higher gross revenues. Effort costs
•
•
•
•
Players - Mack and Myer
Rules - ?
Strategies - Pull or Shirk
Payoffs – No one pulls, each nets $15
– One pulls and the other shirks, puller nets $10, shirker nets
$35
– Both pull, each nets $25
Mack & Myer’s Game
Mack
Myer
Strategy
Pull
Shirk
Nash? Payoffs?
Pull
Shirk
25,25
10, 35
35,10
15,15
Developing a Coordination Device
• Solution is to hire an enforcer
• Pay the enforcer $5 each to hit anyone who shirks.
• Hospitalization costs $15
Mack
Myer
Strategy
Pull
Shirk
Pull
Shirk
20,20
5, 15
15,5
-5,-5
Nash? Payoffs? Damage?
Examples of Coordination Games
• Industry standards
– size of floppy disks
– size of CDs
– industry organizations – UAW, ABA, etc.
• National standards
– electric current
– traffic laws
– HDTV
An Advertising Game
• Two firms (Kellogg’s & General Mills) managers want to
maximize profits
• Strategies consist of advertising campaigns on three
levels
• Punishment for non-cooperation?
• Credible punishment?
Equilibrium to the One-Shot Advertising
Game
Kellogg’s
General Mills
Strategy
None
Moderate
High
None
12,12
20, 1
15, -1
Moderate
1, 20
6, 6
9, 0
Nash Equilibrium
High
-1, 15
0, 9
2, 2
Can collusion work if the game is repeated
2 times?
Kellogg’s
General Mills
Strategy
None
Moderate
High
None
12,12
20, 1
15, -1
Moderate
1, 20
6, 6
9, 0
High
-1, 15
0, 9
2, 2
By backwards induction
• In period 2, the game is a one-shot game, so equilibrium entails
High Advertising in the last period.
• This means period 1 is “really” the last period, since everyone
knows what will happen in period 2.
• Equilibrium entails High Advertising by each firm in both periods.
• The same holds true if we repeat the game any known, finite
number of times.
Can collusion work if firms play the game each year, forever?
• Consider the following “grim-trigger strategy” by each firm:
– “Don’t advertise, provided the rival has not advertised in the past. If the
rival ever advertises, “punish” it by engaging in a high level of advertising
forever after.”
• In effect, each firm agrees to “cooperate” so long as the rival hasn’t
“cheated” in the past. “Cheating” triggers punishment in all future
periods.
• Is this a credible threat?
Profits in an infinitely repeated game
• Suppose we cooperate forever, then:

Vcoop  
 coop

 coop (1  i)
i
• Suppose we play non-cooperatively
forever
after, then:
t 0 (1  i )
t



 noncoop
noncoop
• Suppose we cheat
V once,
 then we receive:

noncoop

 cheat  
t 1
t 1
(1  i)t
 noncoop
(1  i)
t
i
  cheat 
 noncoop
i
Profits in an infinitely repeated game
• Cheat only if it is profitable to do so:
 cheat 
 noncoop
i

