part vi. theory of competition policy · 2020. 11. 14. · •a cartel of k firms is formed, with 1

SlidesIndustrial Organization: Markets and StrategiesPaul Belleflamme and Martin Peitz, 2d Edition © Cambridge University Press 2015

Part VI. Theory of competition policyChapter 14. Cartels and tacit collusion

© Cambridge University Press 2015

So far• Followed mostly a positive approach• Describe, explain workings of imperfectly

competitive marketsIn this part

• Follow mostly a normative approach• Guidance for competitive policy

• Basic postulate: competition is desirable as it promotes economic efficiency

• Problem: firms might be tempted to reduce competition

• Consequence: set of rules aiming at maintaining competition → competition (antitrust) policy

Introduction to Part VI

2


Organization of Part VI• Chapter 14. Collusive practices

• Price-fixing, market-sharing → firms eliminate competition between them

• How does collusion emerge? How is it sustained?• Chapter 15. Horizontal mergers

• Examine potential effects on welfare• Negative: fewer independent decision makers• Positive: increased efficiency (synergies)

• Chapter 16. Strategic incumbent firms• Incumbent may try to make entry more difficult on

their market.• How? To what effect


3


Organization of Part VI (cont’d)

• Chapter 17. Vertically related markets• Market for intermediate products; successive steps in

the value chain• Effects of vertical mergers?

• Positive: elimination of successive margins• Negative: potential foreclosure

• Effects of vertical restraints• Resale-price maintenance, exclusive dealing, …


4

© Cambridge University Press 2015 5

Chapter 14 - Objectives

Chapter 14. Learning objectives• Identify the incentives for a firm to collude.

• Cartel formation• Understand how cartels and other forms of

collusion can be sustained.• Sustainability of tacit collusion• Repeated competition

• Understand how authorities can fight against collusion.• Detecting and fighting collusion


Case. The vitamin cartels• Worldwide market for bulk vitamins• In Europe, sales of bulk vitamins were 800m € in 1998• Production of vitamins is highly concentrated

• Largest firm is Hoffmann-La Roche: market share of 40-50%• BASF: 20-30%• Aventis: 5-15%

• Concentration on the production side• Slow and costly plant construction• Economies of scale in the production technology

• Buyer side is more fragmented.• November 2001: European Commission imposes a fine

of 855.22 m € to 8 companies for participating to secret market-sharing and price-fixing cartels.

Chapter 14 – Cartels and tacit collusion

6


Formation and stability of cartels• Simple market structure

• n symmetric firms produce a homogeneous good • Constant marginal cost c• Competition à la Cournot• Firms face an inverse demand given by P(q) = a – q,

where q is the total quantity produced• 3 alternative procedures

• Firms decide simultaneously whether or not to participate in a single industry-wide cartel.

• Endogenous formation of cartels in a sequential way• Bilateral market-sharing agreements (“I stay out of your

market if you stay out of mine”)

Chapter 14 – Formation and stability of cartels

Simultaneous cartel formation• A cartel of k firms is formed, with 1 < k ≤ n.• The Cournot game is thus played among the other (n – k)

independent firms and the cartel.• All (n – k + 1) players are symmetric.

• Assumption: inside the cartel the division of profits is equitable.• For a given cartel size, profits for firms inside and outside

the cartel are



2

2

)2-()-()(+

=knkcakinπ and 2

2

)2-()-()(

+=

kncakoutπ


Simultaneous cartel formation• Suppose 𝑝𝑝 = 𝑎𝑎 − 𝑏𝑏𝑏𝑏

Π𝑖𝑖𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 =(𝑎𝑎 − 𝑐𝑐)2

𝑏𝑏(𝑁𝑁 + 1)2=

(𝑎𝑎 − 𝑐𝑐)2

(𝑛𝑛 − 𝑘𝑘 + 2)2

• Then the profits for each firm are (𝑎𝑎−𝑐𝑐)2

(𝐶𝐶−𝑘𝑘+2)2.

• For the firms inside the cartelΠ𝑖𝑖𝐶𝐶 𝑘𝑘 =


𝑘𝑘(𝑛𝑛 − 𝑘𝑘 + 2)2

• For the firms outside the cartelΠ𝐶𝐶𝐶𝐶𝐶𝐶 𝑘𝑘 =


(𝑛𝑛 − 𝑘𝑘 + 2)2• If one firm leases cartel, the cartel size is reduced by 1

𝑛𝑛 − 𝑘𝑘 − 1 + 2 = 𝑛𝑛 − 𝑘𝑘 + 3


𝑏𝑏 = 1

𝑁𝑁 = 𝑛𝑛 − 𝑘𝑘 + 1⇒ 𝑁𝑁 + 1 = 𝑛𝑛 − 𝑘𝑘 + 2

• Cartel stability: No cartel member has an incentive to unilaterally leave the cartel,



π in (k) ≥ π out (k − 1) ⇔

(a - c)2

k(n - k + 2)2 ≥(a - c)2

(n - k + 3)2

• Lesson: Consider the formation of a single cartel on a Cournot market with homogeneous goods and constant marginal costs. If there are at least three firms in the industry, all firms remain independent. If there are just 2 firms in the industry, the 2 firms form a cartel.


Cartel stability: No cartel member has an incentive to unilaterally leave the cartel.

• Rewrite the inequality, yields(𝑛𝑛 − 𝑘𝑘)2+6 𝑛𝑛 − 𝑘𝑘 + 9 ≥ 𝑘𝑘 𝑛𝑛 − 𝑘𝑘 2 + 4𝑘𝑘 𝑛𝑛 − 𝑘𝑘 + 4𝑘𝑘⇒ (1 − 𝑘𝑘)(𝑛𝑛 − 𝑘𝑘)2 + 6 − 4k n − k + (9 − 4k) ≥ 0

• If 𝑘𝑘 ≥ 3, then Π𝑖𝑖𝐶𝐶 𝑘𝑘 < Π𝐶𝐶𝐶𝐶𝐶𝐶 𝑘𝑘 − 1 for all k, for all n• If 𝑘𝑘 = 2, then 𝛱𝛱𝑖𝑖𝐶𝐶 𝑘𝑘 > 𝛱𝛱𝐶𝐶𝐶𝐶𝐶𝐶 𝑘𝑘 − 1 , the above inequality can be written

as −𝑛𝑛2 + 2𝑛𝑛 + 1 > 0, which doesn’t hold for 𝑛𝑛 > 2.


⊖ ⊕ ⊕⊖ ⊖ if 9 ≤ 4𝑘𝑘 ⇒ 𝑘𝑘 ≥ 2.25

• Intuition for this result:• Formation of the cartel induces positive externalities

on the firms outside the cartel (higher market price).• All firms prefer to free-ride on the public good

provided by cartel members.• Result changes if firms produce horizontally

differentiated goods• Competition and free-riding incentive are relaxed.• → It is possible to find stable cartels comprising not

all firms but a strict subset of them (if goods are sufficiently differentiated).

• See next example




Example: Stable partial cartels• Recall:

• Cournot market with homogeneous good, constant marginal cost• Simultaneous formation of a single cartel• All firms remain independent if at least 3 firms.

