Illegal and Legal Behaviour: Evidence Proving Collusion

Dr. Kenneth Danger

OECD

2

Acknowledgements

Greg Werden Andreas Reindl

3

Helpful Articles

Greg Werden “Economic Evidence on the Existence of Collusion: Reconciling Antitrust Law with Oligopoly Theory,” Antitrust Law Journal, 71, 719-800.

Blair D. Blair and Jill Boylston Herndon, Inferring Collusion from Economic Evidence, Antitrust, Summer, 2001.

4

Overview

Classic oligopoly games Some history on economics of coordination Definition and proof of an agreement Plus factors and action contrary to self

interest

5

Classic Oligopoly Games

Cournot Bertrand Dominant firm price leadership

6

Simple Strategic Games

Optimization algorithm Firms choose optimal level of output or price given rival(s)

decisions. Non cooperative equilibrium is the key concept. Best responses to best responses determine the

equilibrium. This is known as the Nash equilibrium concept.

Game is played for one period only.

Simple strategic games we are not concerned with for the moment with include predation, vertical integration, etc.

7

Cournot-Nash (Output Choice)

Assume two firms only Homogeneous good Market demand curve is linear: P(Q) = a – bQ

P = market price Q = total market output q1 is firm 1’s output, q2 is firm 2’s output Thus Q = q1 + q2

Average costs are constant and equal to c for each firm.

8

Two Firm Optimization Problem

Firm 1’s problem Firm 2’s problem

1121

11

1

cq - )]qq b(q - [a

cq - P(Q)q

TC - TR π

2221

22

2

cq - )]qq b(q - [a

cq - qQP

TC - TR π

9

Graphical Representation of Decision Facing Cournot Rival

P

Q

Market demand curve

Marginal cost

Residual demand curve

Market demand curve shifts in by the amount of total rival production leaving a firm with the “residual” (left over) demand.

q

q rival

q rival

10

First Order Optimality ConditionsFirm 1’s problem

Taking the derivative we get

Which implies that

Firm 2’s problem

Taking the derivative we get

Which implies that

11211 cq - )]qq b(q - [a π

0 c - bq - 2bq - a q

π12

2

22212 cq - )]qq b(q - [a π

0 c - bq - 2bq - a q

π21

1

2

q -

2b

c - a q 2

1 2

q -

2b

c - a q 1

2

11

Cournot Reaction Curves

2b

c - a

q1

q2

R2

Note: Another name for reaction function is optimality function.

This graph plots the first order optimalityconditions from the prior slide.R1

2b

c - a3b

c - a

3b

c - a

Firm

2

Firm 1

12

Two Firm Cournot Solution

Solution concept:

Solve all competitors’ optimization problem simultaneously.

Solving gives

Inserting these output back into the demand function we get

P = a – b(q1 + q2) =

3b

c - a q q 21

3

2c a

a – 2bq1 – bq2 – c = 0 and a – 2bq2 – bq1 – c = 0

13

Oligopolistic Interdependence In general when there are few firms

producing a good or service their fortunes are interdependent.

Firm 1’s fortune depends upon what firm 2 does. And, firm 2’s fortune depends upon what firm 1 does.

14

N Firm Cournot Equilibrium

Number of Firms Price P = a – b(q1 + q2 + … + qn)

1 = Monopolist (a + c)/2

2 (a + 2c)/3

3 (a + 3c)/4

4 (a + 4c)/5

5 (a + 5c)/6

6 (a + 6c)/7

7 (a + 7c)/8

8 (a + 8c)/9

9 (a + 9c)/10

10 (a + 10c)/11

Infinite P = (a + nc)/[(n+1)] = c

15

Herfindahl-Herschman Index (HHI)

Hirschman-Herfindahl index (HHI) is a measure of concentration Definition: n firms, each with share si

Example: 5 firms with 15%, 15%, 20%, 20%, 30% market shares HHI=225+225+400+400+900=2150

Merger of 30% with 15% would create a change of 900, to 3050 (Change in HHI = 2s1s2).

HHI is only one measure of concentration and can provide some initial guidance low HHI and low HHI change in correctly defined market can suggest little competitive effect from

merger high HHI and high HHI change does not establish competitive effect.

