Economic Environment of business

1
Economic Environment of business

• Lectures 3 and 4
• Oligopoly and game theory

2
Market structures
3
Part I Overview

• I. Conditions for Oligopoly?
• II. Role of Strategic Interdependence
• III. Game theory
• IV. Profit Maximization in Four Oligopoly
  Settings
• Cournot Model
• Stackelberg Model
• Bertrand Model

4
Oligopoly

• Relatively few firms, usually less than 10.
• Duopoly - two firms
• Triopoly - three firms
• Barriers to entry are moderate
• The products firms offer can be either
  homogeneous or differentiated (colors, location,
  quality).
• Examples Car manufacturers, supermarkets,
  airlines, hotels, construction companies,
  ready-to-eat cereals, telecom., etc.

5
Strategic Interaction

• Your price (or quantity, or advertising, or
  quality, or RD) decisions do affect the profits
  of the rival firms!
• Likewise, what rivals do affects your profits

We deal with these situations using a tool Game
Theory
6
An Example Airlines competition
KLM
British Airways

• Normal-form game
• Players
• Strategies
• Payoffs (1st number in cell refers to BA)

7
Solution in dominant strategies
Strategy 1 dominates another strategy 2 if
Strategy 1 yields larger profit than strategy 2
regardless of the action taken by the rival firm.
If all players have a dominant strategy, then the
game has a solution in dominant strategies. QBA
64, QKLM 64 is a solution in dominant
strategies.
8
Solution in dominant strategies

• Payoff from the DSS QBA 64, QKLM 64 is 4.1
  for both players.
• They could do better if they set 48.
• Why dont they cooperate?

9
Nash Equilibrium
10
Nash equilibrium
NE Set of strategies such that no firm wants to
change its strategy given what everyone else is
doing. In a NE every firm plays a best-response,
i.e., maximizes its profits given its (correct)
beliefs about its rivals strategies.
QBA 48, QKLM 64 is a NE QBA 64, QKLM
48 is also a NE
11
A pollution game no NE (in pure strategies)
Government
Firm
Mixed strategy equilibrium G inspects 80 of
the times and F pollutes 37.5 of the times.
Government Inspect 0.3755 0.6254 4.375 Not
to inspect 0.375(-5)0.62510 4.375
Firm Pollute 0.85 0.210 6 Not to pollute 6
12
Example mixed strategies
13
Penalty kick

• Strategies for player left or right corner?
• Strategies for keeper left or right corner?

keeper
player
14
Three classical models of strategic interaction

• Cournot model (due to Augustin Cournot, 1838)
• Bertrand model (due to Joseph Bertrand, 1883)
• Stackelberg model (due to Heinrich von
  Stackelberg, 1934)

15
Cournot Model

• A few firms produce goods that are either
  homogeneous (perfect substitutes) or
  differentiated (imperfect substitutes)
• Firms set output to maximize profit
• Interaction is for one period
• Each firm believes their rivals will hold output
  constant if it changes its own output (rivals
  output is viewed as given or fixed)
• Barriers to entry exist

16
Cournot Duopoly Model

• 2 firms
• Market demand is
• P100-Q
• Firm i cost is C(q)40q
• Firm i acts in the belief that firm j will put
  some amount qj in the market.
• Then firm i maximizes profits obtained from
  serving the residual demand
• Residual demand is P(100-qj)-qi

P
demand P100-Q
100
100-qj
Residual Demand P(100-qj)-qi
qj
MC
qi
qi(qj)
MRr
17
Cournot Model

• Max(100-qj-qi)qi-40qi
• defines best-response (or reaction) function a
  schedule summarizing the quantity q1 firm 1
  should produce in order to maximize its profits
  for each quantity q2 produced by firm 2.
• Products are (perfect) substitutes an increase
  in firm 2s output leads to a decrease in the
  profit-maximizing amount of firm 1s product (?
  reaction functions are downward sloping).

18
Cournot Equilibrium

• Situation where each firm produces the output
  that maximizes its profits, given the the output
  of rival firms
• No firm can gain by unilaterally changing its own
  output
• We look for a pair of outputs (q1 , q2 ) such
  that
• The output q1 maximizes firm 1s profits, given
  that firm 2 produces q2
• The output q2 maximizes firm 2s profits, given
  that firm 1 produces q1
• Neither firm has an incentive to change its
  output, given the output of the rival
• Beliefs are consistent In equilibrium, each firm
  thinks rivals will stick to their current
  output -- and they do so!