• However, if firms produce horizontally differentiated goods competition and free-riding incentive are relaxed.

• Consider the following inverse demand functions


pi = a − qi − γ qj

j ≠ i∑ , where γ ∈ 0,1[ ]

measures the strength of product substitutability



Example: Stable partial cartels• Suppose n = 3, γ = 1/2 and a – c = 1.• Nash equilibrium in which 2 firms form a cartel

while the 3rd remains independent• Cartel firms choose q1 and q2 to maximize their joint

profits

• Symmetry leads to q1 = q2 = q12 and joint profits

• FOC: Derive the cartel’s reaction function


2312132112 )(211()(

211( qqqqqqqq

+−−+

+−−=Π

( ) ( )3312 261 qqq −=


Π12 = 2 1 −32 𝑏𝑏12 −

12 𝑏𝑏3 𝑏𝑏12


• Independent firm chooses q3 to maximize

• Reaction function (from FOC)

• Equilibrium quantities q12 = 3/11 and q3 = 4/11

• Equilibrium profits π1 = π2 = πin (2) = 27/242and π3 = πout (2) = 32/242

• Free-riding effect is still present asπout (2) > πin (2)


3121233 )(211 qqqq

+−−=π

( ) ( )12123 121 qqq −=


© Cambridge University Press 2015 16© Cambridge University Press 2015

• Two requirements for the cartel to be stable• Internal stability (no leaving)

• If firms leave the cartel, 3 firms would be independent.• Stability as long as π in (2) ≥ π out (1) which is true as

27/242 ≈ 0.1116 > 1/9 ≈ 0.1111• External stability (no entry into the cartel)

• Compute the profits firm 3 would obtain by joining firms 1 and 2 in the cartel.

• No incentive to join as long as π out (2) ≥ π in (3) which is trueas 32/242 ≈ 0.132 > 1/8 ≈ 0.125

• End of example



Sequential cartel formation• Game where multiple cartels can be formed

• Exogenous specification of the ordering of the firms; 1st firm proposes a cartel; if all prospective members accept, cartel is formed; otherwise, 1st firm in the ordering that refuses proposes another cartel; etc.


Source: Bloch, 199517


Sequential cartel formation (cont’d)

• Sequentiality entails important differences• Firms can commit to stay out of the cartel.• At equilibrium, first firms remain independent and

free-ride on cartel that last firms will eventually form.• Firms prefer to form a cartel of size k than to remain

independent if


π in (k) ≥ π out (1) ⇔(a - c)2

k(n - k + 2)2 ≥(a - c)2

(n + 1)2

⇔ (k − 1)(−k2 + (2n − 3)k − (n + 1)2 ) ≥ 0

⇔ k > 12 2n + 3 − 4n + 5( )> 0.8n

18



• 𝑘𝑘 > 2𝐶𝐶+3− 4𝐶𝐶+52

≡ 𝑘𝑘∗ ⇒ 𝑘𝑘 > 𝑘𝑘∗ for cartel to be accepted.• Divide by n, yields

𝑘𝑘𝑛𝑛

>𝑘𝑘∗

𝑛𝑛=2𝑛𝑛 + 3 − 4𝑛𝑛 + 5

2𝑛𝑛

• If 𝑛𝑛 = 2, 𝑘𝑘∗

𝐶𝐶= 0.84

• If 𝑛𝑛 = 3, 𝑘𝑘∗

𝐶𝐶= 0.81

• If 𝑛𝑛 = 4, 𝑘𝑘∗

𝐶𝐶= 0.802 …


Market share of cartel



• Intuition• Simultaneous cartel formation: each firm has an

incentive to leave the cartel.• Sequential cartel formation: first firms can commit to

stay out and cartel can then form


• Lesson: Consider a Cournot market with homogenous goods. The first (n – k*) firms remain independent while the last k* firms form a cartel, with k* being larger than 80% of the firms in the industry.

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Network of market-sharing agreements• Bilateral collusive agreements• Market-sharing agreements

• 2 firms are active on different geographical markets or serve distinct consumer segments

• Refraining from competing on the other firm’s territory• Constitute a collusive structure, a collusive network

• Network stability if• No pair of firms has an incentive to form a new link.• No firm has an incentive to unilaterally destroy an

existing link.


• Lesson: If collusive network are negotiated bilaterally, they may lead to full collusion, with every firm a monopoly on its own market.

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Network of market-sharing agreements (cont’d)• Collusive network• N firms• Link between firm 𝑖𝑖 and 𝑗𝑗 is 𝑖𝑖𝑗𝑗 by signing a market sharing

agreement.• Network 𝑔𝑔 of links• 𝑛𝑛𝑖𝑖(𝑔𝑔) is the number of active firms in market 𝑖𝑖.• The total profit of firm 𝑖𝑖 is

Π𝑖𝑖 𝑔𝑔 =(𝑎𝑎 − 𝑐𝑐)2

(𝑛𝑛𝑖𝑖 𝑔𝑔 + 1)2+ �

𝑗𝑗𝑤𝑤𝑤𝑤𝑤𝐶𝐶𝑤𝑤 𝑖𝑖𝑗𝑗∉𝑔𝑔


(𝑛𝑛𝑗𝑗 𝑔𝑔 + 1)2


Cournot profits in whole market for firm 𝑖𝑖

Profits from Cournot that firm I earns in all foreign markets without market sharing agreement.


Network of market-sharing agreements (cont’d)• Firm 𝑖𝑖’s incentive to sign agreement with 𝑗𝑗.• Π𝑖𝑖 𝑔𝑔 + 𝑖𝑖𝑗𝑗 − Π𝑖𝑖 𝑔𝑔

=(𝑎𝑎 − 𝑐𝑐)2

(𝑛𝑛𝑖𝑖 𝑔𝑔 )2+ �

𝑘𝑘≠𝑗𝑗


(𝑛𝑛𝑘𝑘 𝑔𝑔 + 1)2−


(𝑛𝑛𝑖𝑖 𝑔𝑔 + 1)2+ �

𝑗𝑗𝑤𝑤𝑤𝑤𝑤𝐶𝐶𝑤𝑤 𝑖𝑖𝑗𝑗∉𝑔𝑔



=(𝑎𝑎 − 𝑐𝑐)2

(𝑛𝑛𝑖𝑖 𝑔𝑔 )2−

𝑎𝑎 − 𝑐𝑐 2

(𝑛𝑛𝑖𝑖 𝑔𝑔 + 1)2−




One fewer firm j in my home market after signing agreement

Profit gain from less competition in home market.

Profit loss after abandoning 𝑗𝑗’s market.