 coop (1  i )
i
i   cheat   noncoop   coop (1  i )
i   cheat   noncoop   coop  i   coop
 coop   noncoop
i
 cheat   coop
Suppose General Mills adopts this trigger
strategy. Kellogg’s profits?
VCooperate = 12(1+i)/i
Vnon-coop = 2/i
cheat = 20
General Mills
Strategy
None
Kellogg’s Moderate
High
None
12,12
20, 1
15, -1
Moderate
1, 20
6, 6
9, 0
High
-1, 15
0, 9
2, 2
Kellogg’s Gain to Cheating:
Cheat - Coop = 20 - 12
coop - non-coop = 12 - 2
8/10 > 1/i
If i > 1.25 or 125% interest rate
Kellogg’s
General Mills
Strategy
None
Moderate
High
None
12,12
20, 1
15, -1
Moderate
1, 20
6, 6
9, 0
High
-1, 15
0, 9
2, 2
Key Insight
• Collusion can be sustained as a Nash equilibrium when
there is no certain “end” to a game.
• Doing so requires:
–
–
–
–
Ability to monitor actions of rivals
Ability (and reputation for) punishing defectors
Low interest rate
High probability of future interaction
Real World Examples of Collusion
•
•
•
•
Garbage Collection Industry
OPEC
NASDAQ
Airlines
2. OPEC
• Cartel founded in 1960 by Iran, Iraq, Kuwait, Saudi Arabia, and
Venezuela
• Currently has 11 members
• “OPEC’s objective is to co-ordinate and unify petroleum policies among
Member Countries, in order to secure fair and stable prices for
petroleum producers…” (www.opec.com)
• Cournot oligopoly (quantity-based competition)
• Absent collusion: PCompetition < PCournot < PMonopoly
Cournot Game in Normal Form
Saudi Arabia
Venezuela
Strategy
High Q
Med Q
Low Q
High Q
5, 3
6, 7
8, 1
Med Q
9,4
12,10
10, 18
Low Q
3, 6
20, 8
18, 15
One-Shot Cournot
(Nash) Equilibrium
Saudi Arabia
Venezuela
Strategy
High Q
Med Q
Low Q
High Q
5, 3
6, 7
8, 1
Med Q
9,4
12,10
10, 18
Low Q
3, 6
20, 8
18, 15
Repeated Game Equilibrium*
Saudi Arabia
Venezuela
Strategy
High Q
Med Q
Low Q
High Q
5, 3
6, 7
8, 1
* (Assuming a Low Interest Rate)
Med Q
9,4
12,10
10, 18
Low Q
3, 6
20, 8
18, 15
OPEC’s Demise
40
35
Low Interest
Rates
High Interest
Rates
30
25
20
15
10
5
0
1970
-5
1972
1974
1976
1978
Real Interest Rate
1980
1982
1984
Price of Oil
1986
Caveat
• Collusion is a felony under Section 2 of the Sherman
Antitrust Act.
• Conviction can result in both fines and jail-time (at the
discretion of the court).
• OPEC isn’t illegal; US laws don’t apply
• DeBeers?
U.S. Law
• Sherman Antitrust Act
– Section 1 Every contract, combination in the form of a trust or
otherwise, or conspiracy , in restraint of trade or commerce ... is
hereby declared to be illegal.
– Section 2 Every person who shall monopolize, or attempt to
monopolize, or combine or conspire with any person or persons, to
monopolize any part of the trade or commerce among the several
states, or with foreign nations, shall be deemed guilty of
misdemeanor ...
U.S. Law
• Clayton Antitrust Act
– Section 2 [I]t shall be unlawful for any person engaged in
commerce ... to discriminate in price between different
purchasers of commodities of like grade and quality ... where
the effect of such discrimination may be substantially to
lessen competition or tend to create a monopoly ...
– Section 3 It shall be unlawful ... to lease or [sell] goods ... on
the condition, agreement, or understanding that the lessee
or purchaser thereof shall not use or deal in the goods ... of
a competitor or competitors of the lessor or seller, where the
effect ... may be to substantially lessen competition or tend
to create a monopoly in any line of commerce.
– Section 7 [N]o corporation engaged in commerce shall
acquire ... the whole or any part of the stock or other share
capital ... of another corporation engaged also in commerce,
where ... the effect of such acquisition may be substantially
to lessen competition, or tend to create a monopoly ...
U.S. Law
• Federal Trade Commission Act
– Section 5(a)(1) Unfair methods of competition in or affecting
commerce, and unfair or deceptive acts or practices in or
affecting commerce, are hereby declared unlawful.
• Munn v. Illinois
– Clothed in public interest
– Subject to regulation
Alternating Mover Games
•
•
•
•
One player acts then the other reacts
Look forward, reason backward
Sub-game perfect equilibrium (SPE)
New elements
– Information node
– Information set
– Order of play
Pricing to Prevent Entry: An Application of
Game Theory
• Two firms: an incumbent and potential entrant
• The game in extensive form:
The Entry Game in Extensive Form
No Price War 10, 10
Incumbent
Enter
Price War
Entrant
-20, -10
Don’t Enter
0, 30
Divide into Sub-games
(each node)
No Price War 10, 10
Incumbent
Enter
Price War
Entrant
-20, -10
Don’t Enter
0, 30
Solve Each Sub-game
No Price War 10, 10
Incumbent
Enter
Price War
Entrant
-20, -10
Don’t Enter
0, 30
One Subgame Perfect Equilibrium
No Price War 10, 10
Incumbent
Enter
Price War
Entrant
-20, -10
Don’t Enter
0, 30
Pricing to Prevent Entry
• Suppose you want to fight a war to create a
reputation?
– What’s the price of the reputation?
– What’s the gain?
• Suppose you want to buy out the entrant?
– What is an acceptable price?
– What is an affordable price?
– What sort of dynamic does this create?
Technology Adoption
• 2 firms
• Alternating movers
Technology Adoption
Adopt
70, 40
Follower
Adopt
Not Adopt
100, 30
Leader
Adopt
50, 30
Not Adopt
Follower
Not Adopt
80, 40
Technology Adoption
Adopt
70, 40
Follower
Not Adopt
Adopt
100, 30
Leader
Adopt
50, 30
Not Adopt
Follower
Not Adopt
80, 40
Technology Adoption
with different timing
Leader
Strategy
Adopt
Follower
Not Adopt
Adopt
40, 70
30, 100
Not Adopt
30, 50
40, 80
Uncertainty and the first-mover advantage
• First-mover advantage is the gain associated with
being first
• Market foreclosure
• Customer loyalty
• Examine information that is available.
Uncertainty and the first-mover advantage
in capacity choice
Large
Large
Follower
Leader
Small
10, 8
Small
12, 6
Large
4, 9
Follower
High
Demand
Case
6, 4
Large
-12, -10
Small
-15, 4
Large
3, 2
Small
5, 3
Follower
Leader
Small
Large
Follower
Low
Demand
Case
Uncertainty and the first-mover advantage
in capacity choice
Large
Large
Follower
Leader
Small
10, 8
Small
12, 6
Large
4, 9
Follower
High
Demand
Case
6, 4
Large
-12, -10
Small
-15, 4
Large
3, 2
Small
5, 3
Follower
Leader
Small
Large
Follower
Low
Demand
Case
Uncertainty and the first-mover advantage
in capacity choice
Large
Large
Follower
Leader
Small
10, 8
Small
12, 6
Large
4, 9
Follower
High
Demand
Case
6, 4
Large
-12, -10
Small
-15, 4
Large
3, 2
Small
5, 3
Follower
Leader
Small
Large
Follower
Low
Demand
Case