19
Cournot Equilibrium
?iC400
q220
q120
20
More efficient firms put more units in the market
21
Rationale for collusion
22
Types of collusion

• Cartel agreements an institutional form of
  collusion (also called explicit collusion or
  secret agreements)
• Unlawful (Sherman Act and Art. 85 Treaty of Rome)
• Requires evidence of communication
• Tacit or Implicit collusion attained because
  firms interact over and over again and find
  natural focal points.
• This second type make things complicated for
  antitrust authorities

23
How can firms collude without explicit
communication to coordinate actions?

• Consider the Cournot model analyzed before.
• Suppose now that firms interact in the market
  over an infinite number of periods
• Then, the following trigger strategy by each
  firm is a Nash equilibrium
• Start producing qi15 (half monopoly quantity)
• Continue producing qi15 period after period as
  long as the rival produces qj15. If he/she
  deviates, then punish him by producing the
  Cournot quantity qi20 forever.
• In effect, each firm agrees to cooperate so
  long as the rival hasnt cheated in the past.
  Cheating triggers punishment in all future
  periods.

24
Suppose firm 2 adopts this trigger strategy.
Does it pay to deviate?

• ?Cooperate 450 450/(1r) 450/(1r)2
  450/(1r)3
• 450 (11/r)

?Cheating 506.25 400/(1r) 400/(1r)2
400/(1r)3 506.25 400/r
When deviating, the best quantity is 22.5 (from
the reaction function), and this yields a payoff
of 506.25.
It does not pay to deviate iff r lt 0.8888
25
Can collusion work if interaction lasts just a
few (2) periods? NO

• In period 2, the game is a one-shot game, so
  equilibrium entails High Production 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 production by each
  firm in both periods.
• The same holds true if we repeat the game any
  known, finite number of times.

26
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

27
A real world example of Collusion OPEC

• Cartel founded in 1960 by Iran, Iraq, Kuwait,
  Saudi Arabia, and Venezuela
• Currently has 11 members
• (www.opec.org) OPECs 11 members are all
  developing countries whose economies are heavily
  reliant on oil export revenues. They therefore
  seek stable oil prices that are fair and
  reasonable for both producers and consumers of
  oil.
• Cournot oligopoly
• Absent collusion PCompetition lt PCournot lt
  PMonopoly

28
Cournot GameOne-Shot Cournot (Nash) Equilibrium
Venezuela
Saudi Arabia
29
Repeated Game Equilibrium
Venezuela
Saudi Arabia

• (Assuming a Low Interest Rate)

30
OPECs Cartel
Low Interest Rates
High Interest Rates
31
Factors that favors the sustainability of tacit
collusion
Gains from deviating
Losses from punishment
32
Collusion is more likely

• with fewer firms
• in homogeneous product markets
• with more symmetric firms
• in markets with no capacity constraints
• in very transparent markets (cheating is seen
  easily)
• no hidden discounts
• no random demand
• observability lags

33
Bertrand Model

• Few firms
• Firms produce identical products at constant
  marginal cost.
• Each firm independently sets its price in order
  to maximize profits
• Barriers to entry
• Consumers enjoy
• Perfect information
• Zero transaction costs

34
Bertrand Equilibrium

• Firms set P1 P2 MC! Why?
• Suppose MC lt P1 lt P2
• Firm 1 earns (P1 - MC) on each unit sold, while
  firm 2 earns nothing
• Firm 2 has an incentive to slightly undercut firm
  1s price to capture the entire market
• Firm 1 then has an incentive to undercut firm 2s
  price. This undercutting argument continues...
• Equilibrium Each firm charges P1 P2 MC

35
Bertrand Paradox

• Two firms are enough to eliminate market power
• If firms are symmetric, market power is
  eliminated entirely
• If firms are asymmetric, market power is
  substantially reduced
• Solutions
• Capacity constraints
• Repeated interaction
• Product differentiation
• Imperfect information

36
Strategic Moves

• The chicken game
• 2 guys, cars aligned, first to turn coward,
  chicken
• How to win this game? Commit, tie your hands
• Burning the bridges game
• 2 armies, advance or retreat how to gain this
  game? By burning the bridges behind the army, a
  general converts the threat I will not retreat
  into credible.
• Stackelberg game

37
Strategic MovesStackelberg Model

• Few firms
• Producing differentiated or homogeneous products
• Barriers to entry
• One firm is the leader
• The leader commits to an output before all other
  firms
• Remaining firms are followers.
• They choose their outputs so as to maximize
  profits, given the leaders output.

38
Stackelberg game

• Cournot players threat each other I will flood
  the market so you better dont put many units in
  the market otherwise the price will be too low.
• Stackelberg leader firm gets to move first and
  indeed floods the market this strategic move
  confers a competitive advantage.