Network of market-sharing agreements (cont’d)• Empty network • 𝑛𝑛𝑖𝑖 𝑔𝑔 = 𝑛𝑛𝑗𝑗 𝑔𝑔 = 𝑛𝑛• The benefit is


𝑛𝑛−


𝑛𝑛 + 1 2 −𝑎𝑎 − 𝑐𝑐 2

𝑛𝑛 + 1 2 =𝑎𝑎 − 𝑐𝑐 2(−𝑛𝑛2 + 2𝑛𝑛 + 1)

𝑛𝑛2(𝑛𝑛 + 1)2• Suppose now two firms in a non-empty network 𝑔𝑔 have an incentive to

sign an agreement

𝛱𝛱𝑖𝑖 𝑔𝑔 − 𝛱𝛱𝑖𝑖 𝑔𝑔 − 𝑖𝑖𝑗𝑗 ≥ 0 ⇒𝑎𝑎 − 𝑐𝑐 2

(𝑛𝑛𝑖𝑖 𝑔𝑔 + 1)2≥


(𝑛𝑛𝑖𝑖 𝑔𝑔 + 2)2−



𝛱𝛱𝑗𝑗 𝑔𝑔 − 𝛱𝛱𝑗𝑗 𝑔𝑔 − 𝑖𝑖𝑗𝑗 ≥ 0 ⇒𝑎𝑎 − 𝑐𝑐 2

(𝑛𝑛𝑗𝑗 𝑔𝑔 + 1)2≥


(𝑛𝑛𝑗𝑗 𝑔𝑔 + 2)2−


(𝑛𝑛𝑖𝑖 𝑔𝑔 + 2)2

• Letting 𝑛𝑛𝑖𝑖 𝑔𝑔 = 𝑛𝑛𝑗𝑗 𝑔𝑔 = 𝑥𝑥

⇒𝑎𝑎 − 𝑐𝑐 2

(𝑥𝑥 + 1)2≥

2 𝑎𝑎 − 𝑐𝑐 2

𝑥𝑥 + 2 2 ⇒ 2 ≥ 𝑥𝑥2

• If 𝑥𝑥 = 1, 2 ≥ 𝑥𝑥2 holds.


Only positive for 𝑛𝑛 = 2


Tacit collusion• ‘Meeting of the minds’ between colluding firms• Analysis of ‘tacit agreements’ is also highly

relevant for explicit agreements• Sustainability necessary for cartels as long as

punishments cannot be legally binding• Considering 2 firms

• Offer perfect substitutes at constant marginal costs c• Compete over time (each period t = 1,2, …T, firms

repeat the ‘static’ game)

Chapter 14 – Sustainability of tacit collusion

• Lesson: If competition is repeated over a finitenumber of periods, firms play according to the (unique) Nash equilibrium of the static game in each period. Tacit collusion cannot emerge.

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Tacit collusion: Infinite horizon• Infinite time horizon (no known end to the game)• Tacit collusion may emerge.• Consider the grim trigger strategy

• Firm i starts by choosing the action that maximizes total profits.

• Firm i keeps on choosing this action as long as both firms have done so in all previous periods.→ cooperation phase

• If one firm deviates, deviation ‘triggers’ the start of the punishment phase.

• Firms choose the action that corresponds to the Nash equilibrium of the static game.


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Grim trigger Strategy• Cooperative action: both obtain π c = π m/2• If one plays the cooperative action and the other

optimally deviates, the deviating firm obtains π d• At the Nash equilibrium of the static game, both

firms obtain π n, with π d > π c > π n.• Trade-off between

• immediate gain from deviation• future losses resulting from the other firm’s

punishment• Trade-off depends on

• magnitude of the deviation and the punishment profits with respect to the collusive profits

• the firms’ discount factor

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Grim trigger Strategy (cont’d)• Cooperative phase: present discounted value

• If firm 1 deviates, it will obtain π d in the current period and π n in all subsequent periods

• Follow the grim trigger strategy if and if only

V D = π d + δπ n + δ 2π n + ... = π d +δ

(1− δ )π n



V C = π c + δπ c + δ 2π c + ... =1

1 − δπ c

V C ≥ V D ⇔1

1− δπ c ≥ π d +

δ1− δ

π n

⇔δ

1− δπ c − π n( ) ≥ π d − π c

Discounted long term losses

Short term gain

⇔ δ ≥π d − π c

π d − π n ≡ δmin

28

Application to price competition• Bertrand competition model with constant and

identical marginal costs• If both firms collude, they make a profit of π c = π m/2• Undercutting the rival‘s price leads to deviation profits

of π d = π m – ε• After deviation has occurred, π n = 0• Minimum discount factor



• Lesson: In the infinitely repeated Bertrand duopoly game, any profit level between zero and the monopoly profit can be supported in a subgame perfect equilibrium if the discount factor is sufficiently large, δ ≥ 1/2.

δminBert ≥

π d − π c

π d − π n =π m − (π m / 2)

π m − 0=

12

29

Application to price competition (cont’d)• Suppose n firms operate in the market

• Total collusive profits have to be shared among nfirms: π c = π m/n

• Critical discount factor is increasing in n



δminBert (n)

V C ≥ V D ⇔1

1− δπ m

n≥ π m ⇔ δ ≥ 1−

1n

≡ δminBert (n)

• Lesson: In the infinitely repeated Bertrand price-setting game, the set of discount factors that can support collusion is larger the smaller the number of firms in the market.

30


Application to price competition (cont’d)


Application to quantity competition• n-firm Cournot model with constant and identical

marginal costs• Inverse demand P(q) = a – q• Resulting collusive profits:

• Recalling Cournot Nash equilibrium profits:

• If other firms play the collusive quantity q m/n, then



π c =π m

n=

14n

(a − c)2

π n =1

(n + 1)2 (a − c)2

π d =(n + 1)2

16n2 (a − c)2

32

δminCour (n) ≡

π d − π c

π d − π n =

(n + 1)2 (a − c)2

16n2 −(a − c)2

4n(n + 1)2 (a − c)2

16n2 −(a − c)2

(n + 1)2

=(n + 1)2

n2 + 6n + 1



( )nCourminδ

33

Application to quantity competition (cont’d)• Minimum discount factor to allow firms to sustain the

monopoly outcome:

• increases with n• as n → ∞, the critical discount factor converges to 1


Application to quantity competition (cont’d)



Optimal punishment of deviating firms• Under price competition, reversion to the Nash

equilibrium generates zero profits for all firms.• Most severe credible punishment

• Under quantity competition, reversion to the Nash equilibrium gives rise to positive profits.• Possible to design more severe punishment schemes

• But, punishment must be credible• Reversion to the Nash equilibrium forever ensures

this credibility.• With more severe punishments, credibility can be

restored by shortening the punishment phase, eventually coming back to the collusive outcome.


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Optimal punishment of deviating firms (cont’d)

• Stick-and-carrot strategies1. Start the game by playing the collusive output q*, as

prescribed by the collusive agreement.2. Cooperate as long as the collusive output has been

observed in all preceding periods.3. If one of the players deviates from the collusive

agreement at period t, play �𝑏𝑏 at period t + 1(punishment phase) and return to the collusive agreement at period t + 2.

4. If one of the players chooses a quantity 𝑏𝑏 ≠ �𝑏𝑏 during the punishment phase, start the punishment phase again at the following period.


