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

3. Managerial Economics & Business Strategy
Chapter 10
Game Theory: Inside Oligopoly

4. Overview I. Introduction to Game Theory
II. Simultaneous-Move, One-Shot Games
III. Infinitely Repeated Games
IV. Finitely Repeated Games
V. Multistage Games

5. Elements of Games
Environment
Rules
Players
Strategies
Payoffs

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

7. Important Strategic Considerations
Credible vs. non-credible threats (strategies)
Equilibria:
Nash
Sub-game Perfect

8. 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

9. 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

10. The Normal Form of Prisoner’s Dilemma
Bonnie
16,16
1, 23
Clyde
23,1
3,3

11. 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

12. The Market-Share Game in Normal Form
Manager 2
Manager 1

13. 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.

14. No and multiple equilibria
Not all games will have a single equilibrium
Scissors, rock, paper
Battle of the Sexes

15. Child’s play
Player 2
Player 1

16. Multiple Equilibria - Battle of the Sexes
Him
Her

17. 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

18. 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

19. Mack & Myer’s Game
Mack
Myer
25,25
10, 35
35,10
15,15
Nash? Payoffs?

20. Developing a Coordination Device
Solution is to hire an enforcer
Pay the enforcer $5 each to hit anyone who shirks.
Hospitalization costs $15
Mack
20,20
5, 15
Myer
15,5
-5,-5
Nash? Payoffs? Damage?

21. 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

22. 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?

23. Equilibrium to the One-Shot Advertising Game
General Mills
Kellogg’s
Nash Equilibrium

24. Can collusion work if the game is repeated 2 times?
General Mills
Kellogg’s

25. 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.

26. 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?

27. 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:

28. Profits in an infinitely repeated game
Cheat only if it is profitable to do so:

29. Suppose General Mills adopts this trigger strategy. Kellogg’s profits?
VCooperate = 12(1+i)/i
Vnon-coop = 2/i
pcheat = 20
General Mills
Kellogg’s

30. Kellogg’s Gain to Cheating:
pCheat - pCoop =
pcoop - pnon-coop =
8/10 > 1/i
If i > 1.25 or 125% interest rate
General Mills
Kellogg’s

31. 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

32. Real World Examples of Collusion
Garbage Collection Industry
OPEC
NASDAQ
Airlines

33. 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…” (
Cournot oligopoly (quantity-based competition)
Absent collusion: PCompetition < PCournot < PMonopoly

34. Cournot Game in Normal Form
Venezuela
Saudi Arabia

35. One-Shot Cournot (Nash) Equilibrium
Venezuela
Saudi Arabia

36. Repeated Game Equilibrium*
Venezuela
Saudi Arabia
(Assuming a Low Interest Rate)

37. OPEC’s Demise
Low Interest
Rates
High Interest
Rates

38. 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?

39. 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 ...

40. 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 ...

41. U.S. Law Federal Trade Commission Act Munn v. Illinois
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

42. 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

43. Pricing to Prevent Entry: An Application of Game Theory
Two firms: an incumbent and potential entrant
The game in extensive form:

44. The Entry Game in Extensive Form
Entrant
Don’t Enter
Enter
Incumbent
No Price War
Price War
10, 10
-20, -10
0, 30

45. Divide into Sub-games (each node)
10, 10
No Price War
Incumbent
Enter
Price War
Entrant
-20, -10
0, 30
Don’t Enter

46. Solve Each Sub-game 10, 10 No Price War Incumbent Enter Price War
Entrant
-20, -10
0, 30
Don’t Enter

47. One Subgame Perfect Equilibrium
10, 10
No Price War
Incumbent
Enter
Price War
Entrant
-20, -10
0, 30
Don’t Enter

48. 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?

49. Technology Adoption
2 firms
Alternating movers

50. Technology Adoption 70, 40 100, 30 50, 30 80, 40 Leader Follower Adopt
Not Adopt
Adopt
Not Adopt
Not Adopt

51. Technology Adoption 70, 40 100, 30 50, 30 80, 40 Leader Follower Adopt
Not Adopt
Adopt
Adopt
Not Adopt
Not Adopt

52. Technology Adoption with different timing
Leader
Follower

53. 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.

54. 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
Low
Demand
Case
High
Large
Small

55. Uncertainty and the first-mover advantage in capacity choice
Large
10, 8
Large
Follower
High
Demand
Case
Small
12, 6
Leader
Large
4, 9
Small
Follower
6, 4
Large
-12, -10
Large
Follower
Low
Demand
Case
Small
-15, 4
Leader
Large
Small
3, 2
Follower
Small
5, 3

56. Uncertainty and the first-mover advantage in capacity choice
Large
10, 8
Large
Follower
High
Demand
Case
Small
12, 6
Leader
Large
4, 9
Small
Follower
6, 4
Large
-12, -10
Large
Follower
Low
Demand
Case
Small
-15, 4
Leader
Large
Small
3, 2
Follower
Small
5, 3