Oligopoly and Game Theory

1
Session 9

• Oligopoly and Game Theory

2
Oligopoly

• Relatively few firms, usually less than 10.
• Duopoly - two firms
• Triopoly - three firms
• The products firms offer can be either
  differentiated or homogeneous.

3
Role of Strategic Interaction

• What you do affects the profits of your rivals
• What your rival does affects your profits

4
An Example

• You and another firm sell differentiated products
• How does the quantity demanded for your product
  change when you change your price?

5
Key Insight

• The effect of a price reduction on the quantity
  demanded of your product depends upon whether
  your rivals respond by cutting their prices too!
• The effect of a price increase on the quantity
  demanded of your product depends upon whether
  your rivals respond by raising their prices too!
• Strategic interdependence You arent in
  complete control of your own destiny!

6
Gaming Overview

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

7
Game Theory

• Price nonprice competition can be examined
• Assumes competitors choose optimal strategy
  firm develops best counter strategy

8
Strategic Behavior

• Plan of action taken by oligopolist after
  considering all possible reactions of competitors
• Because there are only a few firms, each must
  consider the actions of others

9
Normal Form Game

• A Normal Form Game consists of
• Players
• Strategies or feasible actions
• Payoffs
• SIMULTANEOUS-MOVE GAME - players make decisions
  without knowledge of the other players decisions

10
Simultaneous-Move, One-Shot Games

• Strategy - action a player will take at each
  decision point
• normal-form game - representation of a game
  indicating the players, their possible
  strategies, and the payoffs resulting from
  alternative strategies
• Dominant strategy - one that results in the
  highest payoff to a player regardless of the
  opponents action

11
A Normal Form Game
Player 2
12,11
11,12
14,13
Player 1
12
Normal Form GameScenario Analysis

• Suppose 1 thinks 2 will choose A.

Player 2
12,11
11,12
14,13
Player 1
13
Normal Form GameScenario Analysis

• Then 1 should choose a.
• Player 1s best response to A is a.

Player 2
12,11
11,12
14,13
Player 1
14
Normal Form GameScenario Analysis

• Suppose 1 thinks 2 will choose B.

Player 2
12,11
11,12
14,13
Player 1
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Normal Form GameScenario Analysis

• Then 1 should choose a.
• Player 1s best response to B is a.

Player 2
12,11
11,12
14,13
Player 1
16
Normal Form GameScenario Analysis

• Similarly, if 1 thinks 2 will choose C
• Player 1s best response to C is a.

Player 2
12,11
11,12
14,13
Player 1
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Dominant Strategy

• Regardless of whether Player 2 chooses A, B, or
  C, Player 1 is better off choosing a!
• a is Player 1s Dominant Strategy!

Player 2
12,11
11,12
14,13
Player 1
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Putting Yourself in your Rivals Shoes

• What should player 2 do?
• 2 has no dominant strategy!
• But 2 should reason that 1 will play a.
• Therefore 2 should choose C.

Player 2
12,11
11,12
14,13
Player 1
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The Outcome
Player 2
12,11
11,12
14,13
Player 1

• This outcome is called a Nash equilibrium
• a is player 1s best response to C.
• C is player 2s best response to a.

20
Key Insights

• Look for dominant strategies
• Put yourself in your rivals shoes

21
Dominant Strategy
Demonstration Problem 10-1 Does Player B have a
dominant strategy?
22
A Market Share Game

• Two managers want to maximize market share
• Strategies are pricing decisions
• Simultaneous moves
• One-shot game

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The Market-Share Game in Normal Form
Manager 2
Manager 1
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Market-Share Game Equilibrium
Manager 2
Manager 1
Nash Equilibrium
25
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.

26
Game Theory Example

• 2 Firms
• Decision about how much to spend for advertising

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Payoff matrix
28
Payoff Matrix

• All boxes unstable except bottom right box, both
  firms follow strategy of high advertising
  expenditures
• Each firm earns 8 in profits even though they
  could earn more with low advertising

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Nash Equilibrium

• Situation where each player chooses optimal
  strategy, given strategy chosen by the other
  player
• No player can improve her/his payoff by changing
  her/his own strategy, given the other players
  strategies
• High advertising for Firm 1 and 2 is NASH
  EQUILIBRIUM

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Nash Equilibrium

• Secure strategy - one that guarantees the highest
  payoff given the worst possible scenario
• Demonstration Problem 10-2
• What is the secure strategy for player B?
• Demonstration Problem 10-3
• What is Nash Equilibrium for AB?