37



• 𝜋𝜋𝑚𝑚 = 𝑃𝑃 𝑏𝑏𝑚𝑚 − 𝑐𝑐 𝑏𝑏𝑚𝑚 ⇒ 𝜋𝜋𝑐𝑐 = 𝜋𝜋𝑚𝑚𝐶𝐶

• Punishment phase:𝑉𝑉𝑝𝑝 ≡ 𝜋𝜋 �𝑏𝑏 + 𝛿𝛿𝜋𝜋 𝑏𝑏∗ + 𝛿𝛿2𝜋𝜋 𝑏𝑏∗ + ⋯ = 𝜋𝜋 �𝑏𝑏 +

𝛿𝛿1 − 𝛿𝛿

𝜋𝜋 𝑏𝑏∗

• Instead, a deviation from the punishment would yields𝜋𝜋𝑑𝑑 �𝑏𝑏 + 𝛿𝛿𝑉𝑉𝑝𝑝

• So we need 𝑉𝑉𝑝𝑝 ≥ 𝜋𝜋𝑑𝑑 �𝑏𝑏 + 𝛿𝛿𝑉𝑉𝑝𝑝 ⇒ 1 − 𝛿𝛿 𝑉𝑉𝑝𝑝 ≥ 𝜋𝜋𝑑𝑑 �𝑏𝑏

⇒ 𝛿𝛿 𝜋𝜋 𝑏𝑏∗ − 𝜋𝜋 �𝑏𝑏 ≥ 𝜋𝜋𝑑𝑑 �𝑏𝑏 − 𝜋𝜋 �𝑏𝑏


Punishment output Back to cooperation

Not implementing punishment while everyone else dose

The value of punishment which starts tomorrow

Credibility condition

Profit loss Profit gain


Optimal punishment of deviating firms (cont’d)• After a history of cooperation, firms abide by the collusive

agreement as long as𝜋𝜋 𝑏𝑏∗ + 𝛿𝛿𝜋𝜋 𝑏𝑏∗ + 𝛿𝛿2𝜋𝜋 𝑏𝑏∗ + ⋯ ≥ 𝜋𝜋𝑑𝑑 𝑏𝑏∗ + 𝛿𝛿𝜋𝜋 �𝑏𝑏 + 𝛿𝛿2𝜋𝜋 𝑏𝑏∗ + ⋯

⇒ 𝛿𝛿 𝜋𝜋 𝑏𝑏∗ − 𝜋𝜋 �𝑏𝑏 ≥ 𝜋𝜋𝑑𝑑 𝑏𝑏∗ − 𝜋𝜋 𝑏𝑏∗

• Practice!• The book assumes 𝑝𝑝 = 𝑎𝑎 − 𝑏𝑏, 𝑐𝑐 = 𝑐𝑐. • Instead we assume 𝑎𝑎 = 1, 𝑐𝑐 = 0, the goal is to find �𝑏𝑏 as a function of 𝛿𝛿.


Unilateral deviation from collusive 𝑏𝑏∗

Profit loss Profit gain

Sustainability condition




• Lesson: In the infinitely repeated Cournot quantity setting game, the set of discount factors that can support full collusion is larger when firms use the optimal punishment of the stick-and-carrot strategy rather than the reversion to the Nash equilibrium of the grim trigger strategy.

40

Collusion and frequency of interaction• Suppose

• n firms, Bertrand competition, grim-trigger strategy• Scenario 1: firms compete only every k periods

• Scenario 2: price are set for k periods

• In both cases, cooperation is preferable if• Threshold ↑ with k



V1C =

π m

n+ δ k π m

n+ δ 2k π m

n+ ... =

11− δ k

π m

n and V1

D = π m

V2

C =1

1 − δπ m

n and V2

D = π m (1+ δ ++ δ k −1) + δ k × 0 =1 − δ k

1 − δπ m

δ ≥ 1− 1n( )1/k

• Lesson: Firms find it harder to sustain collusion when they interact less frequently or when price adjustments are less frequent.

41


Collusion and frequency of interaction (cont’d)Scenario 1• Suppose firms interact in period 1, period 𝑘𝑘 + 1, period 2𝑘𝑘 +

1,…• For instance, if 𝑘𝑘 = 3, firms will interact in period 1,4,7, …• 𝑉𝑉1𝑐𝑐 = 𝜋𝜋𝑚𝑚

𝐶𝐶+ 𝛿𝛿 � 0 + 𝛿𝛿2 � 0 + ⋯+ 𝛿𝛿𝑘𝑘−1 � 0 + 𝛿𝛿𝑘𝑘 𝜋𝜋

𝑚𝑚

𝐶𝐶+ 0 + ⋯+ 0 + 𝛿𝛿2𝑘𝑘 𝜋𝜋

𝑚𝑚

𝐶𝐶

= 𝜋𝜋𝑚𝑚

𝐶𝐶1 + 𝛿𝛿𝑘𝑘 + 𝛿𝛿2𝑘𝑘 + ⋯

= 11−𝛿𝛿𝑘𝑘

𝜋𝜋𝑚𝑚

𝐶𝐶

• 𝑉𝑉1𝑐𝑐 = 11−𝛿𝛿𝑘𝑘

𝜋𝜋𝑚𝑚

𝐶𝐶is decreasing in 𝑘𝑘.

• If deviated𝑉𝑉1𝑑𝑑 = 𝜋𝜋𝑚𝑚 + 𝛿𝛿 � 0 + 𝛿𝛿2 � 0 + ⋯ = 𝜋𝜋𝑚𝑚

• Collusive can be sustained if

𝑉𝑉1𝑐𝑐 ≥ 𝑉𝑉1𝑑𝑑 ⇒ 𝛿𝛿 ≥ 1 −1𝑛𝑛

1𝑘𝑘


No interaction during 𝑘𝑘 − 1 periods

p=c, GTS


Collusion and frequency of interaction (cont’d)Scenario 2• If firms commit to price during 𝑘𝑘 periods.

𝑉𝑉2𝑐𝑐 =𝜋𝜋𝑚𝑚

𝑛𝑛+ δ

𝜋𝜋𝑚𝑚

𝑛𝑛+ ⋯ =

11 − 𝛿𝛿

𝜋𝜋𝑚𝑚

𝑛𝑛• If deviate

𝑉𝑉2𝑑𝑑 = 𝜋𝜋𝑚𝑚 + 𝛿𝛿𝜋𝜋𝑚𝑚 + ⋯+ 𝛿𝛿𝑘𝑘−1𝜋𝜋𝑚𝑚 + 𝛿𝛿𝑘𝑘 � 0 + ⋯ =1 − 𝛿𝛿𝑘𝑘

1 − 𝛿𝛿𝜋𝜋𝑚𝑚

• 𝑉𝑉2𝑐𝑐 ≥ 𝑉𝑉2𝑑𝑑 if 11−𝛿𝛿

𝜋𝜋𝑚𝑚

𝐶𝐶≥ 1−𝛿𝛿𝑘𝑘

1−𝛿𝛿𝜋𝜋𝑚𝑚 ⇒ 𝛿𝛿 ≥ 1 − 1

𝐶𝐶

1𝑘𝑘


Deviation yields 𝜋𝜋𝑚𝑚 during 𝑘𝑘 − 1 periods since firms cannot alter prices to punish deviation

Punishment phase 𝑝𝑝 = 𝑐𝑐

Collusion and multimarket contact• What if firms face same competitors on several

markets? Does this facilitate tacit collusion?• 2 effects

• Deviation more profitable → it can take place on all markets at the same time

• Deviation more costly → deviators can be punished on all markets

• The 2 effects cancel out if identical markets, identical firms and constant return to scale.

