Game Theory: Inside Oligopoly

Pertemuan 19 - 20

Matakuliah : J0434/EKONOMI MANAJERIALTahun : 2008

Managerial Economics & Business Strategy

Chapter 10Game Theory: Inside Oligopoly

Overview

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

Strategy Rat Don't RatRat

Don't Rat

Bonnie

Clyde16,16 1, 23

23,1 3,3

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

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

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

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

Multiple Equilibria -Battle of the Sexes

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

Him

Her

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

Strategy Pull ShirkPull

Shirk

Mack

Myer25,25 10, 35

35,10 15,15

Nash? Payoffs?

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?

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

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

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

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:

• 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(

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(

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

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

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

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

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

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

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

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

Entrant

Don’t Enter

Enter

Incumbent

No Price War

Price War

10, 10

-20, -10

0, 30

Divide into Sub-games(each node)

Entrant

Don’t Enter

Enter

Incumbent

No Price War

Price War

10, 10

-20, -10

0, 30

Solve Each Sub-game

Entrant

Don’t Enter

Enter

Incumbent

No Price War

Price War

10, 10

-20, -10

0, 30

One Subgame Perfect Equilibrium

Entrant

Don’t Enter

Enter

Incumbent

No Price War

Price War

10, 10

-20, -10

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

Leader

Follower

Follower

100, 30

50, 30

80, 40

70, 40

Adopt

Adopt

Not Adopt

Adopt Not Adopt

Not Adopt

Technology Adoption

Leader

Follower

Follower

100, 30

50, 30

80, 40

70, 40Adopt

Adopt

Adopt

Not Adopt

Not Adopt

Not Adopt

Technology Adoptionwith different timing

Strategy Adopt Not AdoptAdopt 40, 70 30, 50

Not Adopt 30, 100 40, 80Follower

Leader

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

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

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

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