31
Applications of One-Shot Games
Advertising and Quality Decisions In
oligopolies, advertising increases the demand for
a firms product Classic example is the breakfast
cereal industry can lead to situation where each
firm advertises just to cancel out effects of
other firms advertising - lower
profits Demonstration Problem 10-4
32
Cartels

• MARKET SHARING CARTEL - Each member has
  exclusive right to operate in a geographical area
  (DUPONT IN U.S. IMPERIAL CHEMICALS IN U.K.)
• CENTRALIZED CARTEL - Formal agreement to set
  monopoly price (OPEC)

33
Cartel Cheating

• Prisoners dilemma
• Oligopolies face this problem
• Refers to a situation in which each firm adopts
  its dominant strategy but could do better by
  cooperating.

34
Prisoners Dilemma

• Two suspects are arrested for robbery
• If convicted, they would each receive maximum
  sentence of 10 years
• Unless one or both confesses they would be
  convicted on the minor charge and receive a
  maximum sentence of 1 year

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Prisoners Dilemma

• Are not allowed to communicate
• Each told that if they confess, they go free and
  the other receives 10 years
• If both confess, each gets 5 years
• What is the dominant strategy?

36
Payoff Matrix (Negative)

37
Price Competition and the Prisoners Dilemma

• Prisoners dilemma can be used to analyze price
  and nonprice competition in oligopolistic markets
• It can also be used to illustrate cartels
  incentives to cheat

38
Examples of Coordination Games

• Industry standards
• size of floppy disks
• size of CDs
• etc.
• National standards
• electric current
• traffic laws
• etc.

39
Applications of One-Shot Games
Coordination Decisions Where industry
coordinates their efforts to earn higher profits
(ie 120 or 90 volt) The firms do better by
coordinating their decisions Game has two Nash
equilibria
40
Coordination Decisions
41
Coordination Decisions
Once they agree to produce either 120-volt
appliances or 90-volt appliances, there is no
incentive to cheat on this agreement it is NOT a
game of conflicting interests Inside Business
10-1, Coordinating Activities How Hard Is It?
42
A Coordination Game in Normal Form
Player 2
Player 1
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A Coordination Problem Three Nash Equilibria!
Player 2
Player 1
44
Key Insights

• Not all games are games of conflict.
• Communication can help solve coordination
  problems.
• Sequential moves can help solve coordination
  problems.

45
Applications of One-Shot Games
Monitoring Employees Game between worker and a
manager Manager can (1) monitor or (2) not
monitor the worker Worker can (1) work or (2)
shirk
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Monitoring Workers
47
Monitoring Workers

• Does not have a Nash equilibrium. Why?
• Workers and managers want to keep their actions
  secret
• Players find it in their interest to engage in
  mixed, or randomized strategies.
• IE manager flips a coin to decide whether or
  not to monitor.

48
An Advertising Game

• Two firms (Kelloggs General Mills) managers
  want to maximize profits
• Strategies consist of advertising campaigns
• Simultaneous moves
• One-shot interaction
• Repeated interaction

49
A One-Shot Advertising Game
General Mills
Kelloggs
50
Equilibrium to the One-Shot Advertising Game
General Mills
Kelloggs
Nash Equilibrium
51
Extensions of Game Theory
Factors Affecting Collusion in Pricing
Games Number of Firms Firm Size History of the
Market (Tacit collusion) Punishment Mechanisms
(if a single price is charged to all customers,
it is easier to punish rival than if there are
quoted different prices)
52
Infinitely Repeated Games
Agree to charge high price, provided neither has
ever cheated in the past If they cheat and
charge low price, other will punish them by
charging the low price in every period
thereafter. Because firms compete repeatedly
there is a future cost of cheating If the PV of
costs of cheating gt one-time benefit of cheating,
it does not pay for firm to cheat - high prices
sustained.
53
Infinitely Repeated Games
54
Infinitely Repeated Games
Firm has no incentive to cheat if PV cheat Firm
A 50 lt 10(1 I)/I PV Coop firm A This is
true if I lt 1/4 or 25 When oligopolies compete
repeatedly over time, it is possible for them to
collude and charge high prices Leads to
dead-weight loss Demonstration Problem 10-6, page
378
55
Can collusion work if the game is repeated 2
times?
General Mills
Kelloggs
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No (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.