• Otherwise, 2nd effect dominates• Collusion easier to sustain with multimarket contacts• Applications

• Differing markets• Differing firms



44


Application: differing markets• Different frequency of interaction

• Suppose that firms can change prices more frequently in market 1 than in market 2

• Multimarket contact opens up the possibility that a deviation in market 2 can be (immediately) punished in market 1

• Pooling of incentive constraints across the two markets facilitates collusion

• Different number of firms• Suppose that firms A and B are both present in markets 1 and

2, firms C is only present on market 2• Idea: to induce firm C to collude by

• leaving it a larger market share on market 2• Using the interaction on market 1 as a disciplining device




Application: differing markets (cont’d)Different frequency of interaction• 2 firms 𝐴𝐴 and 𝐵𝐵 interacting in both markets 1 and 2.• Market 1: 𝑘𝑘 = 1• Market 2: 𝑘𝑘 = 2• In market 1, collusion can be sustained if

𝛿𝛿 ≥ 1 −12

=12

= 0.5

• In market 2, collusion can be sustained if

𝛿𝛿 ≥ 1 −12

12≈ 0.7


Collusion cannot be sustained in market 1 and 2

Collusion can only be sustained in market 1

Collusion can be sustained in both market 1 and 2


Application: differing markets (cont’d)• Pooling in incentive constraints

• 𝑉𝑉𝑐𝑐 = 11−𝛿𝛿

𝜋𝜋𝑚𝑚

2+ 1

1−𝛿𝛿𝜋𝜋𝑚𝑚

2= 𝜋𝜋𝑚𝑚

1−𝛿𝛿• 𝑉𝑉𝑑𝑑 = 𝜋𝜋𝑚𝑚 + 𝛿𝛿 � 0 + 𝛿𝛿 � 0 + 𝛿𝛿2 � 0 + ⋯+ 𝜋𝜋𝑚𝑚 + 𝛿𝛿𝜋𝜋𝑚𝑚 + 𝛿𝛿2 � 0 = (2 + 𝛿𝛿)𝜋𝜋𝑚𝑚

• 𝑉𝑉𝑐𝑐 ≥ 𝑉𝑉𝑑𝑑

⇒𝜋𝜋𝑚𝑚

1 − 𝛿𝛿≥ 2 + 𝛿𝛿 𝜋𝜋𝑚𝑚 ⇒ 𝛿𝛿2 + 𝛿𝛿 − 1 ≥ 0 ⇒ 𝛿𝛿 ≥ 0.62


Optimal deviation in market 1

Optimal deviation in market 2


Application: differing markets (cont’d)Different number of firms• 3 firms 𝐴𝐴,𝐵𝐵 and 𝐶𝐶. • Market 1: 𝐴𝐴,𝐵𝐵 → 𝛿𝛿 ≥ 1 − 1

2= 1

2

• Market 2: 𝐴𝐴,𝐵𝐵,𝐶𝐶 → 𝛿𝛿 ≥ 1 − 13

= 23


Collusion cannot be sustained in market 1 and 2

Collusion can only be sustained in market 1

Collusion can be sustained in both market 1 and 2


Application: differing markets (cont’d)• Firms 𝐴𝐴 and 𝐵𝐵 give a share 𝑠𝑠 of monopoly profits from

𝑀𝑀2 to firm 𝐶𝐶, then 𝐶𝐶 doesn’t deviate if 𝑠𝑠𝜋𝜋𝑚𝑚

1 − 𝛿𝛿≥ 𝜋𝜋𝑚𝑚 + 𝛿𝛿 � 0 + 𝛿𝛿 � 0 + 𝛿𝛿2 � 0 + ⋯

⇒ 𝑠𝑠 ≥ 1 − 𝛿𝛿⇒ 𝑠𝑠 = 1 − 𝛿𝛿⇒ 1 − 𝑠𝑠 = 𝛿𝛿

• Every firm (𝐴𝐴 or 𝐵𝐵) prefers to not deviate if1

1 − 𝛿𝛿𝜋𝜋𝑚𝑚

2+

11 − 𝛿𝛿

𝜋𝜋𝑚𝑚

2≥ 2𝜋𝜋𝑚𝑚 + 𝛿𝛿 � 0 + 𝛿𝛿 � 0 + 𝛿𝛿2 � 0 + ⋯ ⇒ 𝛿𝛿 ≥

35


Remaining 1 − 𝑠𝑠 goes to 𝐴𝐴 and 𝐵𝐵, that is, 𝛿𝛿 goes to 𝐴𝐴 and 𝐵𝐵. ⇒ 𝛿𝛿

2goes to 𝐴𝐴, 𝛿𝛿

2goes to 𝐵𝐵.

Profit from 𝑀𝑀𝑀 Profit from 𝑀𝑀2 Deviation in 𝑀𝑀𝑀 and 𝑀𝑀2

Collusion in 𝑀𝑀𝑀 and 𝑀𝑀2 by giving 1 − 𝑠𝑠 to firm 𝐶𝐶.


Application: differing markets (cont’d)

• Firms A and B are able to sustain collusion in both markets although they would not be able to collude on market 2 were they only active on that market


• Lesson: With multimarket contact on different markets, collusion may become sustainable in several markets, even though deviations would be profitable if firms were active only in one of the markets.


Application: Differing firms• 2 markets (1 and 2)• 2 firms (A and B)

• firm A is installed in market 1• firm B is installed in market 2

• Each firm• produces a homogenous good at constant marginal cost c• faces a transportation costs of τ to move one unit of output from

its 'home‘ to the 'foreign‘ market• Demand on both markets is given by Q(p)= a – p• Monopoly price for home firm is • To ensure competition, we assure marginal cost of the

foreign firm is smaller than the monopoly price


2/)-()( cacpm =

c + τ < (a + c) / 2 or 2τ < a − c



Benchmark: Market-sharing agreements in one market• As a benchmark, we first examine the optimal

collusive outcome that would prevail if firms were only competing in one market.

• Assuming Bertrand competition, the optimal punishment consists for both firms in setting their price equal to c in every future period following a deviation

• Let sh + sf denote the respective market shares of the home and the foreign firm(by definition, sh + sf =1)


• If the collusive price is p ≥ c + τ• A deviating firm with cost ci will slightly undercut

and achieve immediate profit equal to

with ci =c for the home firm and ci =c + τ• Hence both firms abide by the collusive

agreement as long as

(home firm)

(foreign firm)


))((),( pacpcp iid −−=π

))(())((1

1 pacppacpsh −−≥−−−δ

))(())((1

1 pacppacps f −−−≥−−−−

ττδ

δ−≥1hs

δ−≥1fs


• We can sum the two conditions and conclude that only if δ ≥ 1/2 the firms can sustain collusive prices above c + τ

• But a large enough market share must be allocated to the inefficient foreign firm to keep it from deviating

• It must be that 𝑠𝑠𝑓𝑓 ≥ 1 − 𝛿𝛿




Market-sharing agreements in two markets• Focus on symmetric collusive outcomes

• Both firms set the same price p on both markets• The home firm receives a share sh

• For a given p ≥ c + τ, the best collusive outcome involves sh=1 which implies that each firm completely withdraws from the foreign market.

