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Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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Page 1: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.
Page 2: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Game Theory: Inside Oligopoly

Pertemuan 19 - 20

Matakuliah : J0434/EKONOMI MANAJERIALTahun : 2008

Page 3: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Managerial Economics & Business Strategy

Chapter 10Game Theory: Inside Oligopoly

Page 4: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Overview

I. Introduction to Game TheoryII. Simultaneous-Move, One-Shot GamesIII. Infinitely Repeated GamesIV. Finitely Repeated GamesV. Multistage Games

Page 5: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Elements of Games

• Environment• Rules• Players• Strategies• Payoffs

Page 6: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Some Possible Game Structures• 0-sum vs. variable sum• co-operative vs. non-cooperative• simultaneous mover vs. alternating mover

Page 7: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Important Strategic Considerations

• Credible vs. non-credible threats (strategies)• Equilibria:

– Nash– Sub-game Perfect

Page 8: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 9: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 10: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

The Normal Form of Prisoner’s Dilemma

Strategy Rat Don't RatRat

Don't Rat

Bonnie

Clyde16,16 1, 23

23,1 3,3

Page 11: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

A Market Share Game

• Two managers want to maximize market share (0-sum game)

• Strategies are pricing decisions– Customers move to low priced product– Limits?

• Capacity• Loyalty• Heterogeniety and preferences

• Simultaneous moves• One-shot game

Page 12: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

The Market-Share Game in Normal Form

Strategy P=$10 P=$5 P = $1P=$10 .5, .5 .2, .8 .1, .9P=$5 .8, .2 .5, .5 .2, .8P=$1 .9, .1 .8, .2 .5, .5

Manager 2

Man

ager

1

Page 13: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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.

Page 14: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

No and multiple equilibria

• Not all games will have a single equilibrium– Scissors, rock, paper– Battle of the Sexes

Page 15: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Child’s play

Strategy Scissors Rock PaperScissors 0, 0 -1, 1 1, -1

Rock 1, -1 0, 0 -1, 1Paper -1, 1 1, -1 0, 0

Player 2

Player 1

Page 16: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Multiple Equilibria -Battle of the Sexes

Strategy Ballet BoxingBallet 4, 5 0 , 0Boxing 1, 1 5, 4

Him

Her

Page 17: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 18: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 19: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Mack & Myer’s Game

Strategy Pull ShirkPull

Shirk

Mack

Myer25,25 10, 35

35,10 15,15

Nash? Payoffs?

Page 20: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Developing a Coordination Device

• Solution is to hire an enforcer• Pay the enforcer $5 each to hit anyone who

shirks.• Hospitalization costs $15

Strategy Pull ShirkPull

Shirk

Mack

Myer20,20 5, 15

15,5 -5,-5

Nash? Payoffs? Damage?

Page 21: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 22: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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?

Page 23: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Equilibrium to the One-Shot Advertising Game

Strategy None Moderate HighNone 12,12 1, 20 -1, 15

Moderate 20, 1 6, 6 0, 9High 15, -1 9, 0 2, 2

General Mills

Kel

logg

’s

Nash Equilibrium

Page 24: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Can collusion work if the game is repeated 2 times?

Strategy None Moderate HighNone 12,12 1, 20 -1, 15

Moderate 20, 1 6, 6 0, 9High 15, -1 9, 0 2, 2

General Mills

Kel

logg

’s

Page 25: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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.

Page 26: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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?

Page 27: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Profits in an infinitely repeated game

• Suppose we cooperate forever, then:

• Suppose we play non-cooperatively forever after, then:

• Suppose we cheat once, then we receive:

i

i

iV coop

tt

coopcoop

)1(

)1(0

iiV coopnon

tt

coopnoncoopnon

1 )1(

iicoopnon

cheatt

t

coopnoncheat

1 )1(

Page 28: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Profits in an infinitely repeated game

• Cheat only if it is profitable to do so:

coopcheat

coopnoncoop

coopcoopcoopnoncheat

coopcoopnoncheat

coopcoopnoncheat

i

ii

iii

i

i

)1(

)1(

Page 29: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Suppose General Mills adopts this trigger strategy. Kellogg’s profits?