In general an investigation must develop much more evidence

n

1i

2isHHI

16

Cournot Model (Identical Firms) and

Herfindahl – Hirshman Index (HHI)Cournot Optimization problem is:

Differentiating we get

Multiplying both sides by s gives

iii cq - P(Q)q π

η

s

P

c - P0 c - q

q

P(Q) P(Q)

q

πi

ii

i

η

s

P

c - Ps

2

Summing up over n firms gives

Rearranging gives

η

HHI

P

c - P

E.g., Cournot prediction is that a 20% increase in the HHI leads to a 20% in themargin. And if costs are constant (as they are here) then prices rise by 20%.

Note η is the market elasticity of demand.

17

More General Link Between Cournot and HHI

When firms have different cost structures market shares will differ under Cournot.

General relationship between HHI and margins is:

η

HHI

P

c - Ps

i

ii

The Cournot prediction is that the weighted average margin is proportional to the HHI.

18

Is This Type of Behaviour Illegal?

Imagine that you have 3 markets with the following fact patterns.

Firms compete in a Cournot fashion and marginal cost is identical andconstant across firms and markets and equal to 3.

What would you do?

Market 1

3 firms

Market 2:

5 firms

Market 5

9 firms

P = 7.25

Si = 1/3

6.4

Si = 1/5

4.7

Si = 1/9

19

Bertrand-Nash (Price Choice)

Essential Features of Bertrand Model Two firms selling homogeneous products Each sells from the same location Each firm chooses price Each firm’s demand is a function of its own price

and that of its rival Average cost is constant and equal to c

20

The Bertrand Solution and “Paradox”1. Assume firm 2 sets the monopoly price. Then firm 1 should

set a price just below firm 2 and get the entire market.

2. If firm 1 sets a price just below firm 2 then firm 2 sells nothing. Firm 2 needs to lower its price to below firm 1 and if it does it will get the entire market.

3. This process continues until each firm sets its price at

marginal cost and earns zero profits.

Only two firms are required to achieve the competitive outcome.This is known as the Bertrand paradox.

21

Bertrand Competition With 3 Or More Firms

Adding more firms to the forgoing analysis does not make the market more competitive.

Shares decline, though they need not for everyone.

22

Heterogeneous Goods and Bertrand Competition

The less differentiated the products are, the lower the equilibrium price. When the goods are perfect substitutes perfect competition is obtained.

The more differentiated the products are the higher the price. When the products cease to be come substitutes at all the monopoly price is obtained.

23

Is This Type of Behaviour Illegal? Imagine you have 3 firms. Firms compete on

the basis of price. Two firms innovate and lower their production costs. The third does not.

Bertrand price competition implies that the third firm will be driven out of business.

Is this illegal? What would you do?

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Dominant Firm Price Leadership First some basics.

If Firm A’s supply curve is P = a + bQA and Firm B’s supply curve is P = a + bQB we can the combined supply curve.

First we solve for Q and get

Q = P/b – a/b for both firms. Adding up the supply at any given price means that the total supply at a given price is

QA + QB = QS = P/b – a/b + P/b – a/b = 2P/b – 2a/b.

Rearranging gives P = a + bQS/2.

This means that the supply curve rotates around the intercept. But be careful when you have different intercepts. The above cannot be done as the true function is piecewise linear.

25

Graphic Representation of Adding Supply Curves

Supply curve for A and B lie on same line

QA, QB

QS

Sum of supply curves

Supply curve rotates out when underlying supply curves have the same intercept.

P

Q

26

Dominant Firm Price Leadership Model There are two types of industry participants:

A large firm with low costs and A large number of smaller firms (the competitive

fringe) all with costs that are higher than the “dominant firm.”

27

Graphical Analysis of Dominant Firm Model

P

Q

Sf

Pf

Qf

If fringe supply all output, price is setat Pf and output is Qf.

Market Demand

28

Graphical Analysis of Dominant Firm Model

P

Q

Sf

PfAt prices below Pf the fringe do not supplyenough output to meet demand. Theresidual demand is the demand that is leftover at prices below Pf.

Market Demand

Residual Demand

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Graphical Analysis of Dominant Firm Model

P

Q

Sf

Pf

Market DemandResidual Demand

Associated with the residual demandcurve is a marginal revenue curve.

Marginal revenue curve

30

Graphical Analysis of Dominant Firm Model

P

Q

Sf

Pf

Market DemandResidual Demand

Dominant firm output is associated Found at nexus of MCD and MR

Marginal revenue curve

MCD

QD

31

Graphical Analysis of Dominant Firm Model

P

Q

Sf

Pf

Market DemandResidual Demand

Notice price in market is lower with a low cost, but large firm and total output is higher.