• Best collusive price is pm(c) = (a + c)/2• Present value of abiding by the market-sharing

agreement

4)(

11 2caV c −−

=δ



• The best deviation consists in entering the foreign market and undercutting the home firm.• immediate profit of (p m(c) – c – τ)(a – p m(c))• Meanwhile, in this period, the firm is keeping the

monopoly profit on its home market.• As before the punishment that follows the

deviation yields a continuation profit of zero.• So the present discounted value of deviation is

• Therefore a market-sharing agreement can be sustained if Vc ≥ Vd or


δ1− δ

(a − c)2

4≥

(a − c)(a − c − 2τ )4

⇔ δ ≥12

a − c − 2τa − c − τ

4)2)((

4)( 2 τ−−−

+−

=cacacaV D



Market-sharing agreements with differing firms

• Lesson: The optimal market-sharing agreement can be sustained over a larger set of discount factors than the most profitable collusive outcome that firms can achieve when they are present on one market only.



Case. Multimarket contact in the U.S. airline industry• Markets: different city-pair routes• Multimarket contact may facilitate collusion when

• Firms differ in their production costs across markets• Markets themselves differ

• Both conditions are relevant in this industry.• Hub and spoke model

• Significant cost advantage to the carrier operating the hub• Significant cross-route differences• Experts claimed: airlines refrain from pricing aggressively

in a given route for fear of retaliation in another jointly contested route.

• Fares are (on average) higher on routes where the competing carriers have extensive interroute contacts.



Tacit collusion and cyclical demand• Many markets are characterized by demand fluctuations• Extension of the single-market analysis

• 2 demand states: demand is either good QG(p) or bad QB(p) withQG(p) > QB(p), for all p

• Firms observe state of demand before setting their price.

• Intuition• Punishment entails loss of an average of high and low profits

→ it is less severe than if the good demand state persisted• Hence, fully collusive outcome is more difficult to sustain than

under demand certainty.

• Lesson: Under demand uncertainty, the critical discount factor above which the fully collusive outcome can be sustained is larger than under demand certainty.



Tacit collusion and cyclical demand (cont’d)• We are looking for a pair of prices (𝑝𝑝𝐵𝐵,𝑝𝑝𝐺𝐺), where• 𝑝𝑝𝐵𝐵 is the collusive price under bad demand.• 𝑝𝑝𝐺𝐺 is the collusive price under good demand.• Deviations are non-profitable in both demand scenario.• (𝑝𝑝𝐵𝐵,𝑝𝑝𝐺𝐺) is Pareto dominant if there are other equilibrium.

𝑉𝑉𝑐𝑐 = �𝐶𝐶=0

∞

𝛿𝛿𝐶𝐶12𝑄𝑄𝐵𝐵 𝑝𝑝𝐵𝐵

2𝑝𝑝𝐵𝐵 − 𝑐𝑐 +

12𝑄𝑄𝐺𝐺 𝑝𝑝𝐺𝐺

2𝑝𝑝𝐺𝐺 − 𝑐𝑐

= 11−𝛿𝛿

12𝑄𝑄𝐵𝐵 𝑝𝑝𝐵𝐵

2𝑝𝑝𝐵𝐵 − 𝑐𝑐 + 1

2𝑄𝑄𝐺𝐺 𝑝𝑝𝐺𝐺

2𝑝𝑝𝐺𝐺 − 𝑐𝑐



Tacit collusion and cyclical demand (cont’d)• Full collusion• Charge 𝑝𝑝𝐵𝐵𝑚𝑚 if 𝐵𝐵, 𝑝𝑝𝐺𝐺𝑚𝑚 if 𝐺𝐺, where• 𝑝𝑝𝐵𝐵𝑚𝑚 solves max

𝑝𝑝(𝑝𝑝 − 𝑐𝑐)𝑄𝑄 𝑝𝑝𝐵𝐵 → 𝜋𝜋𝐵𝐵𝑚𝑚

• 𝑝𝑝𝐺𝐺𝑚𝑚 solves max𝑝𝑝

(𝑝𝑝 − 𝑐𝑐)𝑄𝑄 𝑝𝑝𝐺𝐺 → 𝜋𝜋𝐺𝐺𝑚𝑚

𝑉𝑉𝑐𝑐 =1

1 − 𝛿𝛿12𝜋𝜋𝐵𝐵𝑚𝑚

2𝑝𝑝𝐵𝐵 − 𝑐𝑐 +

12𝜋𝜋𝐺𝐺𝑚𝑚

2𝑝𝑝𝐺𝐺 − 𝑐𝑐 =

11 − 𝛿𝛿

𝜋𝜋𝐵𝐵𝑚𝑚 + 𝜋𝜋𝐺𝐺𝑚𝑚

4• 𝑉𝑉𝑑𝑑 = 𝜋𝜋𝑠𝑠𝑚𝑚, where 𝑠𝑠 = {𝐵𝐵,𝐺𝐺}• For full collusion to be sustained at period 𝑡𝑡 given demand

is 𝑠𝑠 today, we need𝜋𝜋𝑠𝑠𝑚𝑚

2+ 𝛿𝛿𝑉𝑉𝑐𝑐 ≥ 𝜋𝜋𝑠𝑠𝑚𝑚 ⇒

𝜋𝜋𝑠𝑠𝑚𝑚

2+


𝜋𝜋𝐵𝐵𝑚𝑚 + 𝜋𝜋𝐺𝐺𝑚𝑚

4≥ 𝜋𝜋𝑠𝑠𝑚𝑚

⇒ 2 1 − 𝛿𝛿 𝜋𝜋𝑠𝑠𝑚𝑚 ≤ 𝛿𝛿(𝜋𝜋𝐵𝐵𝑚𝑚 + 𝜋𝜋𝐺𝐺𝑚𝑚)



Tacit collusion and cyclical demand (cont’d)• Under 𝐺𝐺 demand

2 1 − 𝛿𝛿 𝜋𝜋𝐺𝐺𝑚𝑚 ≤ 𝛿𝛿(𝜋𝜋𝐵𝐵𝑚𝑚 + 𝜋𝜋𝐺𝐺𝑚𝑚)• Solving for 𝛿𝛿

𝛿𝛿 ≥2𝜋𝜋𝐺𝐺𝑚𝑚

𝜋𝜋𝐵𝐵𝑚𝑚 + 3𝜋𝜋𝐺𝐺𝑚𝑚=

1

1 + 𝜋𝜋𝐵𝐵𝑚𝑚 + 𝜋𝜋𝐺𝐺𝑚𝑚2𝜋𝜋𝐺𝐺𝑚𝑚

≡ 𝛿𝛿0

⇒12

< 𝛿𝛿0 <23


Between 12

and 1

Whether partial collusive can be sustained here?