VCooperate = 12(1+i)/i

Strategy None Moderate HighNone 12,12 1, 20 -1, 15

Moderate 20, 1 6, 6 0, 9High 15, -1 9, 0 2, 2

General Mills

Kellogg’s

Vnon-coop = 2/i

cheat = 20

Page 30: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Kellogg’s Gain to Cheating:

Cheat - Coop = 20 - 12

coop - non-coop = 12 - 2

8/10 > 1/iIf i > 1.25 or 125% interest rate

Strategy None Moderate HighNone 12,12 1, 20 -1, 15

Moderate 20, 1 6, 6 0, 9High 15, -1 9, 0 2, 2

General Mills

Kel

logg

’s

Page 31: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 32: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Real World Examples of Collusion

• Garbage Collection Industry• OPEC• NASDAQ• Airlines

Page 33: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 34: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Cournot Game in Normal Form

Strategy High Q Med Q Low QHigh Q 5, 3 9,4 3, 6Med Q 6, 7 12,10 20, 8Low Q 8, 1 10, 18 18, 15

Venezuela

Sau

di A

rab

ia

Page 35: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

One-Shot Cournot (Nash) Equilibrium

Strategy High Q Med Q Low QHigh Q 5, 3 9,4 3, 6Med Q 6, 7 12,10 20, 8Low Q 8, 1 10, 18 18, 15

Venezuela

Sau

di A

rab

ia

Page 36: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Repeated Game Equilibrium*

Venezuela

Strategy High Q Med Q Low QHigh Q 5, 3 9,4 3, 6Med Q 6, 7 12,10 20, 8Low Q 8, 1 10, 18 18, 15

* (Assuming a Low Interest Rate)

Sau

di A

rab

ia

Page 37: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

OPEC’s Demise

-5

0

5

10

15

20

25

30

35

40

1970 1972 1974 1976 1978 1980 1982 1984 1986

Real Interest Rate Price of Oil

Low Interest Rates

High Interest Rates

Page 38: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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?

Page 39: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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 ...

Page 40: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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 ...

Page 41: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 42: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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

Page 43: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Pricing to Prevent Entry: An Application of Game Theory

• Two firms: an incumbent and potential entrant• The game in extensive form:

Page 44: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

The Entry Game in Extensive Form

Entrant

Don’t Enter

Enter

Incumbent

No Price War

Price War

10, 10

-20, -10

0, 30

Page 45: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Divide into Sub-games(each node)

Entrant

Don’t Enter

Enter

Incumbent

No Price War

Price War

10, 10

-20, -10

0, 30

Page 46: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Solve Each Sub-game

Entrant

Don’t Enter

Enter

Incumbent

No Price War

Price War

10, 10

-20, -10

0, 30

Page 47: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

One Subgame Perfect Equilibrium

Entrant

Don’t Enter

Enter

Incumbent

No Price War

Price War

10, 10

-20, -10

0, 30

Page 48: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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?

Page 49: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Technology Adoption

• 2 firms• Alternating movers

Page 50: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Technology Adoption

Leader

Follower

Follower

100, 30

50, 30

80, 40

70, 40

Adopt

Adopt

Not Adopt

Adopt Not Adopt

Not Adopt

Page 51: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Technology Adoption

Leader

Follower

Follower

100, 30

50, 30

80, 40

70, 40Adopt

Adopt

Adopt

Not Adopt

Not Adopt

Not Adopt

Page 52: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Technology Adoptionwith different timing

Strategy Adopt Not AdoptAdopt 40, 70 30, 50

Not Adopt 30, 100 40, 80Follower

Leader

Page 53: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

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.

Page 54: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Uncertainty and the first-mover advantage in capacity choice

12, 6

4, 9

6, 4

-12, -10

-15, 4

3, 2

5, 3

10, 8

Leader

Follower

Leader

Follower

Follower

Follower

LowDemand

Case

HighDemand

Case

Large

Large

Large

Large

LargeSmall

LargeSmall

Small

Small

Small

Page 55: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Uncertainty and the first-mover advantage in capacity choice

12, 6

4, 9

6, 4

-12, -10

-15, 4

3, 2

5, 3

10, 8

Leader

Follower

Leader

Follower

Follower

Follower

LowDemand

Case

HighDemand

Case

Large

Large

Large

Large

LargeSmall

LargeSmall

Small

Small

Small

Page 56: Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah: J0434/EKONOMI MANAJERIAL Tahun: 2008.

Uncertainty and the first-mover advantage in capacity choice

12, 6

4, 9

6, 4

-12, -10

-15, 4

3, 2

5, 3

10, 8

Leader

Follower

Leader

Follower

Follower

Follower

LowDemand

Case

HighDemand

Case

Large

Large

Large

Large

LargeSmall

LargeSmall

Small

Small

Small