Marginal revenue curve

MCD

QD

PD

Qf

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Some Implications of Dominant Firm Price Leadership

There is one price in market Dominant firm’s low cost advantage enables

them to earn profits at the margin (P > MC) while the competitive fringe sets price equal to marginal cost (P = MC).

33

Is This Type of Behaviour Illegal? If an industry is appropriately characterized

by this model and the dominant firm’s cost decreases then All firm’s follow the price leader (the dominant

firm) and simultaneously lower price The dominant firm’s market share increases Some fringe firms exit Is it predation, collusion, both or something else?

What would you do?

34

Summary of Some Implications From Classic Oligopoly Games Dominant firm, Cournot and Bertrand Games

indicate a variety of outcomes are possible, yet none of them indicate that firms are colluding.

Alternatively, all three models do indicate that mergers can be harmful. Essential mechanism is that demand facing firms becomes more inelastic and firm’s price higher in response.

35

Some History On The Economics Of Coordination

Chamberlin’s impact Coordinated effects Merger law

Game theory Stigler’s model Repeated games

36

Chamberlin’s Impact On Understanding Coordination

Edward Chamberlin wrote that the usual assumption of profit maximization implies “a monopoly price for any fairly small number of sellers,” because no competitor has any incentive to cut price below the monopoly level, realizing “his move has a considerable effect upon his competitors, and that this makes it idle to suppose that they will accept without retaliation the losses he forces upon them” by cutting price.

Chamberlin indicated that this form of interdependent pricing should not be viewed as the product of an agreement: [W]hen there are only two or a few sellers, their fortunes are not independent…. Each is forced by the situation to take into account the policy of his rival in determining his own, and this cannot be construed as a ‘tacit agreement’ between the two.”

See Werden, Gregory J. “Economic Evidence on the Existence of Collusion: Reconciling Antitrust Law with Oligopoly Theory,” Antitrust Law Journal, 71, 719-800.

37

Note On Coordination And Merger Law Chamberlin had a significant impact in

merger law.

In many jurisdictions, mergers can be enjoined if the effect of the acquisition tends to substantially lessen competition through an increase in coordinated activity.

38

Chamberlin’s Impact on Defence Analyses Chamberlin’s analysis naturally helped

defence teams in their analysis. They could now argue that evidence on non-competitive performance was simply an outcome of interdependent decision making

39

Game Theory: Prisoners’ Dilemma

Prisoner 1 Denies Prisoner 1 Confesses

Prisoner 2 Denies Both Get Off Without Charge

Prisoner 2 Serves 10 Years, Prisoner 1 Serves 0 Years

Prisoners 2 Confesses

Prisoner 2 Serves 0 Years, Prisoner 1 Serves 10 Years

Both Serve 2 Years

40

Lessons From The Prisoners’ Dilemma(One Period Game) Time served is lowest each suspect does not confess.

However, each suspect’s private interest conflicts with their collective interest.

Dominant strategy for both players is to confess.

Assuming a similar setup, the key lesson for competition policy is that the best response for each firm, regardless of what the other is doing, is to compete.

41

Stigler’s Model

Basic idea: Firms want to collude to raise profits. However, “if any member of any agreement can violate it,

he will gain larger profits than by conforming to it.” Thus, firms should focus on problem of policing of

agreement. Implications

1. Note: how very different Stigler’s theory is from Chamberlin’s.

2. Firms infer cheating if they lose unexpectedly many sales or gain too few new sales.

42

Repeated Games – Folk Theorem Basic idea is that firms can be induced to act in the collective interests,

rather than in their individual interest. Folk theorem does not state that the set of jointly profit maximizing prices is

the equilibrium but only one equilibrium of an infinite set. In other words, anything can happen.

The folk theorem only goes through with infinite repetition (see next slide). Folk theorem says nothing about how the rules of the game become known

to players and how the equilibrium is evolved toward. Folk theorem has predicted monopoly outcomes even with a large number of

competitors (400!).1

Uncertainty creates price wars in repeated game models as competitors cannot be certain if a player has defected or if demand has fallen.2

Other models predict that when demand is high defection occurs as that is when it pays the most to defect.3

1. See Val Eugene Lambson, “Self Enforcing Collusion in Large Dynamic Markets,” 34, Journal of Economic Theory, 282, (1984)

2. See Edward J. Green and Robert H. Porter, Noncooperative Collusion Under Imperfect Price Information, 52 Econometrica, 87 (1984).