Collusion holds with demand uncertainty

With demand certainty, collusion holds for all 𝛿𝛿 ≥ 1

2


Tacit collusion and cyclical demand (cont’d)

• Partial collusion for lower discount factors• Full collusion sustained in the bad demand state but

not in the good demand state • Bad demand: firms charge the monopoly price.• Good demand: firms set prices more aggressively than

under monopoly.• Possible result: firms price lower in the good than in

the bad demand state• Model can generate lower prices after a positive

demand shock and countercyclical prices and markups.



Tacit collusion and cyclical demand (cont’d)• Partial collusion• 𝛿𝛿 ∈ 1

2, 𝛿𝛿0

• 𝑝𝑝𝐵𝐵 = 𝑝𝑝𝐵𝐵𝑚𝑚 if bad demand• 𝑝𝑝𝐺𝐺 < 𝑝𝑝𝐺𝐺𝑚𝑚 if good demand

max𝑝𝑝𝐵𝐵,𝑝𝑝𝐺𝐺

11 − 𝛿𝛿

12𝜋𝜋𝐵𝐵(𝑝𝑝𝐵𝐵)

2+

12𝜋𝜋𝐺𝐺(𝑝𝑝𝐺𝐺)

2

𝑠𝑠. 𝑡𝑡.𝜋𝜋𝐵𝐵(𝑝𝑝𝐵𝐵)

2≤



2+



2≤



2+


2• We can ignore the first constraint


More demanding


Tacit collusion and cyclical demand (cont’d)• Rewriting the second constraint


𝜋𝜋𝐵𝐵(𝑝𝑝𝐵𝐵)4

≥ 𝜋𝜋𝐺𝐺(𝑝𝑝𝐺𝐺)12−


14

⇒ 𝛿𝛿𝜋𝜋𝐵𝐵 𝑝𝑝𝐵𝐵 ≥ 2 − 3𝛿𝛿 𝜋𝜋𝐺𝐺 𝑝𝑝𝐺𝐺⇒ 𝛿𝛿

2−3𝛿𝛿𝜋𝜋𝐵𝐵 ≥ 𝜋𝜋𝐺𝐺

• we can sustain partial collusion if 𝛿𝛿 ≥ 12


> 1, if 2 − 3𝛿𝛿 ≤ 𝛿𝛿 ⇒ 𝛿𝛿 ≥ 12



max𝑝𝑝𝐵𝐵, 𝑝𝑝𝐺𝐺

14(1 − 𝛿𝛿)

(𝜋𝜋𝐵𝐵 + 𝜋𝜋𝐺𝐺)

• Rewriting PMPmax𝑝𝑝𝐵𝐵,𝑝𝑝𝐺𝐺

𝜋𝜋𝐵𝐵 + 𝜋𝜋𝐺𝐺

𝑠𝑠. 𝑡𝑡.𝛿𝛿

2 − 3𝛿𝛿𝜋𝜋𝐵𝐵 ≥ 𝜋𝜋𝐺𝐺

• If 𝐺𝐺 demand constraint holds with equality, and evaluated at 𝑝𝑝𝐵𝐵𝑚𝑚, which means 𝛿𝛿

2−3𝛿𝛿𝜋𝜋𝐵𝐵𝑚𝑚 𝑝𝑝𝐵𝐵𝑚𝑚 = 𝜋𝜋𝐺𝐺(𝑝𝑝𝐺𝐺). Solve for 𝑝𝑝𝐺𝐺, we

can obtain �𝑝𝑝𝐺𝐺 price in partial collusion with good demand.• Then, �𝑝𝑝𝐺𝐺< 𝑝𝑝𝐺𝐺𝑚𝑚 but �𝑝𝑝𝐺𝐺 ≶ 𝑃𝑃𝐵𝐵𝑚𝑚.

• �𝑝𝑝𝐺𝐺 − 𝑐𝑐 < 𝑝𝑝𝐵𝐵𝑚𝑚 − 𝑐𝑐 → counter cyclical price margins• Or �𝑝𝑝𝐺𝐺 − 𝑐𝑐 > 𝑝𝑝𝐵𝐵𝑚𝑚 − 𝑐𝑐 → cyclical price margins




• Illustration: market for antibiotic tetracycline• Firms were confronted with a positive demand shock

when the Armed Service Medical Procurement Agency placed a large order in October 1956.

• Thereafter, pure discipline among firms broke down.

• Lesson: When full collusion cannot be sustained, firms may partially collude by setting the respective monopoly price in the bad demand state and setting a price lower than the respective monopoly price in the good demand state. This result is compatible with counter-cyclical prices and markups.

67



Tacit collusion with unobservable actions• Here, firms do not observe deviations

• As before, demand uncertainty. But, no observation of state of demand, nor of rivals’ prices → no way to infer deviations from market outcomes.

• Model• 2 firms, homogeneous product, constant marginal

cost c, Bertrand competition• Bad demand state (probability α): no demand• Good demand state (probability 1−α): Q(p) > 0 for all

p ≥ c.• If firm faces zero demand, signal extraction problem:

• Is it because rival deviated or because of bad demand?

68



Tacit collusion with unobservable actions (cont’d)

• Structure of punishment?• Punishment forever after zero demand? Too harsh

as zero demand may result from bad state.• But milder punishment → lower discipline...

• Proposed strategies for both firms:1. Start with the collusive phase and charge price p m

until one firm makes zero profit (which along the equilibrium path, occurs in the low demand state)

2. If one firm makes zero profits, this triggers a punishment phase for T periods in which each firm charges c. After T periods firms return to step 1.




𝑉𝑉𝑐𝑐 = 1 − 𝛼𝛼12𝜋𝜋𝑚𝑚 + 𝛿𝛿𝑉𝑉𝑐𝑐 + 𝛼𝛼(0 + 𝛿𝛿𝑉𝑉𝑝𝑝)

𝑉𝑉𝑝𝑝 = 0 + 0 + ⋯+ 𝛿𝛿𝑇𝑇−10 + 𝛿𝛿𝑇𝑇 𝑉𝑉𝑐𝑐

• The incentive constraint is 𝑉𝑉𝑐𝑐 ≥ 1 − 𝛼𝛼 𝜋𝜋𝑚𝑚 + 𝛿𝛿𝑉𝑉𝑝𝑝 + 𝛼𝛼(0 + 𝛿𝛿𝑉𝑉𝑝𝑝)