57
Can collusion work if firms play the game each
year, forever?

• Consider the following trigger strategy by each
  firm
• Dont 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 hasnt cheated in the past.
  Cheating triggers punishment in all future
  periods.

58
Suppose General Mills adopts this trigger
strategy. Kelloggs profits?

• ?Cooperate 12 12/(1i) 12/(1i)2 12/(1i)3
  
• 12 12/i

Value of a perpetuity of 12 paid at the end of
every year
?Cheat 20 2/(1i) 2/(1i)2 2/(1i)3
20 2/i
59
Kelloggs Gain to Cheating

• ?Cheat - ?Cooperate 20 2/i - (12 12/i) 8
  - 10/i
• Suppose i .05
• ?Cheat - ?Cooperate 8 - 10/.05 8 - 200 -192
• It doesnt pay to deviate.
• Collusion is a Nash equilibrium in the infinitely
  repeated game!

General Mills
Kelloggs
60
Benefits Costs of Cheating

• ?Cheat - ?Cooperate 8 - 10/i
• 8 Immediate Benefit (20 - 12 today)
• 10/i PV of Future Cost (12 - 2 forever after)
• If Immediate Benefit gt PV of Future Cost
• Pays to cheat.
• If Immediate Benefit ? PV of Future Cost
• Doesnt pay to cheat.

General Mills
Kelloggs
61
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

62
Real World Examples of Collusion

• Garbage Collection Industry
• OPEC
• NASDAQ
• Airlines

63
Garbage Collection Industry

• Homogeneous products
• Oligopoly
• Identity of customers is known
• Identity of competitors is known

64
Normal Form Game
Firm 2
Firm 1
65
One-Shot (Nash) Equilibrium
Firm 2
Firm 1
66
Potential Repeated Game Equilibrium Outcome
Firm 2
Firm 1
67
2. OPEC

• Cartel founded in 1960 by Iran, Iraq, Kuwait,
  Saudi Arabia, and Venezuela
• Currently has 11 members
• OPECs 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)
• Oligopoly
• Absent collusion PCompetition lt PCournot lt
  PMonopoly

68
Current OPEC Members
69
Cournot Game in Normal Form
Venezuela
Saudi Arabia
70
One-Shot Cournot (Nash) Equilibrium
Venezuela
Saudi Arabia
71
Repeated Game Equilibrium
Venezuela
Saudi Arabia

• (Assuming a Low Interest Rate)

72
Effect of Collusion on Oil Prices
Price
30
15
World Demand for Oil
Quantity of Oil
Medium
Low
73
OPECs Demise
Low Interest Rates
High Interest Rates
74
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).
• Some NASDAQ dealers and airline companies have
  been charged with violations
• OPEC isnt illegal US laws dont apply

75
Simultaneous-Move Bargaining

• Management and a union are negotiating a wage
  increase.
• Strategies are wage offers wage demands
• Successful negotiations lead to 600 million in
  surplus, which must be split among the parties
• Failure to reach an agreement results in a loss
  to the firm of 100 million and a union loss of
  3 million
• Simultaneous moves, and time permits only
  one-shot at making a deal.

76
The Bargaining Game in Normal Form
Union
Management
77
Three Nash Equilibria!
Union
Management
78
Fairness The Natural Focal Point
Union
Management
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Nash Bargaining
There are 3 Nash Equilibriums. Best to ask for
50 - 50. Why? Demonstration Problem 10-5
80
Lessons in Simultaneous Bargaining

• Simultaneous-move bargaining results in a
  coordination problem
• Experiments suggests that, in the absence of any
  history, real players typically coordinate on
  the fair outcome
• When there is a bargaining history, other
  outcomes may prevail

81
Single Offer Bargaining

• Now suppose the game is sequential in nature, and
  management gets to make the union a
  take-it-or-leave-it offer.
• Analysis Tool Write the game in extensive form
• Summarize the players
• Their potential actions
• Their information at each decision point
• The sequence of moves and
• Each players payoff