3. Julio J. Rotermberg and Garth Saloner, “A supergame-theoretic Model of Price Wars During Booms, 76. American Economic Review, 390, (1986).

43

Note On Repeated Games that End In general optimal strategies are found by working

backwards. Such backward induction leads to games that are said to be sub-game perfect. Consider the following two period game. Period 2 is in red box and Period 1 is in blue.

20,20 5,30 21,21 6,31

30,5 1,1 31,6 2,2

Period 1 profits are higher by the Nash equilibrium amounts in period 2.

Player 2

Pla

yer

1

High Low

Hig

hLo w

Player 2High Low

44

Summary on Some History on the Economics of Coordination

Firms want to achieve higher (monopoly) profits, but if an agreement is achieved they are tempted to cheat

Firms can achieve higher (monopoly) profits without an explicit agreement, yet here too they are tempted to “cheat” in ways that increase private profits at the expense of other firms

45

Definition And Proof Of An Agreement Types of agreements Selected cases

Eastern States Masonite American Tobacco

46

Agreement Nomenclature

Spoken agreement results from anything akin to language and the product of a spoken agreement is a traditional conspiracy. Because winks, nods and the like communicate much as words do, laws probably should not require the exchange of mutual assurances. Sometimes explicit or express agreement might be used or even

explicit or express collusion.

Unspoken agreement results from communications purely in the form of marketplace actions. It does not stretch the meaning of the terms to say that communication occurs when rivals observe each others’ prices, outputs, and other marketplace actions. Examples include Bertrand and Cournot communications as well as communications in repeated play such as Tit-for-Tat. Sometimes tacit agreement might be used or even tacit collusion but

you have to be careful with these terms because people get confused.

47

Eastern States

Defendant lumber retailers in Eastern States circulated “blacklists” containing the names of lumber wholesalers selling directly to consumers. This had the effect of causing such retailers to withhold their purchases from the list of concern. Information supplied during the case indicated that when a dealer was added to the list, retailers stopped purchasing from him and his trade was directly and appreciably impaired.

Did lumber retailers come to an agreement to collectively boycott offending lumber wholesalers?

1. Easters States Retail Lumber Dealers’ Association v. United States, 234 U.S. 600 (1914).

48

Eastern States

Is exchanging certain kinds of information the same thing as agreeing to boycott.

Were their actions in their self interest or their collective interest? What evidence might you look for?

E.g., high costs of switching from one wholesaler to another might imply action contrary to self interest

49

Masonite

Masonite held several patents on a hardboard product that continues to bear its names, and it sued competing hardboard producers for patent infringement. After one appeals court sustained an infringement finding, Masonite began to enter into agreements with the competitors under which they acknowledged the validity of Masonite’s patents and became its agents, selling Masonite board at prices set by Masonite.

Did Masonite practices facilitate an agreement among firms selling Masonite products? Was Masonite the ringmaster of the cartel?

United States v. Masonite Corp., 316 U.S. 265 (1942)

50

Masonite findings By Supreme Court “In negotiating and entering into the first agreements, each

appellee other than Masonite, acted independently of the others, negotiated only with Masonite, desired the agreement regardless of the action that might be taken by any of the others, did not require as a condition of its acceptance that Masonite make such an agreement with any of the others, and had no discussions with any of the others. It is not clear at what precise time each of the appellee became aware of the fact that its contract was not an isolated transaction but part of a larger arrangement. But it is clear, that as the arrangement continued, each became familiar with it purpose and scope. It is enough that, knowing that concerted action was contemplated and invited, the distributors gave their adherence to the scheme and participated in it.”

Does knowledge of other dealings create an unlawful concert of action?

51

American Tobacco

American Tobacco involved three big tobacco companies and their purchases of tobacco and in the sale of cigarettes. The court record indicates that on June 23, 1931, in the depth of the Depression, the big three all increased prices of their leading brands to the same level, and no economic justification for the raise was demonstrated. Other parallel price changes followed over the next few years.

Was there an agreement?

American Tobacco Company v. United States, 328 U.S. 781, (1946).

52

Summary of Definition and Proof of an Agreement

There is a significant difference between spoken agreements and learning about competitor prices, outputs and

strategies through market place actions and “understanding” what others are communicating.

Price increases that are not cost justified are indicative of explicit collusion, however they can also be indicative of non collusive strategic behaviour.

53

Plus Factors and Action Contrary to Self Interest

Defining plus factors Examples Foley

Action contrary to self interest Petroleum Products Antitrust Litigation Reserve Supply

54

What Is A Plus Factor?