If high demand If low demand which triggers punishment tomorrow

𝑝𝑝 = 𝑐𝑐

If high demand If low demand

Expected profit of deviating without knowing demand


Tacit collusion with unobservable actions (cont’d)• Rewriting the inequality

1 − 𝛼𝛼12𝜋𝜋𝑚𝑚 + 𝛿𝛿𝑉𝑉𝑐𝑐 + 𝛼𝛼𝛿𝛿𝑉𝑉𝑝𝑝 ≥ 1 − 𝛼𝛼 𝜋𝜋𝑚𝑚 + 𝛿𝛿𝑉𝑉𝑝𝑝 + 𝛼𝛼𝛿𝛿𝑉𝑉𝑝𝑝

⇒ 1 − 𝛼𝛼 𝛿𝛿(𝑉𝑉𝑐𝑐 − 𝑉𝑉𝑝𝑝) ≥ 1 − 𝛼𝛼12𝜋𝜋𝑚𝑚

⇒ 𝑉𝑉𝑐𝑐 = 1 − 𝛼𝛼12𝜋𝜋𝑚𝑚 + 𝛿𝛿𝑉𝑉𝑐𝑐 + 𝛼𝛼𝛿𝛿𝑇𝑇+1𝑉𝑉𝑐𝑐

⇒ 𝑉𝑉𝑐𝑐 =1 − 𝛼𝛼 1

2𝜋𝜋𝑚𝑚

1 − 1 − 𝛼𝛼 𝛿𝛿 − 𝛼𝛼𝛿𝛿𝑇𝑇+1

⇒ 𝑉𝑉𝑝𝑝 = 𝛿𝛿𝑇𝑇1 − 𝛼𝛼 1

2𝜋𝜋𝑚𝑚

1 − 1 − 𝛼𝛼 𝛿𝛿 − 𝛼𝛼𝛿𝛿𝑇𝑇+1

• Since 𝑉𝑉𝑐𝑐 ≥ 1 − 𝛼𝛼 𝜋𝜋𝑚𝑚 + 𝛿𝛿𝑉𝑉𝑝𝑝 + 𝛼𝛼(0 + 𝛿𝛿𝑉𝑉𝑝𝑝)

1 − 𝛼𝛼 𝛿𝛿 1 − 𝛿𝛿𝑇𝑇1 − 𝛼𝛼 1

2𝜋𝜋𝑚𝑚

1 − 1 − 𝛼𝛼 𝛿𝛿 − 𝛼𝛼𝛿𝛿𝑇𝑇+1≥ 1 − 𝛼𝛼

12𝜋𝜋𝑚𝑚

⇒ 2 1 − 𝛼𝛼 𝛿𝛿 1 − 𝛿𝛿𝑇𝑇 + 𝛿𝛿𝛿𝛿𝑇𝑇 ≥ 1 ⇒ 1 − 𝛼𝛼 𝛿𝛿 ≥12




• Proposed strategies (cont’d)• Clearly leads to higher profits than repeated static

Bertrand equilibrium.• Objective: find T that maximizes expected present

discounted value under constraint that strategies constitute an equilibrium. (see details in book)

• Lesson: Even if firms cannot observe deviations of other firms from equilibrium play, collusion can still be supported to some extent. However, the conditions for collusion to be sustainable are stricter than in a world in which deviations can be immediately observed and punished. In addition, profits are lower.

72



Detecting and fighting collusion• Why do competition authorities mainly try to

uncover explicit agreements such as price-fixing cartels if firms have other means to sustain collusion?

• Answer (Lesson): Without the information sharing within a cartel, collusion is more likely to be infeasible. Even if it is feasible, collusion may not be supported over the whole time-horizon but firms may alternate between collusive and punishment phases (over varying length) in which they switch between a high and a low price.

Chapter 14 – Detecting, fighting collusion


Detecting and fighting collusion• Communication is central to collusion; thus it can

be used to detect collusion.• Collusion might leave significant pieces of evidence.

• Permanent records of meetings or agreements• Telephone conversations may have been tapped.

• Competition authorities have designed policies to encourage cartel members to bring evidence to the authorities by themselves.

• Simply looking at possible high price-cost margins is not sensible.• as we have seen in Chapter 3 about market power



The difficulty in detecting collusion• Four methods to detect collusion

1. Is the firm’s behaviour consistent or not with properties or behaviour that are supposed to hold under a wide class of competitive models?

2. Are there structural breaks in the firm’s behaviour?3. Does the behaviour of suspected colluding firms

differ from competitive firm’s behaviour?• If only a subset of firms in the industry colludes and they

can be identified a comparison can be directly carried out.• Otherwise one can resort to comparison across markets

and across periods.4. Which model (competitive or collusive) better fits the

data?

SCR

EENIN

GVER

IFICATIO

N



The difficulty in detecting collusion (cont’d)

• All 4 methods suffer from 2 general problems:1. Necessary data to identify firm’s behaviour often not

available (cost is often unobservable).2. Firms have incentive to misreport private information.

• Authorities are likely to suffer from the so-called indistinguishability theorem

• → firms misreport cost information to make prices appear as resulting from competitive − and not collusive − behaviour

• Even if needed data are available, estimation of firm’s behaviour may be extremely sensitive to model specifications.

76



Leniency and whistleblowing programmes• To obtain evidence for the existence of cartels

and collusion, competition authorities introduced• Corporate leniency programmes

• Reduced sentences for firms that cooperate with the authorities and provide evidence for the existence of a cartel

• Whistleblowing programmes• Shielding individual informants from criminal sanctions

• Results of law enforcement• Make cartels less stable• Break-up existing cartels• Prevent the formation of cartels



Case. The vitamin cartels (cont’d)• For violation of article 81 of the Community Treaty and

article 53 of the European Economic Area Agreement, 8 companies were fined for forming a cartel.

• Hoffmann-La Roche (462m €) and BASF (296,16m €) were considered the joint leaders and instigators of the cartels.

• Aventis received significantly lower fines as the first company to cooperate both with the US Department of Justice and the European Commission.



Case. The beer cartel in the Netherlands• 4 Dutch beer brewers formed a cartel on the beer market

(a branded consumer good market) in the Netherlands.• Coordinated prices and price changes (at the wholesale level)• Operated in 2 market segments

• Consumption on the premises (bars, restaurants, hotels) →Coordinated rebate policies, market-sharing agreements

• Retail (mostly supermarkets) → Market-sharing agreements• In 2007 the European Commission fined the 3 leading

Dutch brewers Heineken, Grolsch and Bavaria a total amount of 274m EUR for operating this cartel between at least 1996 and 1999.

• InBev (also part of the cartel) provided essential information that led to surprise inspections and hard evidence (handwritten notes, proof of secret meeting dates)

• Under the Commissions leniency programme, InBev did not have to pay fines.



Leniency programme• Considering a corporate leniency programme

whereby a cooperating firm is granted a reward (or, at least, a reduced fine).

• The condition for the sustainability of collusion becomes more stringent.

• Lesson: Reducing fines for firms which report incriminating evidence may deter collusion. However, for some cartels, competition authorities have to grant sufficiently large positive rewards to deter collusion.



Whistleblowing programme• Complementation of the corporate leniency

programme by granting a positive reward to employees reporting incriminating evidence.

• Firms will have to bribe informed employees to prevent them form disclosing information.

• Collusion becomes less profitable and thus harder to sustain.

• Lesson: Corporate leniency and individual whistleblowing programmes are complementary in the fight against collusion.



Chapter 14 - Review questions

Review questions• Contrast the conditions for cartels to be stable when they

form in a simultaneous versus sequential way.• Explain how a collusive outcome may emerge

noncooperatively as the equilibrium of a repeated game. Discuss how the horizon of the game, the number of firms, the frequency of interaction and multimarket contact affect the sustainability of collusion.

• Explain why tacit collusion is harder to sustain when demand fluctuates and the rival’s actions cannot be observed.

• Explain why competition authorities encourage colluding firms and their employees to report incriminating evidence through leniency and whistleblowing programmes.

part vi. theory of competition policy · 2020. 11. 14. · •a cartel of k firms is formed, with 1

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