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Industrial OrganizationCollusion

Univ. Prof. dr. Maarten JanssenUniversity of ViennaSummer semester 2013 - Week 17

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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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Q2

Q1Q1

M

r1

Q2*

Q1*

Firm 1’s Profits

Firm 2’s Profits

r2

Q2M Scope for collusion

Scope for Collusion with quantity choice

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Scope for Collusion under price setting

R1(p2)

R2 (p1)

Scope for colusion

p2B

p1B

p2

p1

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2. How many firms will form a cartel?

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Not an obvious answer

N=2, 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-n+1)

Given this reaction cartel maximizes (1 – nqc)qc/(N-n+1) wrt qc or qc = 1/2n Individual output noncartel firm: q = 1/2(N-n+1)

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How many firms in Cournot setting II Profits of cartel and noncartel firms:

Cartel members πc(n): 1/4n(N-n+1) Others π(n): 1/4(N-n+1)2

Firms want to join cartel as long as this yield more profits, i.e., when π(n) < πc(n+1) 1/(N-n+1)2 < 1/(n+1)(N-n)

Firms want quit the cartel as long as this yield more profits, i.e., when π(n-1) > πc(n) 1/(N-n+2)2 > 1/n(N-n+1)

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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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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Example of collusion

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

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

Consider the following “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.

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Suppose General Mills adopts this trigger strategy. Kellogg’s profits?Cooperate = 12 +12/(1+i) + 12/(1+i)2 + 12/(1+i)3 + …

= 12 + 12/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

Kel

logg

’s

Value of a perpetuity of $12 paid at the end of every year

Cheat = 20 +2/(1+i) + 2/(1+i)2 + 2/(1+i)3 + = 20 + 2/i

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Kellogg’s 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 doesn’t pay to deviate.

Collusion is a Nash equilibrium in the infinitely repeated 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

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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 > PV of Future Cost Pays to “cheat”.

If Immediate Benefit PV of Future Cost Doesn’t pay to “cheat”.

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

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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 Πi(si,s-i) firm’s profit given strategies of all firms Πi* = Πi(s*i,s*-i) static Nash equilibrium profits There are strategies s’i,s’-i s.t. Πi’ = Πi(s’i,s’-i) ≥

Πi(s*i,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 (s’ i,s’-i)

as long as all other players do so, otherwise refer forever after to your part of (s*i,s*-i)

Alternatively, tit-for-tat

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Equilibrium condition

π is best possible static deviation pay-off Equilibrium condition: Πi’/(1-δ) ≥ π + δΠi*/(1-δ)

if everyone has the same discount factor Alternatively δ ≥ (π - Πi’)/(π - Πi*). Generally depends on N: the more firms the

more stringent the requirement on δ.

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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: Πi’/(1-δ) ≥ (1+δ) π + δ2Πi*/(1-δ) or δ ≥ {(π - Πi’)/(π - Πi*)}1/2.