Plus factors is a term that is used to denote practices other than mere parallel pricing or other parallel practices that can be shown to support the inference of an agreement.

Such factors when taken alone may not support the inference of an illegal spoken agreement, but when taken together and put in the context of the case point toward that conclusion.

55

Why Are Plus Factors Important “Consciously parallel business behaviour is circumstantial

evidence from which an agreement …. can be inferred but … such evidence, without more, is insufficient unless circumstances under which it occurred make the inference of rational independent choice less attractive than that of concerted action.”

This would be true even more so in criminal cases where the standard is beyond a “reasonable doubt”.

See Bogosian v. Gulf Oil Corp., 561 F. 2d 434, 446 (3d Cir. 1977)

56

But What Are Plus Factors?

Publication of retail prices and price announcements? Outside meetings and conversations between competitors? Nearly simultaneous price increases? Refusals to deals with suppliers that compete in downstream market? Decisions by orthopaedists to oppose podiatrist privileges at hospital based

on quality concerns? Meeting a competitors price? Encouragement by marketing manager to gather information on competitor

prices (including price lists) and to improve margins? Low prices in areas with a greater number of competitors? Capacity announcements and decisions to put in place less capacity than

announced? Past history of collusion? Advance knowledge of price moves?

What do you think of these plus factors? Are any unambiguous?

57

Ambiguous Evidence

the ambiguity of economic evidence has led to a greater emphasis on direct evidence in public cartel enforcement.

58

Should All Ambiguous Evidence Be Excluded Some have argued that ambiguous evidence does

not assist the decision maker reach the conclusion that collusion is a more likely hypothesis than not and should therefore be excluded.

Others argue that the story woven by the plaintiff is important in understanding the ambiguous evidence and that lots of ambiguous evidence counts (potentially a lot).

59

Foley

At a dinner party attended by leading realtors, Mr. Foley announced that his firm was raising its commission rate from six to seven percent. After the announcement there was discussion about the rate increase. Following the dinner party there were many subsequent discussions about whether particular firms were complying with their agreement. Over the course of the next months the seven percent commission rate was substantially adopted.

60

Defining Action Contrary to Self Interest Actions that are taken, that but for the hypothesis of

joint action, would not be in its own interest.

It is behaviour that could better be explained on the hypothesis of collusion than on the hypothesis that each was embarked on an individual rather than concerted course of action. Evidence consistent with both independent and collection

action does not do much when examined alone Criminal cases require significantly more evidence than

that suggested above.

61

Reserve Supply – Actions Contrary To Self Interest?

Reserve Supply involved insulation. Facts indicated a series of parallel price increases during a period of weak demand.

Defendants claimed that “it would have been irrational to attempt to increase sales by maintaining lower prices, because lower prices would be met by their competitors, leaving no increase in market share and reduced profit levels.”

Court concluded that failing to maintain lower prices “does not suggest that [the defendants] acted in a way that, but for a hypothesis of joint action, would not have been in [their] interest.’”

What do you think of the defence statements? What do you think of the courts reasoning?

Reserve Supply Corp. v. Owens-Corning Fiberglas Corp., 971 F. 2d 37 (1992).

62

Reserve Supply Analysis

Court did not appreciate the fact that competition among firms leads to lower prices as firms pursue their unilateral self interests.

US courts tend to appreciate evidence that indicates that firms did something that is inconsistent with their own unilateral self interests as also seen in American Tobacco.

63

But Determining Self Interest Can Be Difficult

Economic models of price leadership imply that the leader adjusts its price and the others follow suit. If the good is homogeneous then prices for the

leader and the rivals will be identical. If the good is heterogeneous the equilibrium price

differentials will remain the same.

64

Events and Self Interest

Pricing behaviour that changes markedly at a point in time and that does not correspond to expected unilateral reactions based on prior behaviour may aid the decision maker in reaching a finding of agreement Obviously changes in cost and demand need to

be accounted for in this kind of analysis

65

Summing Up

1. Something more than parallel behaviour must be shown before an agreement can be inferred.

2. The existence of an agreement cannot be inferred from actions that are consistent with Nash, noncooperative equilibrium such as Cournot, Bertrand, or price leader models.

3. Action contrary to self interest is a critical plus factor.

4. The existence of an agreement should not be inferred absent some evidence of communication of some kind among defendants through which an agreement could have been negotiated.

1. If this is not a requirement what would be the remedy?