39
The Stackelberg game in Extensive Form
payoffs
Solution Subgame Perfect equilibriumSet of
strategies constituting a Nash equilibrium in
every subgame (stage)
40
Another look at Cournot decisions

• Firm 1s Isoprofit Curve combinations of outputs
  of the two firms that yield firm 1 the same level
  of profit

Q2
r1
B
C
A
D
Q1M
Q1
41
Another Look at Cournot Decisions
Q2
r1
Q1 Firm 1s best response to Q2
Q1M
Q1
42
Another Look at Cournot Equilibrium
Q2
Firm 2s Profits
r1
Q2M
Q2
Firm 1s Profits
r2
Q1M
Q1
Q1
43
Stackelberg Equilibrium
Q2
Followers Profits Decline
Stackelberg Equilibrium
Q2
Q2S
r2
Leaders Profits Rise
Q1
Q1S
Q1
44
Stackelberg Summary

• Stackelberg model illustrates how commitment can
  enhance profits in strategic environments
• Leader produces more than the Cournot equilibrium
  output
• Larger market share, higher profits
• First-mover advantage
• Follower produces less than the Cournot
  equilibrium output
• Smaller market share, lower profits

45
Summary

• Different oligopoly scenarios give rise to
  different optimal strategies and different
  outcomes
• Your optimal price and output depends on
• Beliefs about the reactions of rivals
• Your choice variable (P or Q) and the nature of
  the product market (differentiated or homogeneous
  products)
• Your ability to commit to quantity

46
Application A Market Share Game

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

47
The Market-Share Game in Normal Form
Manager 2
Manager 1
48
Market-Share Game Equilibrium
Manager 2
Manager 1
Nash Equilibrium
49
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.

50
Application Coordination Games

• Feature Non-rivalry between the players.
• Industry standards
• size of floppy disks
• size of CDs
• quality standards (ISO).
• National standards
• electric current (110/220 volts)
• traffic laws (priority to the drivers on your
  right), etc.

51
A Coordination Game in Normal Form
Player 2
Player 1
52
A Coordination Problem Three Nash Equilibria!
Player 2
Player 1
53
Key Insights

• Not all games are games of conflict.
• Multiplicity of equilibria Problem of
  coordination
• Communication can help solve coordination
  problems.
• Sequential moves can help solve coordination
  problems.
• Government regulation can help solve coordination
  problems

54
Multistage games

• Games where timing of moves is very important

Application Pricing to Prevent Entry

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

55
Sequential games Games where timing of moves is
very important

• Two firms incumbent, potential entrant
• Entrant to enter or not to enter?
• Incumbent if entry, fight or accommodate?
• Game in extensive form (game tree)

56
A game in extensive form
-5, 1
Fight
Incumbent
Enter
Accomodate
5, 5
Entrant
No entry
0, 10
57
Two Nash Equilibria I

• If entry, incumbent better chooses to accomodate
• If incumbent accomodates, entrant prefers to enter

58
Two Nash Equilibria II

• Entrant stays out as it fears a fight
• when there is no entry, incumbents strategy is
  irrelevant.

59
Game in Normal Form
Entrant

Incumbent
60
Which Equilibrium is to be Expected?

• Equilibrium II based on incredible threat
• if entrant would enter, it is not in the interest
  of the incumbent to fight
• Equilibrium I is subgame perfect (only based on
  credible threats)
• strategies induce an equilibrium in every subgame
• can be obtained using backward induction

61
The Entry Game in Extensive Form
-1, 1
Hard
Incumbent
Enter
Soft
5, 5
Entrant
Out
0, 10
Solution Subgame Perfect equilibriumSet of
strategies constituting a Nash equilibrium in
every subgame (stage)
62
Identify Nash and Subgame Perfect Equilibria
Two Nash equilibriaOne subgame perfect
equilibrium
63
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.

64
Price war supermarkets

• Albert Heyn lost market share to Dirk, Aldi,
  C1000 etc.
• One way to gain back market share is by
  decreasing prices

65
Price war supermarkets

•                   The extensive form game for AH
  looks like this
•  Notation (profits AH, profits competitor(s))
•  

(200,300)
Do nothing
(100,100)
Price war
Decrease prices
No reaction competitor
(225, 275)
66
Price war super market

• Competitors might threaten with price war but
  after AH increases prices it is optimal to do
  nothing.
• In repeated setting they might engage in price
  war to build up a reputation, i.e. tit for tat
  strategy

67
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 (possibility of collusion)

68
A One-Shot Advertising Game
General Mills
Kelloggs
69
Equilibrium to the One-Shot Advertising Game
General Mills
Kelloggs
Nash Equilibrium
70
Can collusion work if the game is repeated 2
times?
General Mills
Kelloggs
71
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.

72
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.

73
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
74
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
75
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
76
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

77
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 airline companies have been charged with
  violations
• OPEC isnt illegal National laws dont apply