Industrial Organization or Imperfect Competition Repeated Games and Collusion

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Industrial Organization or Imperfect
Competition Repeated Games and Collusion

• Univ. Prof. dr. Maarten Janssen
• University of Vienna
• Summer semester 2008
• Week 11 (May 25, June 8)

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Different Issues

• What are the incentives to form a cartel?
• In a given industry, how many firms will form a
  cartel if binding agreements can be made?
• What makes it that cartel members stay within the
  cartel?
• All three issues will be dealt with separately in
  three parts

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1. Incentives for Collusion
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Scope for Collusion with quantity choice
Q2
Firm 2s Profits
r1
Q2M
Q2
Firm 1s Profits
r2
Q1M
Q1
Q1
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Scope for Collusion under price setting
R1(p2)
Scope for colusion
R2 (p1)
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2. How many firms will form a cartel?
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Not an obvious answer

• N2, answer is clear
• General N, less obvious
• A noncartel firm benefits from cartel as cartel
  internalizes externality
• Output reduction in case of Cournot
• Price increases in case of (differentiated)
  Bertrand
• Cartel members have to share the cartel profits
  among themselves the more there are, the less
  for each member

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Consider the question in Cournot context with
cartel as market leader

• P 1 Q no cost
• N firms in industry, n firms in cartel
• Individual profit of a firm not belonging to
  cartel (1 nqc (N-n)q)q, where qc (q) is
  output individual cartel (noncartel) member
• Individual reaction noncartel firm 1 nqc
  (N-n-1)q - 2q 0, or q (1 nqc)/(N-n1)
• Given this reaction cartel maximizes
  (1 nqc)qc/(N-n1) wrt qc or qc 1/2n
• Individual output noncartel firm q 1/2(N-n1)

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How many firms in Cournot setting II

• Profits of cartel and noncartel firms
• Cartel members pc(n) 1/4n(N-n1)
• Others p(n) 1/4(N-n1)2
• Firms want to join cartel as long as this yield
  more profits, i.e., when p(n) lt pc(n1)
• 1/(N-n1)2 lt 1/(n1)(N-n)
• Firms want quit the cartel as long as this yield
  more profits, i.e., when p(n-1) gt pc(n)
• 1/(N-n2)2 gt 1/n(N-n1)
• For example when N 10, cartel with 6 members is
  stable.
• Non-cartel members also benefit from cartel and
  stability requires their profits to be very
  similar to that of cartel members!

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3. Why stick to the cartel agreement?
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First Example A One-Shot Advertising Game
General Mills
Kelloggs
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Equilibrium to the One-Shot Advertising Game
General Mills
Kelloggs
Nash Equilibria
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Can collusion work if the game is repeated 2
times?
General Mills
Kelloggs
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Collusion

• Refers to firm conduct intended to coordinate the
  actions of other firms in the industry
• Two problems associated
• Agreement must be reached
• Firms must find mechanisms to enforce the
  agreement

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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 often and find natural focal
  points.
• This second type make things complicated for
  antitrust authorities
• Focus on latter

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Repeated Games advertisement-game I

• In the last period they cannot choose for no
  advertisement
• As both firms have an incentive to cheat as 16
  is a higher pay-off than 12
• Punishment is not possible (as it is the last
  period)

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Repeated Games advertisement-game I

• But in the last period they can choose for no
  advertisement (i.e., collude)
• Strategy
• - Choose No in period 1
• - Choose moderate in period 2 when other
  chooses No in period 1
• Choose high in period 2 when other chooses
  somthing else in period 1
• Punsihment is part of strategy
• Is this an equilibrium?

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Repeated Games advertisement-game III
General Mills
Kelloggs

• Pay-off in equilibrium 12 7
• Max. pay-off if deviate in first period 16 2
• Max. pay-off if deviate in second period 12 5

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Can collusion work if the game is repeated 2
times and game is changed?
General Mills
Kelloggs
How Many Nash equilibria are there now?
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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.

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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.

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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
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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
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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
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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

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Collusion in Cournot and/or Bertrand

• ?i(si,s-i) firms profit given strategies of all
  firms
• ?i ?i(si,s-i) static Nash equilibrium
  profits
• There are strategies si,s-i s.t. ?i
  ?i(si,s-i) ?i(si,s-i), usually leading to
  higher prices and lower consumer benefits
• Can these strategies be sustained in an
  infinitely repeated game?
• Trigger strategies do your part of the
  combination (si,s-i) as long as all other
  players do so, otherwise refer forever after to
  your part of (si,s-i)
• Alternatively, tit-for-tat

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Equilibrium condition

• p is best possible static deviation pay-off
• Equilibrium condition ?i/(1-d) p d?i/(1-d)
  if everyone has the same discount factor
• Alternatively d (p - ?i)/(p - ?i).
• Generally depends on N the more firms the more
  stringent the requirement on d.

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Real World Examples of Collusion

• OPEC
• NASDAQ
• Airlines
• Auctions

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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)
• Cournot oligopoly
• Absent collusion PCompetition lt PCournot lt
  PMonopoly

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Current OPEC Members
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OPECs Demise
Low Interest Rates
High Interest Rates
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Factors that favors the sustainability of tacit
collusion
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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 low demand can be because of
  cheating others or because of low realization of
  demand
• observability lags if you can get cheating
  pay-off for more than 1 period equilibrium
  condition becomes ?i/(1-d) (1d) p
  d2?i/(1-d) or d (p - ?i)/(p - ?i)1/2.

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Facilitating devices

• Exchange of information (trade associations,
  professional associations)
• Price Leadership
• Meet-the-competition clauses
• Guaranteed Lowest prices