82
Step 1 Managements Move
10
5
Firm
1
83
Step 2 Add the Unions Move
Accept
Union
Reject
10
Accept
5
Firm
Union
Reject
1
Accept
Union
Reject
84
Step 3 Add the Payoffs
Accept
100, 500
Union
-100, -3
Reject
10
Accept
300, 300
5
Firm
Union
-100, -3
Reject
1
Accept
500, 100
Union
-100, -3
Reject
85
The Game in Extensive Form
Accept
100, 500
Union
-100, -3
Reject
10
Accept
300, 300
5
Firm
Union
-100, -3
Reject
1
Accept
500, 100
Union
-100, -3
Reject
86
Step 4 Identify the Firms Feasible Strategies

• Management has one information set and thus three
  feasible strategies
• Offer 10
• Offer 5
• Offer 1

87
Step 5 Identify the Unions Feasible Strategies

• Accept 10, Accept 5, Accept 1
• Accept 10, Accept 5, Reject 1
• Accept 10, Reject 5, Accept 1
• Reject 10, Accept 5, Accept 1
• Accept 10, Reject 5, Reject 1
• Reject 10, Accept 5, Reject 1
• Reject 10, Reject 5, Accept 1
• Reject 10, Reject 5, Reject 1

88
Step 6 Identify Nash Equilibrium Outcomes

• Outcomes such that neither the firm nor the union
  has an incentive to change its strategy, given
  the strategy of the other

89
Finding Nash Equilibrium Outcomes
1
Yes
5
Yes
1
Yes
1
Yes
10
Yes
5
Yes
1
Yes
No
10, 5, 1
90
Step 7 Find the Subgame Perfect Nash Equilibrium
Outcomes

• Outcomes where no player has an incentive to
  change its strategy, given the strategy of the
  rival, and
• The outcomes are based on credible actions
  that is, they are not the result of empty
  threats by the rival.

91
Checking for Credible Actions
Yes
No
No
No
No
No
No
No
92
The Credible Union Strategy
Yes
No
No
No
No
No
No
No
93
Finding Subgame Perfect Nash Equilibrium
Strategies
Nash and Credible
Nash Only
Neither Nash Nor Credible
94
To Summarize

• We have identified many combinations of Nash
  equilibrium strategies
• In all but one the union does something that
  isnt in its self interest (and thus entail
  threats that are not credible)
• Graphically

95
There are 3 Nash Equilibrium Outcomes!
Accept
100, 500
Union
-100, -3
Reject
10
Accept
300, 300
5
Firm
Union
-100, -3
Reject
1
Accept
500, 100
Union
-100, -3
Reject
96
Only 1 Subgame-Perfect Nash Equilibrium Outcome!
Accept
100, 500
Union
-100, -3
Reject
10
Accept
300, 300
5
Firm
Union
-100, -3
Reject
1
Accept
500, 100
Union
-100, -3
Reject
97
Re-Cap

• In take-it-or-leave-it bargaining, there is a
  first-mover advantage.
• Management can gain by making a take-it or
  leave-it offer to the union. But...
• Management should be careful, however real world
  evidence suggests that people sometimes reject
  offers on the the basis of principle instead of
  cash considerations.

98
Pricing to Prevent Entry An Application of Game
Theory

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

99
The Entry Game in Extensive Form
-1, 1
Hard
Incumbent
Enter
Soft
5, 5
Entrant
Out
0, 10
100
Identify Nash and Subgame Perfect Equilibria
101
Two Nash Equilibria
102
One Subgame Perfect Equilibrium
103
Insights

• Establishing a reputation for being unkind to
  entrants can enhance long-term profits
• It is costly to do so in the short-term, so much
  so that it isnt optimal to do so in a one-shot
  game.

104
Finitely Repeated Games
Games with an Uncertain Final Period Demonstration
Problem 10-7 Repeated Games with a Known Final
Period The End-of-Period Problem Demonstration
Problem 10-8
105
Applications of the End-of-Period Problem
Resignations and Quits The Snake-Oil Salesman
106
Applications of Multistage Games
The Entry Game Demonstration Problem
10-9 Sequential Bargaining Demonstration Problem
10-10
107
Relevant Articles

• The Race to Call the U.S. 2000 Election, pp.
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• ATT To Open Door to Net Rivals, pp. 5-5 5-6
• Incompatibility Reigns in Internet War, pp. 5-7
  5-8
• Stock Options at Adobe Systems, p. 5-9
• Designing a Managerial Incentive Contract, p.
  5-10